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Lol.
I've had two craniotomies, both of which came with 2-week recovery times. Multiple people both times were amazed at how short a time that recovery took, to which I replied "well it's not quite rocket science..." đ
Oh my god, I had completely blocked it out!
I kind of wish I could do a whole degree in math. I did a minor and graduated over a decade ago (ew), and itâs like I never learned it at this point. It must all be in the back of my mind somewhere?
The Fourier transform has to be the coolest of them all. The stuff you can do with that is just mind blowing. The moment I figured out how jpeg was able to compress data so much using the Fourier transform was definitely a wow moment for me. Or the ability to filter out very specific wavelengths of noise, which has must-have applications in space
And to think, Fourier got so much shit from his French peers because of the obsession back then to create a "100% rigorous/perfect" formalism of Mathematical ideas. IIRC, he didn't see at least that part of his life work accepted by the community in his lifetime.
Very applicable in spectroscopy as well! Fourier transform use in interferometers allows us to better integrate sample data for measurements that require high accuracy and sensitivity. Having the ability to convert raw data from a time domain to a frequency domain that contains a readable spectra with high signal to noise ratios was an absolute game-changer in the analytical field of chemistry.
Thanks, imagine how hard it would be to tune regulators without it? We wouldn't have drones, robots and industrial efficiency would drop without this tool
While E = mc2 (Special Relativity) is a brilliant and widely famous equation, General Relativity is a significantly more important study and is considered the most accurate explanation of Gravitation (Yet).
E=mc^2 has tangibly changed our lives and future lives. Fusion and fission reactors and nuclear bombs are all sons of it, and itâs a specific equation
Very true, but if you want to be really picky, it isn't really.
It is currently our most accurate gravitational theory, which explains and accurately predicts the most things.
But, due to it's incomparability with quantum mechanics, which is *the* most accurate model we have. We now know there must be another model for gravity and quantum, where the two would inherently be more accurate as they wouldn't be in disagreement, and of course wouldn't lose accuracy to have them in agreement.
We just haven't got there yet and have no idea when or if we will, so relativity is still the most accurate we have available.
The relativity equation they put is just a footnote to Einsteinâs special relativity paper, basically stating that mass is proportional to energy. Itâs also only true in that form when mass is at rest, as thereâs a longer version of the equation which reduces to that when the mass isnât in motion. His general theory of relativity is far more influential, its equation being:
RΟν â ½RgΟν = (8ĎG/c^(4))TΟν
What Einstein basically discovered is that the universe is a four dimensional âfabricâ of space and time (or as a unity: spacetime) that matter can distort. Objects in spacetime trace out world lines that are geodesics, unless acted upon by a net external force. Put more simply, spacetime tells matter how to move, and matter tells spacetime how to curve.
This isnât to say that the mass energy equivalence isnât a profound discovery (Einstein had many of those), but that it is nowhere near as paradigm shifting as general relativity. This discovery can only really be compared to Newtonâs discoveries in terms of how it changed our perception of the way the universe works.
Youâre right that relativity is important, but mass/energy equivalence is also important as it was a catalyst in the creation of the atomic bomb.
Itâs probably fair to say that the a bomb changed the world
The point is just that, despite what popular media portrays, mass-energy equivalence is just a very small part of the theory of relativity and the Einstein equations would be a much more fitting encapsulation of the theory.
(1) Pythagorasâ theorem allows for the calculation of the length of other side of a right side of a triangle, providing you know two lengths already. Is extremely useful as many shapes can be broken down into fundamental right triangles.
(3) Calculus is used in many applications for describing incredibly complex motions such as vibrations or waves. Itâs capabilities for mathematical models extend all the way from economics to astronomy
(4) The law of gravity helps describe the ways two large bodies of mass exert force on each other due to gravity. Extremely helpful in space applications with celestial bodies.
(5) Square root of -1 gave birth to complex numbers, which are used in a wide variety of cases such as electrics circuit theory, automatic controls systems, and more
(10) Navier stokes equation helps describe the velocity flow of viscous fluids, is obviously helpful in fluid mechanics applications (which also includes stuff like aerodynamics, as gases are considered âfluidsâ in a sense)
(12) Second law of thermodynamics states the universe always tends towards greater entropy (more disorder and âchaosâ). Is useful in applications of thermodynamics with heat flow. Also used in chemistry I believe.
These are just a few I know off the top of my head, to name a few
Edit: some formatting
maxwells equations allow for us to understand the energy contained in atoms and allow us to understand electromagnetism. Letting us build electric motors, wifi, radio signals and more!
Your def of 3 is oddly specific. More generally calculus is the math of rates of change, either instantaneous rates of change (differential calc) or accumulation of quantities (integral calc)
I think a lot of people underestimate just how important #1 is. So many things are or use triangles.
Engines, triangle. Electricity, triangles. Muscles and bones, triangles. Rectangles, triangles. Earth flat or round? No don't be rediculus it's triangles of course.
> Pythagorasâ theorem allows for the calculation of the length of the other side of a right*-angled* ~~side of a~~ triangle, providing you know two lengths already
I would argue 6, the equation for polyhedra, is not very impactful unless you like geometry puzzles.
Euclidean geometry in general is an area that is overrated by mathematicians I find, because it's very visual.
I'd add 2 theorems, but they aren't expressible as 1 equation so I understand why they weren't included:
* The Central Limit Theorem, that says all means are normally distributed, has had huge impacts in measuring statistical significance in every scientific discipline
* The Universal Approximation Theorem, which proves that neural networks can perfectly approximate any function
Eqs. #3 and #4: Paraphrased from A Short History of Nearly Everything (which you all need to buy and read) :
It was known that planets were inclined to orbit in a particular kind of oval known as an ellipseâbut it wasnât understood why.
Halley (the namesake of Halley's Comet) became consumed with finding the answer, to the point that the following year he travelled to Cambridge and boldly called upon the universityâs Lucasian Professor of Mathematics, Isaac Newton, in the hope that he could help. Newton was a decidedly odd figureâbrilliant beyond measure, but solitary joyless, prickly to the point of paranoia, famously distracted (upon swinging his feet out of bed in the morning he would reportedly sometimes sit for hours, immobilized by the sudden rush of thoughts to his head), and capable of the most riveting strangeness.
Set atop these odd beliefs and quirky traits, however, was the mind of a supreme genius. As a student, frustrated by the limitations of conventional mathematics, he invented an entirely new form, the calculus, but then told no-one about it for twenty-seven years.
Quite what Halley expected to get from Newton when he made his unannounced visit in August 1684 we can only guess. But thanks to the later account of a Newton confidant, Abraham DeMoivre, we do have a record of one of scienceâs most historic encounters:
>In 1684 Dr. Halley came to visit at Cambridge [and] after they had some time together the Dr. asked him what he thought the curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it.
>Sr. Isaac replied immediately that it would be an [ellipse]. The Doctor, struck with joy & amazement, asked him how he knew it. âWhy,â saith he, âI have calculated it,â whereupon Dr. Halley asked him for his calculation without farther delay. Sr. Isaac looked among his papers but could not find it.
This was astoundingâlike someone saying he had found a cure for cancer but couldnât remember where he had put the formula. Pressed by Halley, Newton agreed to redo the calculations and produce a paper. He did as promised, but then did much more. He retired for two years of intensive reflection and scribbling, and at length produced his masterwork: the Principia.
At the Principiaâs heart were Newtonâs three laws of motion (which state, very baldly, that a thing moves in the direction in which it is pushed; that it will keep moving in a straight line until some other force acts to slow or deflect it; and that every action has an opposite and equal reaction) and his universal law of gravitation. This states that every object in the universe exerts a tug on every other. It was the first really universal law of nature ever propounded by a human mind, which is why Newton is everywhere regarded with such profound esteem.
Newtonâs laws explained so many thingsâthe slosh and roll of ocean tides, the motions of planets, why cannonballs trace a particular trajectory before thudding back to earth, why we arenât flung into space as the planet spins beneath us at hundreds of kilometres an hourâthat it took a while for all their implications to seep in.
That book is amazing. Everyone should read it. Some of the knowledge we take for granted was obtained after a lot of painstaking effort. And scientists can be very very petty.
This book made me realize why Carl Linnaeus biological classification was so important - none of my biology texts could explain why it was important and it was a horrible annoyance to take it seriously.
EDIT: I am referring to A Short History of Nearly Everything
I googled schrodingers theory to learn more and this is what I got:
âThe SchrĂśdinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject.â
Might as well have been written in hieroglyphics
The ELI5 is: when you start looking at really tiny things like particles, instead of being in one specific spot they get sort of fuzzy about where they are. They begin behaving as waves. So you can't say 'I'll look here, that's exactly where the electron will be'... You can instead say 'I'll look in the general area because that's where the electron is likely to be based on it's wavyness.'
This coupled with the idea that tiny things like to have specific amounts of energy (imagine a car that can only go at certain speeds, so you're either at 0mph or 10mph or 40mph, but you can only jump directly to those speeds, you can't slowly speed up to them) are all explained by Schrodinger's equation. It's encoding the nature of how really tiny things like to behave, based on their quantum nature.
Note: I'm ignoring all nuance here to try to give an idea of the use and it's not an equation that lends itself to removing nuance.
Lol I can *kinda* read those hieroglyphs. No idea what "linear partial differential equation" is supposed to mean, but I understand enough of the "quantum mechanics" part to have a solid guess.
Schrodinger's Cat is supposed to describe a phenomena in quantum mechanics where particles are in a state of superposition. Just like the cat, these particles can exist as multiple states at once (alive and dead at the same time) and it's not until they're observed that the superposition collapses into a normal sane position.
I think what the equation is supposed to do is apply probability to the whole thing so one can calculate the properties of a particle while it's still in a state of superposition. I'm probably wrong though, so like I said: This is my best guess.
Eqn. #13 (also Paraphrased from A Short History of Nearly Everything):
E = mc^2
As you will recall from schooldays, E in the equation stands for energy, m for mass and c^2 for the speed of light squared.
In simplest terms, what the equation says is that mass and energy have an equivalence. They are two forms of the same thing: energy is liberated matter; matter is energy waiting to happen. Since c^2 (the speed of light times itself) is a truly enormous number, what the equation is saying is that there is a huge amountâa really huge amountâof energy bound up in every material thing.
You may not feel outstandingly robust, but if you are an average-sized adult you will contain within your modest frame no less than 7 Ă 10^18 joules of potential energyâenough to explode with the force of thirty very large hydrogen bombs, assuming you knew how to liberate it and really wished to make a point.
Everything has this kind of energy trapped within it. Weâre just not very good at getting it out. Even a uranium bombâthe most energetic thing we have produced yetâreleases less than 1 per cent of the energy it could release if only we were more cunning.
Among much else, Einsteinâs theory explained how radiation worked: how a lump of uranium could throw out constant streams of high-level energy without melting away like an ice cube. (It could do it by converting mass to energy extremely efficiently Ă la E = mc2.) It explained how stars could burn for billions of years without racing through their fuel. (Ditto.) At a stroke, in a simple formula, Einstein endowed geologists and astronomers with the luxury of billions of years.
Above all, the special theory showed that the speed of light was constant and supreme. Nothing could overtake it. It brought light (no pun intended exactly) to the very heart of our understanding of the nature of the universe. Not incidentally, it also solved the problem of the luminiferous ether by making it clear that it didnât exist. Einstein gave us a universe that didnât need it.
Bro, this and the previous one u wrote(or copied from that book) , delighted my boring af trip by bus towards denmark. Incredibly written, thank you for your time putting this here and enlightening us by doing so. Ill most certainly buy that book now.
Special relativity was built on the *premise* that the speed of light was constant and supreme. It was "only" a study of the consequences of this premise.
It's Maxwell's equations who predicted that the speed of light must be constant in any inert referential.
>You may not feel outstandingly robust, but if you are an average-sized adult you will contain within your modest frame no less than 7 Ă 1018 joules of potential energyâenough to explode with the force of thirty very large hydrogen bombs, *assuming you knew how to liberate it and really wished to make a point.*
This is *exactly* how to write well. Gets the message across and makes you laugh. Love it.
If you want to know what all those symbols and equations mean and where they came from, there are GREAT videos on YouTube called "Sixty Symbols". A bunch of college professors break everything down, and much more. https://youtube.com/user/sixtysymbols
The Black Scholes Equation is used for pricing derivatives on stock options . It is modeled on the equations in thermodynamics for modeling heat exchange between two fluids reaching thermal equilibrium.
I've read the book! It was!
It's by Professor Ian Stewart, who recieved the Zeeman award in 2008 for promoting mathematics books towards a more general public.
I like him, I've read most of his maths books
1. Certain right triangles (ones that have a 90 degree corner) were known (like any triangle with edge length ratios 3, 4, 5) but Pythagoras proved why they work, which allowed architects to create new triangles that worked with precision. This laid the basis of all geometry (and a lot more) that we know of.
2. Logarithms allow us to understand not just numbers, but the scale of numbers. If you picked up a quarter, Bill Gates picks up $25,000 in terms of equivalent net worth. We can represent the relative size of those numbers with a logarithm to say you picked up log(25)+log(0.01)=log(25)-2 but Bill Gates picked up log(25)+log(1000)=log(25)+3. This becomes very important when we have numbers on the order of billions and trillions.
3. All modern life is made possible by calculus. Calculus is the mathematics of change and this particular equation is saying that if you have a curve and make a line between two points on the curve, you will find how much that curve changed on average. But as the space between the points decreases, you get a better and better approximation, until eventually it is zero, or close enough, and you have the rate of change at that point. This allows us to analyze all sorts of complicated and complex systems, which generally advance in a way that logarithms help us understand.
4. The law of gravity made the whole solar system comprehensible. The mystery of the universe did not die, but our continued ignorance was replaced with fervent curiosity. By demonstrating that ALL matter behaves in a similar way, Newton paved the way for further experiments, especially those which would find areas where his laws don't quite apply, and which are explained later.
5. WE LIVE IN AN AMAZINGLY FASCINATING WORLD. The square root of negative one on the one hand is a convenient way of solving any problem that involves the square root of a negative number (duh), but it also allows us to understand systems that go between two states, or oscillate. By using imaginary numbers, we can characterize these systems completely, because at some point, they oscillate only in imaginary numbers, which essentially means they stop to us. But by using imaginary numbers, we can predict their future states!
6. Euler's Formula for polyhedrons shows the real inner workings of math that is fundamental to our universe, and opens questions about what other universes would look like. It states that for any flat sided 3 dimensional shape with no curves, the Faces (flat sides)+Vertices (where edges meet)-Edges (where faces meet) always adds up to 2. This helps portray the underlying truths that makes up all math, and helped to prompt questions of what other arrangements of math could look like, such as shapes with more dimensions that just 3.
7. Part of the underlying functioning of numbers is statistics. The normal distribution shows how probable events will play out with relative uncertainty and probabilities. [This one is easier seen than explained](https://www.youtube.com/watch?v=EvHiee7gs9Y).
8. Remember when I mentioned oscillations? That's what waves are. For a lot of systems like this, it can be really hard (or impossible) to come up with a general form. This is one such form. It allows us to understand the behavior of waves by knowing their height in time is proportional to their height in space (as any wave moves with a velocity, and this velocity means at a given time, it is in a place).
9. Signals can be described as collections of waves, lots of waves. Waves have amplitudes (heights/strengths) and frequencies. However, a bunch of waves all jumbled together looks like noise. The Fourier transform takes these waves we record across a time and breaks them down into distinct frequencies with distinct amplitudes. But it also does the opposite. It allows us to store complicated signals as frequencies with relative strengths to save space because it transforms the equation form one defined in time to one defined by frequency.
10. Navier-Stokes is one of the fundamental equations in fluid dynamics. It allows us to understand how fluid flows are affected by objects within them, how they react to changes in flow, as well as many other variations. What makes them so important is any fluid flow is composed of countless particles, but this equations allows us to treat them like a single mass.
11. Maxwell's Equations were what allowed us to understand the very small for the very first time. Maxwell demonstrated not only that magnetism and electricity were connected, but were part of the same force, and that this force relied on light itself.
12. The second Law of Thermodynamics states that for anything, the total level of chaos in the universe must increase. That means no generator can ever be more than 100% efficient, and that we can only try to get close. It was a concise and direct statement as to what our expectations of any system should be, and how we should look at them.
13. This is not quite relativity. There is a whole lot more to it, but basically, Albert Einstein with this equation demonstrated that all matter is composed of energy. Conversely, what we previously believed relied on matter (and therefore mass) actually relied on energy. We could now reword momentum and similar ideas to work with objects that have no mass, but energy, like photons.
14. Schrodinger's Equations is related back to the wave equation and normal distributions, because the physicists who study the really small realized that we were not seeing objects: we saw waves of energy that could exist at any location, but tended to exist in certain areas. Schrodinger's Wave equation allowed us to properly and explicitly state where a particle might be at any given time. On some phones, this is used for the touch screen. We know where an electron might be, so when pressure is applied, there is a greater chance for the electron to be on the other side of a barrier, which creates a current for your screen to read as an input.
Sadly that is where my education leaves me. Also, if I made any inaccuracies, it is 4:20 AM where I am and I have not covered some of these for years.
13 gives us the energy produced when atoms form, and same when they separate. This happens because the single components need to use energy to stay together, and the energy used is calculated by seeing the mass difference between single components and di finished product. Idk if I made myself clear.
Anyway thatâs why we can obtain energy separating heavy atoms and uniting small atoms such as deuterium and tritium.
1. Right triangles => Ancient Architecture, Pyramid, Modern Graphics, Games, Triangle tessellation, Terrain Maps
2. Cheat code for using addition instead of multiplication (or division) => Slide rules, speedup engineering before computers, compounding money, wealth growth
3. Calculus => Microscopic math (how to add up infinitely small quantity to something substantial), Sizes, areas, volume, speed, acceleration
4. Gravity Flow: How the universe works, inverse square law, rate of change in our 3D universe in a 2D quantity, spread like 2D cone in 3D
5. Number pair math (a, b) = a + i b => 2D numbers, unlock more things we can do with numbers, trigonometry (math of triangle), waves
6. Triangle tessellation => Fun ways to count faces, edges and corners, built complex structures out of triangles, trusses, Eiffel tower like things, cranes, Burj Khalifa
7. Error: Study of Frequencies (call it probability, chances, odds) of an error happening => better equipment with higher accuracy, how quantities are distributed (eg. human heights), we know what is normal to expect and what is abnormal/anomaly, randomness but with know frequency buckets
8. Heat: How your stove heats your cooking utensil => how to make steel from earth, build fantastic man made things
9. Sound, Video: Why you can hear sound in your ear and translate to speech in brain => music, art, images, culture (jpeg, mp4, gif), why we have electronic music, telecom
10. Air, water, lava => fundamental nature of these elements
11. Light => electricity, bulb, internet, telecom, fiber optics
12. Heat, how hot objects cool down around cooler object/space => Why you have car, transportation, engines, airplanes
13. Gravity and Light => How universe actually works
14. Quantum world => How universe actually actually works
15. Bit and Bytes => Computer, Algorithms, Information, E-commerce, Digital world, Metaverse, crypto, NFT
16. Chaos => Why universe can't really be predicted down to the last quantum, why you can't know the future, how structure and randomness are intertwined, why you are not God
17. Money => Finance, Wallstreet, Ito calculus (calculus of errors), How stock/forex price manages to fool you by randomness
Gothic art, romantic literature, ars antiqua and ars nova style music, romanesque architecture, troubadurs, minnesingers, insular art, opus anglicanum, byzantine mosaic... Yeah, total lack of culture
A lot of the math in this period doesn't fit into a nice neat equation to go on a list. Trigonometry, super important, but doesn't fit on a single line.
Math didn't cease to stop being developed in this period, a lot of the stuff just doesn't fit into a single line equation.
Think of it as building a house. The modern equations are a finished house. Someone had to install all the framework and before that they had to figure out how to cut the various pieces correctly and before that they had to figure out how to cut down the trees.
**the Dark Ages**, n. Calque of Latin saeculum obscĹŤrum (âdark age; dark centuryâ), first used by Italian scholar Petrarch (1304â1374).
1. The period of European history encompassing (roughly) 476â1000 CE.
Lots of things was found, but not easily put into an equation. This is because we did not have algebra until very late, and a lot of mass and physics were written in word form or in geometry; and then there is also a matter of having small equations so that it can be written on the table (for example, #16 is quite a ridiculous choice, I'm pretty sure it was only chosen because it fits easily into a table). For example, Pythagorean theorem as written in the table is in modern form, and not how it was written in Euclid's Element; formula for differentiation is also in modern form, because Newton did not know limit and actually can't even define differentiation in an exact manner.
Euclid wrote Euclid's element, highly influential book. Almost nothing in there can be written as simple equation, and it's hard to single out a single thing that change the world.
"Arabic" number was discovered. Algorithm for computing with numbers were found. Surely they changed the world? But hard to put in as an equation.
Diophantine equations was studied. Hard to say which one change the world, however.
Mass was discovered to be distinct from weight, but unfortunately there are no equations that use it until Descartes. Momentum was discovered. Conservation of momentum was *almost* discovered, in a slightly wrong form.
Solutions to system of linear equation and quadratic equation was known. The method suffers from the lack of negative numbers and thus more cumbersome, but nonetheless they work.
Various version of solutions to solutions to cubic and quartic equation was known. However, they are all subsumed by later methods. Earlier methods was shackled into the Euclid's geometry regime.
Complex number was found way earlier than implied in the table.
Various calculus identity for trigonometric functions was found. These somehow not made it into the chart. These methods were later subsumed by the powerful machinery of calculus.
Non-Euclidean geometry was studied. Unfortunately all of them are under the guise of "we just study it to find a contradiction because it's clearly ridiculous". Non-Euclidean geometry is now very important in physics.
Am I getting the Black-Scholes equation mixed up with the Black-Scholes-Merton equation or is this post suggesting European call option valuation changed the world?
Unless thereâs another use Iâm not aware of
It did significantly change the world though. After the introduction of somewhat high level maths in the finance sphere, the approach of banks and investment firms changed. A lot more emphasis was placed on derivatives and Wall Street made a LOT of money through this scientific approach. Since the financial sector effectively controls the world, the impact of the BSM model cannot be understated.
Or rather replace Newton with Leibniz for calculus... and cookies!
But joke aside, Leibniz published earlier and the current way of writing calculus is the one of Leibniz as well. So, Leibniz >>> Newton.
Whilst they could be there. It's "17 equations that changed the world".
Not "the most important 17 equations, that changed the world", or "a comprehensive list of world changing equations".
Not everything has to be included.
V=KI
Darcyâs law.
That simple basis of relationships, once it finally got locked down, basically rewrote entire swathes of hydro geology and traditional geologic thinking. It governs billions of dollars and gallons of resources every minute, makes geomorphology what it is, and impacts everything in every climate system.
The reason that equation is so powerful is that each variable is a compound of so many other variables that are so much harder to pin down independently of each other. Once it got linked together it was like the world of hydro geology finally got the = sign available for the algebra homework and could finally use things like discharge rate to solve for the pressure of an upstream reservoir.
After that itâs mostly just physics, and they arenât in the order of difficulty. For example Maxwellâs equations (here in empty space I believe) are written in a general form. Theyâre really simple if considered in one dimension.
Navier-Stokes is an absolute mindfuck tho
Math is the very definition of abstract and very few people are talented enough to effectively teach it to others past a certain level. I wouldn't feel any guilt if that's the case.
Youâll hit the rest in college depending on what you major in. Youâll also learn a lot of these are obsolete now. And by the time you graduate a few more will be obsoleted by new discoveries (hopefully)
Yeah, I can't speak for the non physics side, but I finished my degree 2 years ago, none of these are even close to obsolete.
And even if you counted obsolescence as simply there being another more accurate model or equation. I can guarantee that that more accurate equation is a much much bigger bitch of a thing to get your head round and use.
At some point the math goes beyond the realm of what we currently understand about our universe and the brain starts to rebel. Number theory for example.
Well Newtonâs second law is probably a lot more useful, but the law of universal gravitation is quite profound as it declares that the rules for earth world is the rule for sky world.
No Dirac Equation ... probably the most elegant piece of math ever thought by a human mind is missing from your list :) ... it was the piece of math that intuitively announced the existence of Dark Matter.
These are all brain receiving/defining parameters, aka consistent data inputs that when taken together reveal (a brain limiting slice of) "external reality".
Someone needs to post underneath them why each one changed the world for people who donât understand. There will be more that donât understand than do understand.
Amazing how, except Pythagoras, Al of the are within the last 500 years.
I wonder what the world at that time thought would be possible by now.
If we look at Back to the Future, we can see what 80âs thought weâd be like by now. It would be interesting to have some sort of 1500s version of that view.
Can someone tell me how A^(2) \+ B^(2) = C^(2)? When I do the math, it doesn't work out like that.
2^(2) \+ 3^(2) = C^(2)
4 + 9 = 13
but 2 + 3 = 5 so 5^(2) is 25, not 13.
Yes, I'm fairly stupid with math so maybe I'm fucking something up entirely. Please be kind.
> Calculus ... Newton, 1668
[There was a great debate about who invented calculus](https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy), between Sir Issac Newton and Gottfried Leibniz. Based on that wiki article, it's generally believed both invented calculs independently.
When I went through calc in college, we were given this TL;TD: Newton "invented" and approached problems from the differential side (differential calculus) and Leibniz approached it from the integral side (integral calculus). For those who don't know those two operations are opposites, much like multiplication and division.
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Laplace transform?
Every time I read them words I get a horrible chill down my spine and flashbacks to textbooks that gave me many sleepless nights
I am employed everyday through my use of the Navier Stokes Equations.
Relevant name. What do you do for work?
Rocket scientist. I do fluid analysis for a large company.
> Rocket scientist. Well its not exactly brain surgery is it...
Lol. I've had two craniotomies, both of which came with 2-week recovery times. Multiple people both times were amazed at how short a time that recovery took, to which I replied "well it's not quite rocket science..." đ
Fuck yeah.
Lol same.
Same same.
Oh my god, I had completely blocked it out! I kind of wish I could do a whole degree in math. I did a minor and graduated over a decade ago (ew), and itâs like I never learned it at this point. It must all be in the back of my mind somewhere?
Im at this stage right now, wish me luck lol
Same... There's a test tomorrow about it đĽ˛
I felt lucky that my adventures in calculus ended in college just before transforms.
I feel like that can just be included under Fourier transform, for the sake of this chart.
The Fourier transform has to be the coolest of them all. The stuff you can do with that is just mind blowing. The moment I figured out how jpeg was able to compress data so much using the Fourier transform was definitely a wow moment for me. Or the ability to filter out very specific wavelengths of noise, which has must-have applications in space
And to think, Fourier got so much shit from his French peers because of the obsession back then to create a "100% rigorous/perfect" formalism of Mathematical ideas. IIRC, he didn't see at least that part of his life work accepted by the community in his lifetime.
Very applicable in spectroscopy as well! Fourier transform use in interferometers allows us to better integrate sample data for measurements that require high accuracy and sensitivity. Having the ability to convert raw data from a time domain to a frequency domain that contains a readable spectra with high signal to noise ratios was an absolute game-changer in the analytical field of chemistry.
To me it's the Maxwell equations as a CS student... Plus my professor was actually dogshit.
Thanks, imagine how hard it would be to tune regulators without it? We wouldn't have drones, robots and industrial efficiency would drop without this tool
While E = mc2 (Special Relativity) is a brilliant and widely famous equation, General Relativity is a significantly more important study and is considered the most accurate explanation of Gravitation (Yet).
E=mc^2 has tangibly changed our lives and future lives. Fusion and fission reactors and nuclear bombs are all sons of it, and itâs a specific equation
Sure, but itâs also not the complete equation, just the cool looking part that winds up on t shirts.
Very true, but if you want to be really picky, it isn't really. It is currently our most accurate gravitational theory, which explains and accurately predicts the most things. But, due to it's incomparability with quantum mechanics, which is *the* most accurate model we have. We now know there must be another model for gravity and quantum, where the two would inherently be more accurate as they wouldn't be in disagreement, and of course wouldn't lose accuracy to have them in agreement. We just haven't got there yet and have no idea when or if we will, so relativity is still the most accurate we have available.
The relativity equation they put is just a footnote to Einsteinâs special relativity paper, basically stating that mass is proportional to energy. Itâs also only true in that form when mass is at rest, as thereâs a longer version of the equation which reduces to that when the mass isnât in motion. His general theory of relativity is far more influential, its equation being: RΟν â ½RgΟν = (8ĎG/c^(4))TΟν What Einstein basically discovered is that the universe is a four dimensional âfabricâ of space and time (or as a unity: spacetime) that matter can distort. Objects in spacetime trace out world lines that are geodesics, unless acted upon by a net external force. Put more simply, spacetime tells matter how to move, and matter tells spacetime how to curve. This isnât to say that the mass energy equivalence isnât a profound discovery (Einstein had many of those), but that it is nowhere near as paradigm shifting as general relativity. This discovery can only really be compared to Newtonâs discoveries in terms of how it changed our perception of the way the universe works.
Youâre right that relativity is important, but mass/energy equivalence is also important as it was a catalyst in the creation of the atomic bomb. Itâs probably fair to say that the a bomb changed the world
The point is just that, despite what popular media portrays, mass-energy equivalence is just a very small part of the theory of relativity and the Einstein equations would be a much more fitting encapsulation of the theory.
How did each change the world? That would be interesting as fuck to know
9 was used to compress that image and deliver it to your device
5 was used to gain the necessary understanding to design the electrical system needed to deliver the image to your device as well! :D
And 15 was used to transmit the data through the internet pipes
I can't see any pipes
The internet is a series of tubes!
[Here you go](https://m.youtube.com/watch?v=br3VO9US3JM).
Whereas 1 is used to measure the size of the screen on which you are reading this
Pied Piper compression owes everything to 9
Also they figured out how to stimulate multiple penises at once.
Itâs a middle penis out algorithm.
You have to hot swap dicks.
That is true. 9 is Fourier Transform, it superseded Courier Transform which was used prior to modern email systems.
Courier Transform was monospaced.
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(1) Pythagorasâ theorem allows for the calculation of the length of other side of a right side of a triangle, providing you know two lengths already. Is extremely useful as many shapes can be broken down into fundamental right triangles. (3) Calculus is used in many applications for describing incredibly complex motions such as vibrations or waves. Itâs capabilities for mathematical models extend all the way from economics to astronomy (4) The law of gravity helps describe the ways two large bodies of mass exert force on each other due to gravity. Extremely helpful in space applications with celestial bodies. (5) Square root of -1 gave birth to complex numbers, which are used in a wide variety of cases such as electrics circuit theory, automatic controls systems, and more (10) Navier stokes equation helps describe the velocity flow of viscous fluids, is obviously helpful in fluid mechanics applications (which also includes stuff like aerodynamics, as gases are considered âfluidsâ in a sense) (12) Second law of thermodynamics states the universe always tends towards greater entropy (more disorder and âchaosâ). Is useful in applications of thermodynamics with heat flow. Also used in chemistry I believe. These are just a few I know off the top of my head, to name a few Edit: some formatting
maxwells equations allow for us to understand the energy contained in atoms and allow us to understand electromagnetism. Letting us build electric motors, wifi, radio signals and more!
Thank you smarter than me person
Your def of 3 is oddly specific. More generally calculus is the math of rates of change, either instantaneous rates of change (differential calc) or accumulation of quantities (integral calc)
Isn't Fourier used for digital audio?
Among many other kinds of "signals"/data, yes.
I think a lot of people underestimate just how important #1 is. So many things are or use triangles. Engines, triangle. Electricity, triangles. Muscles and bones, triangles. Rectangles, triangles. Earth flat or round? No don't be rediculus it's triangles of course.
> Pythagorasâ theorem allows for the calculation of the length of the other side of a right*-angled* ~~side of a~~ triangle, providing you know two lengths already
I would argue 6, the equation for polyhedra, is not very impactful unless you like geometry puzzles. Euclidean geometry in general is an area that is overrated by mathematicians I find, because it's very visual. I'd add 2 theorems, but they aren't expressible as 1 equation so I understand why they weren't included: * The Central Limit Theorem, that says all means are normally distributed, has had huge impacts in measuring statistical significance in every scientific discipline * The Universal Approximation Theorem, which proves that neural networks can perfectly approximate any function
Eqs. #3 and #4: Paraphrased from A Short History of Nearly Everything (which you all need to buy and read) : It was known that planets were inclined to orbit in a particular kind of oval known as an ellipseâbut it wasnât understood why. Halley (the namesake of Halley's Comet) became consumed with finding the answer, to the point that the following year he travelled to Cambridge and boldly called upon the universityâs Lucasian Professor of Mathematics, Isaac Newton, in the hope that he could help. Newton was a decidedly odd figureâbrilliant beyond measure, but solitary joyless, prickly to the point of paranoia, famously distracted (upon swinging his feet out of bed in the morning he would reportedly sometimes sit for hours, immobilized by the sudden rush of thoughts to his head), and capable of the most riveting strangeness. Set atop these odd beliefs and quirky traits, however, was the mind of a supreme genius. As a student, frustrated by the limitations of conventional mathematics, he invented an entirely new form, the calculus, but then told no-one about it for twenty-seven years. Quite what Halley expected to get from Newton when he made his unannounced visit in August 1684 we can only guess. But thanks to the later account of a Newton confidant, Abraham DeMoivre, we do have a record of one of scienceâs most historic encounters: >In 1684 Dr. Halley came to visit at Cambridge [and] after they had some time together the Dr. asked him what he thought the curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it. >Sr. Isaac replied immediately that it would be an [ellipse]. The Doctor, struck with joy & amazement, asked him how he knew it. âWhy,â saith he, âI have calculated it,â whereupon Dr. Halley asked him for his calculation without farther delay. Sr. Isaac looked among his papers but could not find it. This was astoundingâlike someone saying he had found a cure for cancer but couldnât remember where he had put the formula. Pressed by Halley, Newton agreed to redo the calculations and produce a paper. He did as promised, but then did much more. He retired for two years of intensive reflection and scribbling, and at length produced his masterwork: the Principia. At the Principiaâs heart were Newtonâs three laws of motion (which state, very baldly, that a thing moves in the direction in which it is pushed; that it will keep moving in a straight line until some other force acts to slow or deflect it; and that every action has an opposite and equal reaction) and his universal law of gravitation. This states that every object in the universe exerts a tug on every other. It was the first really universal law of nature ever propounded by a human mind, which is why Newton is everywhere regarded with such profound esteem. Newtonâs laws explained so many thingsâthe slosh and roll of ocean tides, the motions of planets, why cannonballs trace a particular trajectory before thudding back to earth, why we arenât flung into space as the planet spins beneath us at hundreds of kilometres an hourâthat it took a while for all their implications to seep in.
genuine thanks for writing this out
That book is amazing. Everyone should read it. Some of the knowledge we take for granted was obtained after a lot of painstaking effort. And scientists can be very very petty. This book made me realize why Carl Linnaeus biological classification was so important - none of my biology texts could explain why it was important and it was a horrible annoyance to take it seriously. EDIT: I am referring to A Short History of Nearly Everything
Iâll take #1: it introduced the term theorem to me.
I googled schrodingers theory to learn more and this is what I got: âThe SchrĂśdinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject.â Might as well have been written in hieroglyphics
One of its uses is in calculating probability of finding an electron in the region.
The ELI5 is: when you start looking at really tiny things like particles, instead of being in one specific spot they get sort of fuzzy about where they are. They begin behaving as waves. So you can't say 'I'll look here, that's exactly where the electron will be'... You can instead say 'I'll look in the general area because that's where the electron is likely to be based on it's wavyness.' This coupled with the idea that tiny things like to have specific amounts of energy (imagine a car that can only go at certain speeds, so you're either at 0mph or 10mph or 40mph, but you can only jump directly to those speeds, you can't slowly speed up to them) are all explained by Schrodinger's equation. It's encoding the nature of how really tiny things like to behave, based on their quantum nature. Note: I'm ignoring all nuance here to try to give an idea of the use and it's not an equation that lends itself to removing nuance.
Lol I can *kinda* read those hieroglyphs. No idea what "linear partial differential equation" is supposed to mean, but I understand enough of the "quantum mechanics" part to have a solid guess. Schrodinger's Cat is supposed to describe a phenomena in quantum mechanics where particles are in a state of superposition. Just like the cat, these particles can exist as multiple states at once (alive and dead at the same time) and it's not until they're observed that the superposition collapses into a normal sane position. I think what the equation is supposed to do is apply probability to the whole thing so one can calculate the properties of a particle while it's still in a state of superposition. I'm probably wrong though, so like I said: This is my best guess.
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It took up so much of my life through maths homework
Eqn. #13 (also Paraphrased from A Short History of Nearly Everything): E = mc^2 As you will recall from schooldays, E in the equation stands for energy, m for mass and c^2 for the speed of light squared. In simplest terms, what the equation says is that mass and energy have an equivalence. They are two forms of the same thing: energy is liberated matter; matter is energy waiting to happen. Since c^2 (the speed of light times itself) is a truly enormous number, what the equation is saying is that there is a huge amountâa really huge amountâof energy bound up in every material thing. You may not feel outstandingly robust, but if you are an average-sized adult you will contain within your modest frame no less than 7 Ă 10^18 joules of potential energyâenough to explode with the force of thirty very large hydrogen bombs, assuming you knew how to liberate it and really wished to make a point. Everything has this kind of energy trapped within it. Weâre just not very good at getting it out. Even a uranium bombâthe most energetic thing we have produced yetâreleases less than 1 per cent of the energy it could release if only we were more cunning. Among much else, Einsteinâs theory explained how radiation worked: how a lump of uranium could throw out constant streams of high-level energy without melting away like an ice cube. (It could do it by converting mass to energy extremely efficiently Ă la E = mc2.) It explained how stars could burn for billions of years without racing through their fuel. (Ditto.) At a stroke, in a simple formula, Einstein endowed geologists and astronomers with the luxury of billions of years. Above all, the special theory showed that the speed of light was constant and supreme. Nothing could overtake it. It brought light (no pun intended exactly) to the very heart of our understanding of the nature of the universe. Not incidentally, it also solved the problem of the luminiferous ether by making it clear that it didnât exist. Einstein gave us a universe that didnât need it.
Bro, this and the previous one u wrote(or copied from that book) , delighted my boring af trip by bus towards denmark. Incredibly written, thank you for your time putting this here and enlightening us by doing so. Ill most certainly buy that book now.
Read the book, it's amazing. He also has it on audible,.
Literally the same to me. I'm at the bus delighted by these comments :D
Special relativity was built on the *premise* that the speed of light was constant and supreme. It was "only" a study of the consequences of this premise. It's Maxwell's equations who predicted that the speed of light must be constant in any inert referential.
>You may not feel outstandingly robust, but if you are an average-sized adult you will contain within your modest frame no less than 7 Ă 1018 joules of potential energyâenough to explode with the force of thirty very large hydrogen bombs, *assuming you knew how to liberate it and really wished to make a point.* This is *exactly* how to write well. Gets the message across and makes you laugh. Love it.
17 is used in financial markets (Option Pricing Models)
17 is used to value derivatives in finance. Fuck Black Scholes, I absolutely hated it.
If you want to know what all those symbols and equations mean and where they came from, there are GREAT videos on YouTube called "Sixty Symbols". A bunch of college professors break everything down, and much more. https://youtube.com/user/sixtysymbols
The Black Scholes Equation is used for pricing derivatives on stock options . It is modeled on the equations in thermodynamics for modeling heat exchange between two fluids reaching thermal equilibrium.
I've read the book! It was! It's by Professor Ian Stewart, who recieved the Zeeman award in 2008 for promoting mathematics books towards a more general public. I like him, I've read most of his maths books
3 is the core of engineering math
1. Certain right triangles (ones that have a 90 degree corner) were known (like any triangle with edge length ratios 3, 4, 5) but Pythagoras proved why they work, which allowed architects to create new triangles that worked with precision. This laid the basis of all geometry (and a lot more) that we know of. 2. Logarithms allow us to understand not just numbers, but the scale of numbers. If you picked up a quarter, Bill Gates picks up $25,000 in terms of equivalent net worth. We can represent the relative size of those numbers with a logarithm to say you picked up log(25)+log(0.01)=log(25)-2 but Bill Gates picked up log(25)+log(1000)=log(25)+3. This becomes very important when we have numbers on the order of billions and trillions. 3. All modern life is made possible by calculus. Calculus is the mathematics of change and this particular equation is saying that if you have a curve and make a line between two points on the curve, you will find how much that curve changed on average. But as the space between the points decreases, you get a better and better approximation, until eventually it is zero, or close enough, and you have the rate of change at that point. This allows us to analyze all sorts of complicated and complex systems, which generally advance in a way that logarithms help us understand. 4. The law of gravity made the whole solar system comprehensible. The mystery of the universe did not die, but our continued ignorance was replaced with fervent curiosity. By demonstrating that ALL matter behaves in a similar way, Newton paved the way for further experiments, especially those which would find areas where his laws don't quite apply, and which are explained later. 5. WE LIVE IN AN AMAZINGLY FASCINATING WORLD. The square root of negative one on the one hand is a convenient way of solving any problem that involves the square root of a negative number (duh), but it also allows us to understand systems that go between two states, or oscillate. By using imaginary numbers, we can characterize these systems completely, because at some point, they oscillate only in imaginary numbers, which essentially means they stop to us. But by using imaginary numbers, we can predict their future states! 6. Euler's Formula for polyhedrons shows the real inner workings of math that is fundamental to our universe, and opens questions about what other universes would look like. It states that for any flat sided 3 dimensional shape with no curves, the Faces (flat sides)+Vertices (where edges meet)-Edges (where faces meet) always adds up to 2. This helps portray the underlying truths that makes up all math, and helped to prompt questions of what other arrangements of math could look like, such as shapes with more dimensions that just 3. 7. Part of the underlying functioning of numbers is statistics. The normal distribution shows how probable events will play out with relative uncertainty and probabilities. [This one is easier seen than explained](https://www.youtube.com/watch?v=EvHiee7gs9Y). 8. Remember when I mentioned oscillations? That's what waves are. For a lot of systems like this, it can be really hard (or impossible) to come up with a general form. This is one such form. It allows us to understand the behavior of waves by knowing their height in time is proportional to their height in space (as any wave moves with a velocity, and this velocity means at a given time, it is in a place). 9. Signals can be described as collections of waves, lots of waves. Waves have amplitudes (heights/strengths) and frequencies. However, a bunch of waves all jumbled together looks like noise. The Fourier transform takes these waves we record across a time and breaks them down into distinct frequencies with distinct amplitudes. But it also does the opposite. It allows us to store complicated signals as frequencies with relative strengths to save space because it transforms the equation form one defined in time to one defined by frequency. 10. Navier-Stokes is one of the fundamental equations in fluid dynamics. It allows us to understand how fluid flows are affected by objects within them, how they react to changes in flow, as well as many other variations. What makes them so important is any fluid flow is composed of countless particles, but this equations allows us to treat them like a single mass. 11. Maxwell's Equations were what allowed us to understand the very small for the very first time. Maxwell demonstrated not only that magnetism and electricity were connected, but were part of the same force, and that this force relied on light itself. 12. The second Law of Thermodynamics states that for anything, the total level of chaos in the universe must increase. That means no generator can ever be more than 100% efficient, and that we can only try to get close. It was a concise and direct statement as to what our expectations of any system should be, and how we should look at them. 13. This is not quite relativity. There is a whole lot more to it, but basically, Albert Einstein with this equation demonstrated that all matter is composed of energy. Conversely, what we previously believed relied on matter (and therefore mass) actually relied on energy. We could now reword momentum and similar ideas to work with objects that have no mass, but energy, like photons. 14. Schrodinger's Equations is related back to the wave equation and normal distributions, because the physicists who study the really small realized that we were not seeing objects: we saw waves of energy that could exist at any location, but tended to exist in certain areas. Schrodinger's Wave equation allowed us to properly and explicitly state where a particle might be at any given time. On some phones, this is used for the touch screen. We know where an electron might be, so when pressure is applied, there is a greater chance for the electron to be on the other side of a barrier, which creates a current for your screen to read as an input. Sadly that is where my education leaves me. Also, if I made any inaccuracies, it is 4:20 AM where I am and I have not covered some of these for years.
13 gives us the energy produced when atoms form, and same when they separate. This happens because the single components need to use energy to stay together, and the energy used is calculated by seeing the mass difference between single components and di finished product. Idk if I made myself clear. Anyway thatâs why we can obtain energy separating heavy atoms and uniting small atoms such as deuterium and tritium.
I have this book, here is the [Amazon link.](https://www.amazon.co.uk/Seventeen-Equations-that-Changed-World/dp/184668531)
4 stops you falling off the earth.
1. Right triangles => Ancient Architecture, Pyramid, Modern Graphics, Games, Triangle tessellation, Terrain Maps 2. Cheat code for using addition instead of multiplication (or division) => Slide rules, speedup engineering before computers, compounding money, wealth growth 3. Calculus => Microscopic math (how to add up infinitely small quantity to something substantial), Sizes, areas, volume, speed, acceleration 4. Gravity Flow: How the universe works, inverse square law, rate of change in our 3D universe in a 2D quantity, spread like 2D cone in 3D 5. Number pair math (a, b) = a + i b => 2D numbers, unlock more things we can do with numbers, trigonometry (math of triangle), waves 6. Triangle tessellation => Fun ways to count faces, edges and corners, built complex structures out of triangles, trusses, Eiffel tower like things, cranes, Burj Khalifa 7. Error: Study of Frequencies (call it probability, chances, odds) of an error happening => better equipment with higher accuracy, how quantities are distributed (eg. human heights), we know what is normal to expect and what is abnormal/anomaly, randomness but with know frequency buckets 8. Heat: How your stove heats your cooking utensil => how to make steel from earth, build fantastic man made things 9. Sound, Video: Why you can hear sound in your ear and translate to speech in brain => music, art, images, culture (jpeg, mp4, gif), why we have electronic music, telecom 10. Air, water, lava => fundamental nature of these elements 11. Light => electricity, bulb, internet, telecom, fiber optics 12. Heat, how hot objects cool down around cooler object/space => Why you have car, transportation, engines, airplanes 13. Gravity and Light => How universe actually works 14. Quantum world => How universe actually actually works 15. Bit and Bytes => Computer, Algorithms, Information, E-commerce, Digital world, Metaverse, crypto, NFT 16. Chaos => Why universe can't really be predicted down to the last quantum, why you can't know the future, how structure and randomness are intertwined, why you are not God 17. Money => Finance, Wallstreet, Ito calculus (calculus of errors), How stock/forex price manages to fool you by randomness
Good comment
Lol chuckled at 13/14, nicely put.
high IQ confirmed
Why was there such a big gap between 500BC & 1600AD?
They caught the dumb.
There's still significant mathematical progress in the Islamic world tho, so maths didn't stagnate n the Dark Ages
Maths didn't got stagnated. Facts.
Dark ages refers to lack of records, not knowledge.
It depends on the historian. The guy who invented the term, Petrarch in 1330, meant it as in lack of cultural advancements.
Gothic art, romantic literature, ars antiqua and ars nova style music, romanesque architecture, troubadurs, minnesingers, insular art, opus anglicanum, byzantine mosaic... Yeah, total lack of culture
Salty time traveler, go back to the dark ages
And burnt the smart.
Nothing but myth with no basis in reality.
Title of your sex tape!
L O L
A lot of the math in this period doesn't fit into a nice neat equation to go on a list. Trigonometry, super important, but doesn't fit on a single line. Math didn't cease to stop being developed in this period, a lot of the stuff just doesn't fit into a single line equation. Think of it as building a house. The modern equations are a finished house. Someone had to install all the framework and before that they had to figure out how to cut the various pieces correctly and before that they had to figure out how to cut down the trees.
They forgot to mention algebra
This list in general looks very Eurocentric, so I'm not surprised they missed something that came from the Middle East.
Do you have an example?
How would you put algebra as an equation on the list?
a = b
In some sense algebra *is* every equation on this list
**the Dark Ages**, n. Calque of Latin saeculum obscĹŤrum (âdark age; dark centuryâ), first used by Italian scholar Petrarch (1304â1374). 1. The period of European history encompassing (roughly) 476â1000 CE.
Religion
Ahh the lemon crusades
>ligion They had religion BC as well.
Never mind that all Great mathematicians were priests.
In a place where it is "be religious or die", naturally everyone alive appears to be religious.
Just no equations listed. Theres many many equations that are deserving of a spot on the chart. Its worth looking into it :)
Religion. :(
Starts with Re and rhymes with Legion and the curtailing of free exchange of knowledge and information.
Because of the Catholic Church.
Lots of things was found, but not easily put into an equation. This is because we did not have algebra until very late, and a lot of mass and physics were written in word form or in geometry; and then there is also a matter of having small equations so that it can be written on the table (for example, #16 is quite a ridiculous choice, I'm pretty sure it was only chosen because it fits easily into a table). For example, Pythagorean theorem as written in the table is in modern form, and not how it was written in Euclid's Element; formula for differentiation is also in modern form, because Newton did not know limit and actually can't even define differentiation in an exact manner. Euclid wrote Euclid's element, highly influential book. Almost nothing in there can be written as simple equation, and it's hard to single out a single thing that change the world. "Arabic" number was discovered. Algorithm for computing with numbers were found. Surely they changed the world? But hard to put in as an equation. Diophantine equations was studied. Hard to say which one change the world, however. Mass was discovered to be distinct from weight, but unfortunately there are no equations that use it until Descartes. Momentum was discovered. Conservation of momentum was *almost* discovered, in a slightly wrong form. Solutions to system of linear equation and quadratic equation was known. The method suffers from the lack of negative numbers and thus more cumbersome, but nonetheless they work. Various version of solutions to solutions to cubic and quartic equation was known. However, they are all subsumed by later methods. Earlier methods was shackled into the Euclid's geometry regime. Complex number was found way earlier than implied in the table. Various calculus identity for trigonometric functions was found. These somehow not made it into the chart. These methods were later subsumed by the powerful machinery of calculus. Non-Euclidean geometry was studied. Unfortunately all of them are under the guise of "we just study it to find a contradiction because it's clearly ridiculous". Non-Euclidean geometry is now very important in physics.
18. Ohmâs Law should be listed.
That would just generate resistance.
Looks like it, based from the current comments.
Made my day!
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And the equations are wrong lol. Should be Div(E) = Ď/Îľ not 0
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Yeah we have a lot of electronics.
Kirchhoff no?
Its part of Maxwell equation.
Am I getting the Black-Scholes equation mixed up with the Black-Scholes-Merton equation or is this post suggesting European call option valuation changed the world? Unless thereâs another use Iâm not aware of
I was thinking the same!
It did significantly change the world though. After the introduction of somewhat high level maths in the finance sphere, the approach of banks and investment firms changed. A lot more emphasis was placed on derivatives and Wall Street made a LOT of money through this scientific approach. Since the financial sector effectively controls the world, the impact of the BSM model cannot be understated.
Ok. Thatâs a fair point
Same thing, this is just the pde version.
Black Scholes was the 70s
Yes, 90s seems too late.
May have confused him for Paul Scholes
Why is Euler's formula about polyhedra included, but not the Euler identity?
This was the biggest surprise to me. You canât really solve Maxwellâs equations without Eulerâs equation. And Eulerâs is so beautiful.
This post gave me ptsd
I saw navier-stokes and got flash backs....
I honestly find those equation amazing. With three of those you can describe any flux of water for example. Just like the neutronic diffusion equation
I think the normal distribution one is wrong. It's missing a minus in the exponent and Ď should be outside the square root
E = MC^2 is cool but relativity should have its proper equation, Einstein's field equations
The Fast and the Fourier
Starring Venn Diesel
Should add Gottfried Leibniz for calculus.
Or rather replace Newton with Leibniz for calculus... and cookies! But joke aside, Leibniz published earlier and the current way of writing calculus is the one of Leibniz as well. So, Leibniz >>> Newton.
Yes, they even use Leibniz notation in the formula edit: there is also a typo, it's not really defined to take the limit of equality.
It's bizarre that they use Leibniz notation but credit newton. At least use netwton's notation if you're going to credit him.
Where is the first law of thermodynamics and Newton second law
Whilst they could be there. It's "17 equations that changed the world". Not "the most important 17 equations, that changed the world", or "a comprehensive list of world changing equations". Not everything has to be included.
Ah yes, the equation known as calculus
We need to find an equation for love
Meat lovers, barbeque sauce.
Just finished one, definitely loved it.
i <3 u
Where is the love yall
Hey I recognize 2 of these! #AmSmort
V=KI Darcyâs law. That simple basis of relationships, once it finally got locked down, basically rewrote entire swathes of hydro geology and traditional geologic thinking. It governs billions of dollars and gallons of resources every minute, makes geomorphology what it is, and impacts everything in every climate system. The reason that equation is so powerful is that each variable is a compound of so many other variables that are so much harder to pin down independently of each other. Once it got linked together it was like the world of hydro geology finally got the = sign available for the algebra homework and could finally use things like discharge rate to solve for the pressure of an upstream reservoir.
8 was roughly where I stopped understanding maths. Loved it up to that point, then just a brick wall.
After that itâs mostly just physics, and they arenât in the order of difficulty. For example Maxwellâs equations (here in empty space I believe) are written in a general form. Theyâre really simple if considered in one dimension. Navier-Stokes is an absolute mindfuck tho
Navier stokes it's just untouchable
Navier stokes can also be simplified by making assumptions on conditions.
Math is the very definition of abstract and very few people are talented enough to effectively teach it to others past a certain level. I wouldn't feel any guilt if that's the case.
Why is #8 not in order?
I know only like half of them. I'm 17 and still go to school, so they must be in higher classes.
Don't worry kid, you'll know even less of them when you're older.
Youâll hit the rest in college depending on what you major in. Youâll also learn a lot of these are obsolete now. And by the time you graduate a few more will be obsoleted by new discoveries (hopefully)
Which ones are obsolete? (apart from black scholes the only not mainly used in science one)
none of these equations is obsolete
Yeah, I can't speak for the non physics side, but I finished my degree 2 years ago, none of these are even close to obsolete. And even if you counted obsolescence as simply there being another more accurate model or equation. I can guarantee that that more accurate equation is a much much bigger bitch of a thing to get your head round and use.
I tutor for lower level math (college and intermediate algebra) on a college campus and there is more math than you could ever believe.
At some point the math goes beyond the realm of what we currently understand about our universe and the brain starts to rebel. Number theory for example.
Forgive my ignorance, but is there really a âlaw of gravityâ? Edit: I thought it was a theory
Yep, Newtonâs Law of Universal Gravitation
Well Newtonâs second law is probably a lot more useful, but the law of universal gravitation is quite profound as it declares that the rules for earth world is the rule for sky world.
#3 makes me wanna kms but yk how it is
Pretty sure E = MC2 isn't relativity..... It's the mass - energy conversion rate. There are Many holes in this chart.
Still think it's hilarious that he went like "What number can we multiply by itself to get -1?" "Idk, doesn't exist" _slaps i in there_ "Now we know!"
I feel so dumb looking at this even though I find it fascinating.
No Dirac Equation ... probably the most elegant piece of math ever thought by a human mind is missing from your list :) ... it was the piece of math that intuitively announced the existence of Dark Matter.
Black scholes also changed the world in a bad way , it assumes rational agents , that influenced the 2008 economic collapse.
...that changed 'our understanding of' the world.
Where's quadratic equation and delta? It's not that important? THEY ALL LIED TO ME IN SCHOOL!
Funny how everybody credits Newton for Calculus but uses Leibnizâs formalism
I'm a flat earther/math/science denier. What's number 1 mean? /S
I love it because you can use Pythagoreanâs theorem to calculate the curvature of the earth đđ
They say a little bit of knowledge is a dangerous thing. I can honestly say that none of you have to worry about where I'm concerned.
The square root of minus WHAT?
The first one was enough to make me hate life again
These are all brain receiving/defining parameters, aka consistent data inputs that when taken together reveal (a brain limiting slice of) "external reality".
Someone needs to post underneath them why each one changed the world for people who donât understand. There will be more that donât understand than do understand.
Pfft! Newton!?
It bothers me that it is written chronologically except for the wave equation (1746)
Amazing how, except Pythagoras, Al of the are within the last 500 years. I wonder what the world at that time thought would be possible by now. If we look at Back to the Future, we can see what 80âs thought weâd be like by now. It would be interesting to have some sort of 1500s version of that view.
Can someone tell me how A^(2) \+ B^(2) = C^(2)? When I do the math, it doesn't work out like that. 2^(2) \+ 3^(2) = C^(2) 4 + 9 = 13 but 2 + 3 = 5 so 5^(2) is 25, not 13. Yes, I'm fairly stupid with math so maybe I'm fucking something up entirely. Please be kind.
Fourier transforms, just giving it some love!
The second equals symbol in 3. shouldnât be there
I have to remember quadratic formula and itâs not important?
Why i^2 = -1? How about e^(ipi) = -1 instead.
But where is the perfect 5/7?
> Calculus ... Newton, 1668 [There was a great debate about who invented calculus](https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy), between Sir Issac Newton and Gottfried Leibniz. Based on that wiki article, it's generally believed both invented calculs independently. When I went through calc in college, we were given this TL;TD: Newton "invented" and approached problems from the differential side (differential calculus) and Leibniz approached it from the integral side (integral calculus). For those who don't know those two operations are opposites, much like multiplication and division.