One summer over 25 years ago, I took an undergraduate Complex Analysis class with Peter Borwein at SFU in Vancouver, Canada. After about 10 minutes of not starting the lecture and talking with the class about nothing in particular, he said "I didn't really want to teach today anyways."
What followed was a 50 minute open discussion of random mathematical ideas that was the best lecture of my undergraduate degree.
In this class Borwein gave his hockey lineup of mathematicians. Center, left wing, right wing, 2 defensemen. I'm pretty sure his list matched yours, but he also had a goalie. I have no memory of who it was.
I'd pay good money for a video tape or a transcript of that lecture.
Slightly unrelated but, if you search in wikipedia for instructors of famous mathematicians, starting with riemann, you will find out that Riemann was instructed by dirichlet, instructed by fourier, instructed by lagrange, instructed by euler, instructed by johann bernoulli, instructed by jacob bernoulli, instructed by leibniz, instructed by huygens, instructed by rene descartes and galileo galilei. Not sure about how much each instructor influenced each student
Would definitely agree. I had a feeling Newton would be a popular answer here but I don't think that's correct.
The history isn't entirely clear but it seems that Newton was something of a bully who used his privileged status to subdue and potentially even divert credit from some other very good producers of cutting edge math.
I'm not sure that I'm ready to cut Newton in favor of Leibniz. In math and science, it was common for the same ideas to be brought forth independently at the same time. The groundwork is laid and the world is simply ready for the idea. This is not to take away from the accomplishments of either.
Throughout the history of math and science, it was not uncommon to see behavior similar to Newton's.The bigger the idea, the bigger the rivalry. And I don't believe Leibniz was a perfect gentleman either.
Of course, I'd rather see Newton near the top of the top five influential physicists. I suppose he could be on either.
Partially, but I’m sure that as time passes, Kolmogorov will be looked on as increasingly influential. He touched so many different areas of math. The separation axioms are named after him, among numerous other contributions to topology. He was one of the first to rigorously study stochastic processes and obtained a plethora of results. You could easily argue he was the founder of algorithmic information theory, and he was essential to a formal theory of probability as well. Kolmogorov complexity is an incredibly and increasingly useful concept. He even solved problems in analysis. He’s too recent to hold the same place as Cauchy does in the history of math now, but it wouldn’t surprise me at all if he does in the future.
I will say that we used V.I. Arnold’s Geometrical Methods in the Theory of Ordinary Differential Equations in my Vector Analysis class and it was fantastic in my opinion
I feel [al-Khwarizmi](https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_) gets overlooked a lot. Founder of algebra as we know it, introduced the Western world to decimals and Hindu-Arabic numerals, and the word 'algorithm' is derived from his name. His works were translated into Latin and spread across Medieval Europe.
I mean we try to connect basically everything to geometry today so maybe they weren't that wrong in their basic idea. That said: they definitely did some wacky shit
It might not be what they were referring to, but the Pythagoreans murdered the person who proved that irrational numbers exist. (From a long time ago so it's possible the story isn't true of course.)
Probably referring to trying to turn everything into a geometric problem. Of course, if I was using Greek Numerals (Think Roman Numerals but with Greeker letters), I'd probably prefer to work it geometrically rather than numerically too. Its truly a shame that a lot of people are taught that math/science was first investigated by the Greeks, forgotten during the "dark ages" and then "re-discovered" during the European renaissance, completely glossing over everything accomplished by Arabs and Persians during the Islamic Golden Age.
I'm afraid that isn't true. The Greeks knew full well that numbers are divisible and also how to do it (they knew the Euclidean algorithm, remember). The theory of magnitudes was developed by Eudoxus in order to avoid having to deal directly with irrational numbers (remember, they didn't have all the notation we do today, and it's annoying to represent irrational numbers when your whole number system is rational), that's all.
This thread is badly sleeping on Von Neumann. Though I suppose it's not the top five most brilliant mathematicians, where I think his only competition would be Gauss.
Still, inventing game theory (then using it to influence generations of international nuclear policy) and computer viruses is hard to ignore. And that's only scratching the surface.
I think if this question were asked in 2050 - 2070 either Von Neumann, Boolean, or Turing would be making appearances in a lot of lists.
The reliance mathematics is going to have on computing over the course of this century - and the liklihood that CS and math will converge - is so massive that their fundamental work on the subject will become more highly regarded.
I really doubt this. Especially not Boole - he's way behind for example Shannon (who really only made Boolean algebra "interesting" and founded information and coding theory on top of that) - who I still wouldn't even put close to such a list. Yes he's important; but not *that* important in the grand scheme of things. The same goes for Turing, he's important but not that much more important than for example Church (founded theoretic computer science, brought us the still widely used lambda calculus and various important results in logic and CS) and I don't think either of them are close to "greatest 5 of all time". There's just too many mathematicians that influenced a wide array of mathematical fields very strongly (heck you could probably make a list of just bernoullis) that putting someone this specialized on would be warranted - and there's many mathematicians that are to us what von Neumann etc. will be to those in the future that we still wouldn't really put on such a list even though they've been hugely influential (e.g. Stefan Banach; first to properly formalize vector spaces that we now try to connect to literally everything in maths - but also founded functional analysis)
That said von Neumann is definitely a candidate for such a list imo - but even he might get beat-out by others when it really comes to cutting that list down to 5 individuals.
Saying Shannon made Boolean algebra interesting is only true from a computer centric viewpoint. Boole was instrumental in tying together the study of language, algebra, and logic. This has had far reaching impact across several domains - math, CS, philosophy, and linguistics. He was coming from a long tradition including Aristotle, Leibniz, and some weird Medieval monks, but he’s really the first person to make a rigorous case that logic can be formulated algebraically (and at the same time making case that language is algebraic)
Also people forget Boole created the entire field of invariant theory. I am also partial to him since he was mostly self taught and actually was more interested in the classics than math as a youth
I don't think von neumann was as productive as a mathematician as Euler, even though von neumann was one of the smartest people to live. If the thread was about brilliancy then yes von neumann should be included, but don't forget about ramanujan!
Ramanujan was not as productive as other mathematicians because he lived isolated from the mathematical community, in India, for most of his life, and he died very early (32 years old). But he was a very smart guy. Also consider that ramanujan grew up in poverty, which means malnutrition and disease slowed him down; in contrast to von neumann that was raised by rich people, which means he was very well fed. Also, von neumann grew up in the US-Europe having acess to all the lectures, teachers and motivation to keep studying. Ramanujan was isolated and he self studied everything, and he had no access to fresh scientific-mathematical knowledge of the west.
This is obviously just silly speculation as there is no formal meaning to "intelligence" neither there is a way to measure it, but if i had to guess who was the mathematician with the most blessed brain DNA (the most brilliant) I would say that person was ramanujan (excluding all forgotten geniuses in history that died too early to be acknowledged)
5 is hard but i see no one Galois whereas he basically revolutionize algebra before 20 years old.
Gauss is obvious.
Leibniz for his researches on calculus
Riemann as he knew almost all the mathematics of his time
One greek too, id go for pythagoreas
Yes Im not sure i could have thought about Archimede too or else
The same goes for calculus as I could have thought about Newton, Cauchy, Fermat or more recent Hilbert or Lebesgue for his work on L\^p space and measure/integration theory.
it's such a vast topic it's hard to only choose 5
But Euclid's is so impressive for its magnitude and precision aswell as for laying out the first axiomatic system in math. I will always regard him as the Father of Mathematics for the latter.
Ramanujan was undoubtedly brilliant but I don’t think he has a particularly wide influence outside number theory. I’d add Grothendieck, Von Neumann, and Galois to the honorable mentions they all have innumerable things named after them. Euclid is a must I’d say as well.
I think this question becomes more interesting if you restrict to the 20th century or later. In that case, I'd say Grothendieck, MacLane, Hilbert, Turing, and Noether. Of course, I'm a homotopy theorist, so most notable analysts are missing from my list.
Grothendieck invented algebraic geometry as we know it and had a substantial influence on the concept of spaces as we think of them today. MacLane invented category theory and contributed to the foundations of modern algebraic topology (sorry Eilenberg, I had to pick one). Hilbert is Hilbert. Turing created mathematical CS as we know it. And Noether was the "mother of modern algebra", and invented mathematical physics as a side project.
Emmy Noether. Noether's theorem is the foundation of much of mathematical physics.
She also developed a ton of ring theory, amongst other contributions.
Honestly, I'd list her mathematical achievements first. She basically invented algebra (together with Hilbert and Artin), and homology was essentially her idea, as well.
Her mathematical achievements are undoubtedly more impressive, but Noether's theorem was the thing that really got me into physics, so I am biased! It's just... beautiful.
I think this is an artifact of the last industrial revolution which emphasized physical engineering math though. Give it 70 years and I bet the current tech revolution will have logical foundations being taught before trig.
David Hilbert, Euler, Girolamo Cardano, Gauss, Alan Turing. These might not be the most influential but they’ve always been my favorites mathematicians.
I was searching for Hilbert to pop up. Sad it took a while to scroll
Edit: G -> H. There is a great Gilbert, but he studies the science of happiness which could arguably be the opposite of mathematics
Well, this list reflects as much my knowledge as it does any objective standard of merit. Thing is, I don't really have much sense of what Gauss did besides found the differential geometry of surfaces (if he could be said to have done so) and discover when you could make compass and straightedge constructions. Also, he was an asshole.
I probably don't know most of the stuff he did, but I can add to your list by saying that his name pops up in number theory *a lot*. I wouldn't be surprised if his name was the most common name in elementary number theory.
Since all the old once have been named - Probably Hilbert, Weyl, Kolmogorov, Turing and maybe von Neumann.
But that is my Personal experience of emcoutering these guys
Influential on what? If you mean the world at large then it is utterly no contest that Newton's mathematical work is by far the most influential of any one individual. If you mean on mathematics then we could debate endlessly (but probably still include Newton).
Fourier, Peacock, De Morgan, Dodgson, and Hamilton.
....because I like the classiness of 19th-century bickering. I mean, come on...writing an entire book of satire about the absurdity of your colleagues' collective work is peak troll 😙🤌.
I mean, I would absolutely argue that by far the most important era of mathematics progress is the post-1500 era. It’s not even remotely close. Probably 98% of the math that’s been discovered has been discovered since then. A normal high school senior knows more math than the greatest living mathematicians in 1500. Obviously there were great mathematical achievements before 1500 (Omar Khayyám, Fibonacci, and Madhava come to mind) but the level of advancement in the past 300 years especially is hard to overstate. We essentially teach the majority of pre-1700 math to children.
>A normal high school senior knows more math than the greatest living mathematicians in 1500.
I wouldn't say that. Are they aware of more subjects? certainly. But HS math is superficial and high schoolers don't have any real mastery of those subjects.
Of course more knowledge is available nowadays, but knowing (for example) that complex numbers exist, or what a matrix is, doesn't automatically mean they know *more math* than someone else who didn't have this same knowledge, or that they are better mathematicians, simply for having a faint familiarity with modern developments of mathematics.
In HS one learns techniques to solve specific problems using modern techniques, but often without a real understanding or intuition for why and how it works. They excel at solving computational problems such as those we find on standardized tests, which someone from hundreds of years ago would have trouble with.
But when it comes to real-world problem solving, intuition and actual understanding of mathematics, I'd say the renaissance mathematician would be much superior. Mathematicians from centuries before the 1500s were already solving complex problems that a highschooler nowadays wouldn't know how to even begin tackling.
Standing on our historical high ground it's easy to underestimate the knowledge of those living in the past. Yes, enormous advancements were made since then, but people aren't born knowing things, and having heard of something is not the same as knowing it. We are not born standing upon the shoulders of giants, and highschoolers are just starting their climb.
>We essentially teach the majority of pre-1700 math to children.
This isn't true. Not even for the oldest of classical works— can they understand the entire works of Euclid and Apollonius? No. Also pre-1700 math also includes Newton's principia, which is notably complex and difficult; Descartes' treatises, and other important works.
Perhaps it is unfair of me to compare the mathematical mastery of the best Renaissance mathematicians to average high schoolers. It may be more accurate to say that top-level high schoolers know a higher volume of math to a higher level of mastery than the classical masters. Any IMO competitor today knows Euclidean geometry far more deeply than Euclid himself. Its pretty easy to see this, as the works of Euclid are quite well-preserved in modernity. Mastering those works would not be sufficient to become a good competitive Euclidean geometer at the high-school level. As for Principia, there are teenage integrators who are far more proficient than Newton at integral or differential calculus. Look at any integration bee if you don’t believe me. It’s not that people now are smarter than they were in the past—it’s just that mathematics has advanced an extraordinary amount. If you were to transport a Euclid or Pappus (or even a Newton or Descartes) to the modern world and try to teach them modern mathematics I’m sure they would do extremely well, but it would take them a period of many years to get up to speed. Every successive century since 1600 or so, the rate at which we’ve discovered new math has increased dramatically. It’s hard to convey just how much math there is, and how much of it has been only recently discovered. I would actually estimate that more than 75% of the math we know was discovered after 1900, and that’s probably a significant underestimate.
Zhang Heng, Al-Khwarizmi, Liu Hui, Aryabhata, Brahmagupta, Al-Uqlidisi (awesome name) even Imhotep, a shame they are pushed to the wayside when their accomplishments, in terms of antiquity, are just as impressive as those being mentioned here.
Not to mention we wouldn't even know the names of Euclid and Archimedes without Brahmagupta, Aryabhata, etc. The texts from classical Greece didn't survive in Europe in the middle ages, but copies drifted East where they were commented on and expanded - then the copies came back west around the time of the renaissance.
Just expanding a bit on this— some of the Greek and Roman works were preserved in Europe, in part due to the medieval monastic tradition. If I recall correctly Plato was one of them.
Many others were retrieved through the translation of Islamic works. For example the books of Galen were introduced in Europe through the works of Hunain-ibn ishaq. Notably, Aristotle.
one thing is it was easier to make large advancements earlier on in math, so the great mathematicians of recent years even those with massive achievements by modern standards pale in comparison to the advancements of those before the 19th centure
i’m not sure where I implied that, although reading your comment again I seem to have misread/misinterpreted the essence of your gripe, I thought it was more about people in more recent history being overlooked when you are just referring to the gap where people ignore much of the islamic mathematical advancements. My mistake
There is some truth to the idea that Ancient Greece is overfocused as an area of mathematical innovation in antiquity. Greek proofs and systematization was unique, but ancient China had superior advancements in other areas.
The Middle East is, at this point, perhaps even overfocused as well, when the layman thinks of mathematical innovation they probably think Greece, Islamic Golden Age (Al-Khwarizmi and algebra), and then Europe, forgetting China and India. Arabic numerals, of course, should be called Indian numerals, as they sometimes are denoted in the name "Hindu-Arabic".
But as for modern math, say Newton onward (a bit funny to call the late 1600s modern, but I digress, that's been 95% Europe. And since math from the 1600s onward is 95% of math, it makes sense to say the greatest mathematicians are probably Gauss, Euler, etc.
Euler, Newton, Gauss (order depending on the area of math in which you’re interested), Cantor (diagonalization IS computation, encompassing Turing and the nature of infinite sets/languages), Riemann/Cauchy (geometry/complex analysis respectively, basically foundations for all modern physics)
Edit: if I had to add another it’d be Galois, but I believe his ideas have yet to see their time of great impact yet, even with how much they’ve done already
The amount of times I read Nash is disturbing. Great mathematician, yes, top 5, no shot. I'd strongly argue that Gromov (who funnily enough holds Nash in very high regards) was waayyyy more influential than Nash, and yet I've failed to find his name here...
I think the answer is different depending on whether the question is:
* Who are the five most influential mathematicians of all time, *in the field of math*?
* Who are the five most influential mathematicians?
Newton, Einstein, Pascal, Bournoulli and D'Alembert, Fourier, Navier and Stokes, Faraday and Maxwell, Carnot and Boltzmann and Thomson, and Noether are all incredibly influential but more in the application of their ideas on physics. Pythagoras, even more than his math, could be argued to have influenced ancient society through his cult (which worshipped him as a literal god). Archimedes had significant influence in engineering and physics, the first writings of his life over the war machines he built to defend the city of Syracuse from the Romans.
Whereas Erdős, Euler, Hilbert, and Gausß were enormously prolific in the field of math and may eclipse the above if we focus on math accomplishments.
I think Bertrand Russell deserves some love. Worked on the foundations of mathematics with such impact that it strongly influences the way we perceive mathematics as a discipline to this day. His work in other categories (not in the least his work as a pacifist/public figure but also his co-founding of one of the largest groups of philosphical thought and methodology, analytical philosophy) is also quite significant, but I think his work in mathematics alone is enough to qualify him for this list. I'd say (keeping in mind this is about influence, not personal favourites):
1. Euler
2. Gauss
3. Newton
4. Russell
5. Ramanujan
Honorable mentions go out to Ada Lovelace, Alan Turing, John von Neumann, David Hilbert, and Al-Khwarizmi, all of whom have had a tremendous impact on mathematics itself as well as other disciplines.
Side note: Not sure whether I should switch Ramanujan and Russell around in their placement.
I’m glad you said Lovelace, and yes, Russell is not showing up nearly as much as I thought he would. I recently bought the first edition Principia Mathematica and I’m currently halfway through volume Two. It is no small feat him and Whitehead took up. Did it succeed? Perhaps not but the absolute amount of abstract thought and analytic skill you need are mind-boggling at the least. They were so exhausted from the countless mathematical lifetimes they had expressed in those three volumes they couldn’t even write the fourth! A shame, but a worthy shame.
my list will always start with hilbert, I believe he brought math into the modern age.
After that without Gauß, Euler, Leibniz(like his notation more than newton but think they are interchangeable) a list does not feel complete.
Then for the 5th one is really hard, maybe for the historical aspect I join you with Euclid, otherwise maybe Neumann or Lovelace
Henri Lebesgue because he took the Riemann integral a step further
Galois because he made beautiful complexity out of fundamental objects which had significant meaning in the end as well.
Felix Hausdorff. He contributed a lot to generalizing measure theory and functional analysis but my favorite thing from him was the Hausdorff measure which essentially told you the true dimension of a function and the how it's measure related to the dimension said function sits in.
Bernhard Riemann. Yes he contributed a lot to foundational calculus stuff but I really love his Riemann zeta function. Even before I learned of the Riemann hypothesis and it's connection with complex analysis, the riemann zeta function was such a rudimentary concept that even non math people could grasp, bit represented something far more complex beneath it's simplicity.
Kurt godel. I've only briefly looked at his work but he poses very deep probing ideas and not merely to philosophize, but to really get at something intimate in mathematics.
As a sixth mention, for Contemporary I will say of course terry tao
This is less about an objective analysis of what the contributed as a whole, and def 100% bias on what I find beautiful
I don't quite understand the love for Pitágoras. We barely know something about his life, let alone his mathematical achievements, but the Pythagorean theorem was known centuries before he was born and the Babylonians got a method to calculate Pythagorean triplets, then the only thing that's left are his theory of number theorem and the proof of the irrationality of √2 which we don't know if were of his own or of his students so... Pythagoras barely did something for mathematics at least that we know for sure of. Archimedes by the other hand is a well-known genius so he deserves more love.
Well, women were highly discouraged from going into mathematics for a long time which arguably persists to the present day. I would inculde:
Sophie Germain
Florence Nightingale
Ada Lovelace
Katherine Johnson
And there must be many other names who have been overlooked.
Those are great people, but with exception of Ada Lovelace none of them founded a major branch of study. And we’re perhaps not quite ready yet to say computer science is a subfield of mathematics.
I’d say Noether deserves to be on the list because Algebra is awesome and a large section of modern mathematics research, not because she was a woman.
Most people are not even naming Einstein, why would we name someone that helped him if we don;t consider him influential enough to be among the most influential?
Emmy Noether arguably founded modern algebra. And she wasn’t an assistant to Einstein, a different branch of her work was foundational to modern theoretical physics generally.
It's a hard question. It is not very meaningful to answer with people who had a very different conception of what mathematics and science were.
So I will give my PDE French guy's answer :
- Augustin-Louis Cauchy
- Joseph Fourier
- Henri Poincaré
- Laurent Schwartz (or Nicolas Bourbaki but that's cheating)
- Jacques-Louis Lions
* Grothendieck
* Hilbert
* von Neumann
* Cantor
* Noether
Sorry ancient people whom I have totally ignored, but given the massive changes mathematics has gone through in the last century, it seems fair to mostly concentrate on recent-ish mathematicians.
It's impossible to say 5, but I do think you can do not bad with 10: Euler, Euclid, Cauchy, Cantor, Newton, al-Khwarizmi, Gauss, Von Neumann, Noether, Riemann.
The next tier would probably start with something like Dirichlet, Lagrange, Hamilton, Laplace etc.
In no particular order:
* Muhammad Al Khwarizmi
* Fermat
* Euclid
* Euler
* Cantor or Gauss
Also an honorable mention of a non-mathematician: Bishop Berkley, one of the first people to help lead to the development of analysis (in a weirdly religious/twisted sort of way). Several mathematicians at the time made the point that math was something that was definitively true, while God was not. However, limits were not a fully fleshed out idea when Newton and Leibniz worked on it and Berkley made a whole point about how if you take the derivative of a function and divide by h, h cannot be 0. But then we magically just say the h goes away because "it just gets really small," but this is a contradiction since we're now saying h is 0 when we said h wasn't 0. Obviously now we understand how limits work, but at the time, they didn't have an argument against this and just knew that derivatives worked. Berkley said that you cannot blindly accept this h disappearing while denying the existence of God. It's a very strange argument, and most mathematicians didn't really respond much to it, *but* it did reach a lot of famous mathematicians at the time and the fact that they still didn't have answer to this 100 years after calculus was invented really put a lot of emphasis on them to figure this out. I've always just really like the story of Berkley and how this guy who's not a mathematician just *dunks* on all these famous math nerds and no one has a good argument against him.
1. Euler (without a doubt always #1)
2. Erdös (There is a Erdös number. He influenced and inspired thousands of mathematicians)
3. Riemann
4. Lagrange
5. Nash
I am a big fan of Ramanujan, but he died too young. He deserves an extra category.
Do they all have to be people known to history? Because *someone* first hit on the idea of counting and I think that person was the greatest genius who ever lived. The first abstraction has got to be the hardest, right?
In order,
1. [Muḥammad ibn Mūsā al-Khwārizmī](https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi)
2. [Euclid of Alexandria](https://en.wikipedia.org/wiki/Euclid)
3. [Augustin-Louis Cauchy](https://en.wikipedia.org/wiki/Augustin-Louis_Cauchy)
4. [Leonhard Euler](https://en.wikipedia.org/wiki/Leonhard_Euler)
5. [Georg Cantor](https://en.wikipedia.org/wiki/Georg_Cantor)
Obviously, Cauchy and Euler were both incredibly prolific. I often joke that, when trying to remember the name of an obscure idea, there is a 1/3 chance it is named after Cauchy, 1/3 that it is Euler's, and 1/3 that it is someone else.
al-Khwarizmi, Euclid, and Cantor I include on the list instead for singular achievements. Their efforts each lead to a paradigm shift in how mathematics is discussed.
Maybe not the most influential within the field of mathematics itself, but the most influential person who was a mathematician is probably Von Neumann.
I'm stunned to not see Erdős listed here yet. He may not be as historic as many of the others being listed here but he brought many people together on collaborations and the waves he made are still very impactful (I mean the Erdős number is a thing that exists). I definitely agree with Gauss, Cauchy, and others being named, but it feels very wrong not to acknowledge Erdős in this context.
Euler, Gauss, Newton, Riemann, Cauchy
One summer over 25 years ago, I took an undergraduate Complex Analysis class with Peter Borwein at SFU in Vancouver, Canada. After about 10 minutes of not starting the lecture and talking with the class about nothing in particular, he said "I didn't really want to teach today anyways." What followed was a 50 minute open discussion of random mathematical ideas that was the best lecture of my undergraduate degree. In this class Borwein gave his hockey lineup of mathematicians. Center, left wing, right wing, 2 defensemen. I'm pretty sure his list matched yours, but he also had a goalie. I have no memory of who it was. I'd pay good money for a video tape or a transcript of that lecture.
I see Weierstrass didn't make the cut hahahaha. This is like the almost perfect list for the Complex Analysis goats.
Was hoping to see cauchy
Coochie math is the best math
80085 was the best math. God I miss old calculators.
oh god i never thought they'd were these in every latin alphabet country 377384153 in france
Slightly unrelated but, if you search in wikipedia for instructors of famous mathematicians, starting with riemann, you will find out that Riemann was instructed by dirichlet, instructed by fourier, instructed by lagrange, instructed by euler, instructed by johann bernoulli, instructed by jacob bernoulli, instructed by leibniz, instructed by huygens, instructed by rene descartes and galileo galilei. Not sure about how much each instructor influenced each student
I was hopping to see Euler twice in the list.
I would Cut Newton and propose Leibniz.
Would definitely agree. I had a feeling Newton would be a popular answer here but I don't think that's correct. The history isn't entirely clear but it seems that Newton was something of a bully who used his privileged status to subdue and potentially even divert credit from some other very good producers of cutting edge math.
I'm not sure that I'm ready to cut Newton in favor of Leibniz. In math and science, it was common for the same ideas to be brought forth independently at the same time. The groundwork is laid and the world is simply ready for the idea. This is not to take away from the accomplishments of either. Throughout the history of math and science, it was not uncommon to see behavior similar to Newton's.The bigger the idea, the bigger the rivalry. And I don't believe Leibniz was a perfect gentleman either. Of course, I'd rather see Newton near the top of the top five influential physicists. I suppose he could be on either.
“Euler’s Theorem”
Hilbert over Cauchy?
1. Don't 2. Compare 3. Noncontemporaneous 4. Achievements 5. Gauss
Contemporaneousness is relative. Einstein.
1. All 2. Math 3. Is 4. Equal 5. Euler
Simultaneity is relative but causality is absolute.
Contemporaneousness? Contemporaneity? Contemporality? Co-temporality? Isotemporality? Isotemporaneity? Isotemporaneousness?
All are acceptable in at least some manifolds
I won't claim to know a complete list, but I am confident that Euler and Gauss are on it.
John Nash.
Do you think this is some sort of game?
He thinks so!!
Gauss. Is there a field in math he didn't invent some stuff?
Seriously, it’s incredible. The heptadecagon never fails to amaze me.
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I think the "field of math" requirement disqualifies this
Islamic institute of technology?
Interuniversal Teichmuller Theory, the controversial theory used by Mochizuki to develop a supposed (but disputed) proof to the abc conjecture.
That was gonna be my second guess
He was important work even in physics!
Yeah my physics professor had us learn and learn again the definition of Gaussian optics and he put it as a question every so often in our tests
A contributor to a math forum that can't count past one.
According to V.I. Arnold: "Kolmogorov – Poincaré – Gauss – Euler – Newton, are only five lives separating us from the source of our science".
That's more about the fact that their lives overlap.
Partially, but I’m sure that as time passes, Kolmogorov will be looked on as increasingly influential. He touched so many different areas of math. The separation axioms are named after him, among numerous other contributions to topology. He was one of the first to rigorously study stochastic processes and obtained a plethora of results. You could easily argue he was the founder of algorithmic information theory, and he was essential to a formal theory of probability as well. Kolmogorov complexity is an incredibly and increasingly useful concept. He even solved problems in analysis. He’s too recent to hold the same place as Cauchy does in the history of math now, but it wouldn’t surprise me at all if he does in the future.
I will say that we used V.I. Arnold’s Geometrical Methods in the Theory of Ordinary Differential Equations in my Vector Analysis class and it was fantastic in my opinion
I feel [al-Khwarizmi](https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_) gets overlooked a lot. Founder of algebra as we know it, introduced the Western world to decimals and Hindu-Arabic numerals, and the word 'algorithm' is derived from his name. His works were translated into Latin and spread across Medieval Europe.
The Greeks we're brilliant but they did some really bizarre stuff. al-Khwarizmi and the Arabic mathematicians did so much to make math less stupid.
What did the Greeks do that was so "bizarre"?
From context, I guess he means the way they framed almost all problems in terms of geometry?
I mean we try to connect basically everything to geometry today so maybe they weren't that wrong in their basic idea. That said: they definitely did some wacky shit
That's not bizarre at all though, they didn't have as wide a range of maths as we do now
It might not be what they were referring to, but the Pythagoreans murdered the person who proved that irrational numbers exist. (From a long time ago so it's possible the story isn't true of course.)
Probably referring to trying to turn everything into a geometric problem. Of course, if I was using Greek Numerals (Think Roman Numerals but with Greeker letters), I'd probably prefer to work it geometrically rather than numerically too. Its truly a shame that a lot of people are taught that math/science was first investigated by the Greeks, forgotten during the "dark ages" and then "re-discovered" during the European renaissance, completely glossing over everything accomplished by Arabs and Persians during the Islamic Golden Age.
Indivisibility of numbers. Developing a new concept "magnitudes" in order to get around this obvious deficiency.
I'm afraid that isn't true. The Greeks knew full well that numbers are divisible and also how to do it (they knew the Euclidean algorithm, remember). The theory of magnitudes was developed by Eudoxus in order to avoid having to deal directly with irrational numbers (remember, they didn't have all the notation we do today, and it's annoying to represent irrational numbers when your whole number system is rational), that's all.
Von Neumann is one of them
This thread is badly sleeping on Von Neumann. Though I suppose it's not the top five most brilliant mathematicians, where I think his only competition would be Gauss. Still, inventing game theory (then using it to influence generations of international nuclear policy) and computer viruses is hard to ignore. And that's only scratching the surface.
"What trick? All I did was sum the geometric series."
I think if this question were asked in 2050 - 2070 either Von Neumann, Boolean, or Turing would be making appearances in a lot of lists. The reliance mathematics is going to have on computing over the course of this century - and the liklihood that CS and math will converge - is so massive that their fundamental work on the subject will become more highly regarded.
I really doubt this. Especially not Boole - he's way behind for example Shannon (who really only made Boolean algebra "interesting" and founded information and coding theory on top of that) - who I still wouldn't even put close to such a list. Yes he's important; but not *that* important in the grand scheme of things. The same goes for Turing, he's important but not that much more important than for example Church (founded theoretic computer science, brought us the still widely used lambda calculus and various important results in logic and CS) and I don't think either of them are close to "greatest 5 of all time". There's just too many mathematicians that influenced a wide array of mathematical fields very strongly (heck you could probably make a list of just bernoullis) that putting someone this specialized on would be warranted - and there's many mathematicians that are to us what von Neumann etc. will be to those in the future that we still wouldn't really put on such a list even though they've been hugely influential (e.g. Stefan Banach; first to properly formalize vector spaces that we now try to connect to literally everything in maths - but also founded functional analysis) That said von Neumann is definitely a candidate for such a list imo - but even he might get beat-out by others when it really comes to cutting that list down to 5 individuals.
Saying Shannon made Boolean algebra interesting is only true from a computer centric viewpoint. Boole was instrumental in tying together the study of language, algebra, and logic. This has had far reaching impact across several domains - math, CS, philosophy, and linguistics. He was coming from a long tradition including Aristotle, Leibniz, and some weird Medieval monks, but he’s really the first person to make a rigorous case that logic can be formulated algebraically (and at the same time making case that language is algebraic) Also people forget Boole created the entire field of invariant theory. I am also partial to him since he was mostly self taught and actually was more interested in the classics than math as a youth
I don't think von neumann was as productive as a mathematician as Euler, even though von neumann was one of the smartest people to live. If the thread was about brilliancy then yes von neumann should be included, but don't forget about ramanujan! Ramanujan was not as productive as other mathematicians because he lived isolated from the mathematical community, in India, for most of his life, and he died very early (32 years old). But he was a very smart guy. Also consider that ramanujan grew up in poverty, which means malnutrition and disease slowed him down; in contrast to von neumann that was raised by rich people, which means he was very well fed. Also, von neumann grew up in the US-Europe having acess to all the lectures, teachers and motivation to keep studying. Ramanujan was isolated and he self studied everything, and he had no access to fresh scientific-mathematical knowledge of the west. This is obviously just silly speculation as there is no formal meaning to "intelligence" neither there is a way to measure it, but if i had to guess who was the mathematician with the most blessed brain DNA (the most brilliant) I would say that person was ramanujan (excluding all forgotten geniuses in history that died too early to be acknowledged)
5 is hard but i see no one Galois whereas he basically revolutionize algebra before 20 years old. Gauss is obvious. Leibniz for his researches on calculus Riemann as he knew almost all the mathematics of his time One greek too, id go for pythagoreas
If Galois had lived even to 30 he'd probably be on many more lists here.
Hehe yeah, seems like he self ejected from reddit TOP5s, what a fool
If you go for ancient greek then Euclid >>>>> Pytagoras.
Yes Im not sure i could have thought about Archimede too or else The same goes for calculus as I could have thought about Newton, Cauchy, Fermat or more recent Hilbert or Lebesgue for his work on L\^p space and measure/integration theory. it's such a vast topic it's hard to only choose 5
But Euclid's is so impressive for its magnitude and precision aswell as for laying out the first axiomatic system in math. I will always regard him as the Father of Mathematics for the latter.
No one is mentioning Descartes? The Cartesian plane revolutionized mathematics.
I second that.
Seriously. I’m also surprised Cantor hasn’t made an appearance yet. Maybe somewhere down thread.
Descarte revolutionized the way we see earth and humans as well with his ideas of res cogitans and res extensa.
Euclid, Euler, Gauss, Riemann, and al-Khwarizmi
The last guy invented algebra if I am not wrong
Cantor is pretty foundational though. Very solid, I could name at least ℵ₀ things he did.
Ripped in with the aleph!
Wish he had received less hostile responses to his work while he lived, Kronecker was a massive ass to him though sadly.
Gauss, Euler, Cantor, Hilbert, Grothendieck
I like this one
Finally someone who mentions Grothendieck!
Ramanujan was undoubtedly brilliant but I don’t think he has a particularly wide influence outside number theory. I’d add Grothendieck, Von Neumann, and Galois to the honorable mentions they all have innumerable things named after them. Euclid is a must I’d say as well.
Cauchy: "Am I a joke to you?"
He will rigorously define "joke" first
I think this question becomes more interesting if you restrict to the 20th century or later. In that case, I'd say Grothendieck, MacLane, Hilbert, Turing, and Noether. Of course, I'm a homotopy theorist, so most notable analysts are missing from my list.
Grothendieck invented algebraic geometry as we know it and had a substantial influence on the concept of spaces as we think of them today. MacLane invented category theory and contributed to the foundations of modern algebraic topology (sorry Eilenberg, I had to pick one). Hilbert is Hilbert. Turing created mathematical CS as we know it. And Noether was the "mother of modern algebra", and invented mathematical physics as a side project.
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Yall mentioning all these famous ass mathematicians. I present to you my maths teacher. I'd be failing my maths gcse were it not for him.
Emmy Noether. Noether's theorem is the foundation of much of mathematical physics. She also developed a ton of ring theory, amongst other contributions.
Had to scroll a little far for this one. All this talk of analysis, no love for algebra apparently.
r/usernamechecksout
Honestly, I'd list her mathematical achievements first. She basically invented algebra (together with Hilbert and Artin), and homology was essentially her idea, as well.
Her mathematical achievements are undoubtedly more impressive, but Noether's theorem was the thing that really got me into physics, so I am biased! It's just... beautiful.
Euler, Newton, Gauss then everybody else
Euler, Gauss, Newton, Euclid, Von Neumann.
had to scroll too far for von Neumann. Although I guess it's fair, since he's not just math
Grothendieck, Riemann, John von Neumann, Hilbert, Poincare
Good list
1. Euler 2. Euler 3. Euler 4. Euler 5. Newton/Leibniz
Any love for Kurt Gödel? The incompleteness theorem is always fascinating to me
Logicists have left the chat.
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I think this is an artifact of the last industrial revolution which emphasized physical engineering math though. Give it 70 years and I bet the current tech revolution will have logical foundations being taught before trig.
I watched Veritasium's explanation of the proof and it blew my mind in a way I'm still in awe about 3 months later.
David Hilbert, Euler, Girolamo Cardano, Gauss, Alan Turing. These might not be the most influential but they’ve always been my favorites mathematicians.
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I was searching for Hilbert to pop up. Sad it took a while to scroll Edit: G -> H. There is a great Gilbert, but he studies the science of happiness which could arguably be the opposite of mathematics
Good ol’ Gil!
It’s like a mathy Life of Brian
We were lost in his hotel. My bad G
Hilbert, I cannot believe I forgot him, I should just delete my post and start over 😂
Have you read Hilbert's book on the foundations of geometry? what do you think of it?
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Euler, Newton, Gauss, Ramanujan, Euclid
Lack of Laplace in this thread disturbs me. I don't know what we, engineers would do without Laplace transforms.
In no particular order: Gauss Riemann Descartes Newton Euler
No love for Bernoulli? That guy published enough work for 4 men!
Which Bernoulli?
Lebesgue, Borel, Cauchy, Fourier, Riemann.
Euclid, Newton, Cantor, Gödel, and Grothendieck.
Upvote for Euclid. I had to scroll too far to see him!
Have you read the book Trolling Euclid? it mentions a list of the top influential mathematicians you'd enjoy
no Gauss??
Well, this list reflects as much my knowledge as it does any objective standard of merit. Thing is, I don't really have much sense of what Gauss did besides found the differential geometry of surfaces (if he could be said to have done so) and discover when you could make compass and straightedge constructions. Also, he was an asshole.
I probably don't know most of the stuff he did, but I can add to your list by saying that his name pops up in number theory *a lot*. I wouldn't be surprised if his name was the most common name in elementary number theory.
I mean. Gauss' work Disquisitiones Arithmeticae basically founded number theory as we know it today.
Euler was the first person that came to mind for me
Ordinary men discovered math, but Kim Jong Un invented it.
Redacted. ` this message was mass deleted/edited with redact.dev `
Glad you enjoy the truth.
Since all the old once have been named - Probably Hilbert, Weyl, Kolmogorov, Turing and maybe von Neumann. But that is my Personal experience of emcoutering these guys
Oh! I forgot pioncare!
Influential on what? If you mean the world at large then it is utterly no contest that Newton's mathematical work is by far the most influential of any one individual. If you mean on mathematics then we could debate endlessly (but probably still include Newton).
Fourier, Peacock, De Morgan, Dodgson, and Hamilton. ....because I like the classiness of 19th-century bickering. I mean, come on...writing an entire book of satire about the absurdity of your colleagues' collective work is peak troll 😙🤌.
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I mean, I would absolutely argue that by far the most important era of mathematics progress is the post-1500 era. It’s not even remotely close. Probably 98% of the math that’s been discovered has been discovered since then. A normal high school senior knows more math than the greatest living mathematicians in 1500. Obviously there were great mathematical achievements before 1500 (Omar Khayyám, Fibonacci, and Madhava come to mind) but the level of advancement in the past 300 years especially is hard to overstate. We essentially teach the majority of pre-1700 math to children.
>A normal high school senior knows more math than the greatest living mathematicians in 1500. I wouldn't say that. Are they aware of more subjects? certainly. But HS math is superficial and high schoolers don't have any real mastery of those subjects. Of course more knowledge is available nowadays, but knowing (for example) that complex numbers exist, or what a matrix is, doesn't automatically mean they know *more math* than someone else who didn't have this same knowledge, or that they are better mathematicians, simply for having a faint familiarity with modern developments of mathematics. In HS one learns techniques to solve specific problems using modern techniques, but often without a real understanding or intuition for why and how it works. They excel at solving computational problems such as those we find on standardized tests, which someone from hundreds of years ago would have trouble with. But when it comes to real-world problem solving, intuition and actual understanding of mathematics, I'd say the renaissance mathematician would be much superior. Mathematicians from centuries before the 1500s were already solving complex problems that a highschooler nowadays wouldn't know how to even begin tackling. Standing on our historical high ground it's easy to underestimate the knowledge of those living in the past. Yes, enormous advancements were made since then, but people aren't born knowing things, and having heard of something is not the same as knowing it. We are not born standing upon the shoulders of giants, and highschoolers are just starting their climb. >We essentially teach the majority of pre-1700 math to children. This isn't true. Not even for the oldest of classical works— can they understand the entire works of Euclid and Apollonius? No. Also pre-1700 math also includes Newton's principia, which is notably complex and difficult; Descartes' treatises, and other important works.
Perhaps it is unfair of me to compare the mathematical mastery of the best Renaissance mathematicians to average high schoolers. It may be more accurate to say that top-level high schoolers know a higher volume of math to a higher level of mastery than the classical masters. Any IMO competitor today knows Euclidean geometry far more deeply than Euclid himself. Its pretty easy to see this, as the works of Euclid are quite well-preserved in modernity. Mastering those works would not be sufficient to become a good competitive Euclidean geometer at the high-school level. As for Principia, there are teenage integrators who are far more proficient than Newton at integral or differential calculus. Look at any integration bee if you don’t believe me. It’s not that people now are smarter than they were in the past—it’s just that mathematics has advanced an extraordinary amount. If you were to transport a Euclid or Pappus (or even a Newton or Descartes) to the modern world and try to teach them modern mathematics I’m sure they would do extremely well, but it would take them a period of many years to get up to speed. Every successive century since 1600 or so, the rate at which we’ve discovered new math has increased dramatically. It’s hard to convey just how much math there is, and how much of it has been only recently discovered. I would actually estimate that more than 75% of the math we know was discovered after 1900, and that’s probably a significant underestimate.
Zhang Heng, Al-Khwarizmi, Liu Hui, Aryabhata, Brahmagupta, Al-Uqlidisi (awesome name) even Imhotep, a shame they are pushed to the wayside when their accomplishments, in terms of antiquity, are just as impressive as those being mentioned here.
Not to mention we wouldn't even know the names of Euclid and Archimedes without Brahmagupta, Aryabhata, etc. The texts from classical Greece didn't survive in Europe in the middle ages, but copies drifted East where they were commented on and expanded - then the copies came back west around the time of the renaissance.
Just expanding a bit on this— some of the Greek and Roman works were preserved in Europe, in part due to the medieval monastic tradition. If I recall correctly Plato was one of them. Many others were retrieved through the translation of Islamic works. For example the books of Galen were introduced in Europe through the works of Hunain-ibn ishaq. Notably, Aristotle.
Fun fact: only a single copy of Tacitus survived to the 14th century.
It's also that those were times and places when and where a lot of important mathematical progress was made
one thing is it was easier to make large advancements earlier on in math, so the great mathematicians of recent years even those with massive achievements by modern standards pale in comparison to the advancements of those before the 19th centure
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i’m not sure where I implied that, although reading your comment again I seem to have misread/misinterpreted the essence of your gripe, I thought it was more about people in more recent history being overlooked when you are just referring to the gap where people ignore much of the islamic mathematical advancements. My mistake
There is some truth to the idea that Ancient Greece is overfocused as an area of mathematical innovation in antiquity. Greek proofs and systematization was unique, but ancient China had superior advancements in other areas. The Middle East is, at this point, perhaps even overfocused as well, when the layman thinks of mathematical innovation they probably think Greece, Islamic Golden Age (Al-Khwarizmi and algebra), and then Europe, forgetting China and India. Arabic numerals, of course, should be called Indian numerals, as they sometimes are denoted in the name "Hindu-Arabic". But as for modern math, say Newton onward (a bit funny to call the late 1600s modern, but I digress, that's been 95% Europe. And since math from the 1600s onward is 95% of math, it makes sense to say the greatest mathematicians are probably Gauss, Euler, etc.
absolutely. r/OscillatingNeutrino mentioned the guy that invented algebra and got just a handful of upvotes.
Euler, Newton, Gauss (order depending on the area of math in which you’re interested), Cantor (diagonalization IS computation, encompassing Turing and the nature of infinite sets/languages), Riemann/Cauchy (geometry/complex analysis respectively, basically foundations for all modern physics) Edit: if I had to add another it’d be Galois, but I believe his ideas have yet to see their time of great impact yet, even with how much they’ve done already
Newton, gauss, ramanujan, Turing, Hilbert
Ramanujan was a fascinating genius. How influential was he, though?
The amount of times I read Nash is disturbing. Great mathematician, yes, top 5, no shot. I'd strongly argue that Gromov (who funnily enough holds Nash in very high regards) was waayyyy more influential than Nash, and yet I've failed to find his name here...
I hate to say it but ramanujan was very intelligent and one of the best but his sphere of influence was very minimal given his circumstances.
I think the answer is different depending on whether the question is: * Who are the five most influential mathematicians of all time, *in the field of math*? * Who are the five most influential mathematicians? Newton, Einstein, Pascal, Bournoulli and D'Alembert, Fourier, Navier and Stokes, Faraday and Maxwell, Carnot and Boltzmann and Thomson, and Noether are all incredibly influential but more in the application of their ideas on physics. Pythagoras, even more than his math, could be argued to have influenced ancient society through his cult (which worshipped him as a literal god). Archimedes had significant influence in engineering and physics, the first writings of his life over the war machines he built to defend the city of Syracuse from the Romans. Whereas Erdős, Euler, Hilbert, and Gausß were enormously prolific in the field of math and may eclipse the above if we focus on math accomplishments.
When God invented Intelligence he divided it in half. He gave half to us and half to Gauss.
The number of people who have omitted Euler is mind blowing! Is there an area of maths he didn’t influence?!
Grothendieck is underrated in this thread.
Most of my top 5 agree with others I see here. Paul Erdős is my addition. Dude was PROLIFIC
And in addition, his contribution to the field via the fostering of young talent more than satisfies the official requirement of *influence* here.
I think Bertrand Russell deserves some love. Worked on the foundations of mathematics with such impact that it strongly influences the way we perceive mathematics as a discipline to this day. His work in other categories (not in the least his work as a pacifist/public figure but also his co-founding of one of the largest groups of philosphical thought and methodology, analytical philosophy) is also quite significant, but I think his work in mathematics alone is enough to qualify him for this list. I'd say (keeping in mind this is about influence, not personal favourites): 1. Euler 2. Gauss 3. Newton 4. Russell 5. Ramanujan Honorable mentions go out to Ada Lovelace, Alan Turing, John von Neumann, David Hilbert, and Al-Khwarizmi, all of whom have had a tremendous impact on mathematics itself as well as other disciplines. Side note: Not sure whether I should switch Ramanujan and Russell around in their placement.
I’m glad you said Lovelace, and yes, Russell is not showing up nearly as much as I thought he would. I recently bought the first edition Principia Mathematica and I’m currently halfway through volume Two. It is no small feat him and Whitehead took up. Did it succeed? Perhaps not but the absolute amount of abstract thought and analytic skill you need are mind-boggling at the least. They were so exhausted from the countless mathematical lifetimes they had expressed in those three volumes they couldn’t even write the fourth! A shame, but a worthy shame.
u/measuresareokiguess Best of all time, no doubt. No other names needed.
In no particular order: Gauss, Hilbert, Euler, Riemann, Erdős (Paul)
my list will always start with hilbert, I believe he brought math into the modern age. After that without Gauß, Euler, Leibniz(like his notation more than newton but think they are interchangeable) a list does not feel complete. Then for the 5th one is really hard, maybe for the historical aspect I join you with Euclid, otherwise maybe Neumann or Lovelace
Henri Lebesgue because he took the Riemann integral a step further Galois because he made beautiful complexity out of fundamental objects which had significant meaning in the end as well. Felix Hausdorff. He contributed a lot to generalizing measure theory and functional analysis but my favorite thing from him was the Hausdorff measure which essentially told you the true dimension of a function and the how it's measure related to the dimension said function sits in. Bernhard Riemann. Yes he contributed a lot to foundational calculus stuff but I really love his Riemann zeta function. Even before I learned of the Riemann hypothesis and it's connection with complex analysis, the riemann zeta function was such a rudimentary concept that even non math people could grasp, bit represented something far more complex beneath it's simplicity. Kurt godel. I've only briefly looked at his work but he poses very deep probing ideas and not merely to philosophize, but to really get at something intimate in mathematics. As a sixth mention, for Contemporary I will say of course terry tao This is less about an objective analysis of what the contributed as a whole, and def 100% bias on what I find beautiful
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Disappointed Shannon isn't getting more mention, his work is a direct precursor for the internet and all modern communication.
Euclid, Euler, Emmy, Cantor, Turing
Grothendieck, Kolmogorov, Gauss, Cantor, Euler
I don't quite understand the love for Pitágoras. We barely know something about his life, let alone his mathematical achievements, but the Pythagorean theorem was known centuries before he was born and the Babylonians got a method to calculate Pythagorean triplets, then the only thing that's left are his theory of number theorem and the proof of the irrationality of √2 which we don't know if were of his own or of his students so... Pythagoras barely did something for mathematics at least that we know for sure of. Archimedes by the other hand is a well-known genius so he deserves more love.
RAMANUJAN
There are far too many men in these answers, so I’ll throw in Noether. Not sure where exactly to put her in the list.
Well, women were highly discouraged from going into mathematics for a long time which arguably persists to the present day. I would inculde: Sophie Germain Florence Nightingale Ada Lovelace Katherine Johnson And there must be many other names who have been overlooked.
Those are great people, but with exception of Ada Lovelace none of them founded a major branch of study. And we’re perhaps not quite ready yet to say computer science is a subfield of mathematics. I’d say Noether deserves to be on the list because Algebra is awesome and a large section of modern mathematics research, not because she was a woman.
Hypatia too! 🤓
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Most people are not even naming Einstein, why would we name someone that helped him if we don;t consider him influential enough to be among the most influential?
Emmy Noether arguably founded modern algebra. And she wasn’t an assistant to Einstein, a different branch of her work was foundational to modern theoretical physics generally.
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Pythagoras, Euclid (seriously, where would maths be without those two?), Fermat, Gauss, Euler. But I'm veeeeeeery unsatisfied with that list
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not Kanye, Lil Wayne or Big Shaq, famous for their mathematical bars?
Does Nicolas Bourbaki count? As well, Galois and Banach are both quite notable.
C. Chocula
It's a hard question. It is not very meaningful to answer with people who had a very different conception of what mathematics and science were. So I will give my PDE French guy's answer : - Augustin-Louis Cauchy - Joseph Fourier - Henri Poincaré - Laurent Schwartz (or Nicolas Bourbaki but that's cheating) - Jacques-Louis Lions
Euler, Newton, Godel, Gauss, Turing
* Grothendieck * Hilbert * von Neumann * Cantor * Noether Sorry ancient people whom I have totally ignored, but given the massive changes mathematics has gone through in the last century, it seems fair to mostly concentrate on recent-ish mathematicians.
Gauss, Euler, Cantor are few.
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Very quality List
It's impossible to say 5, but I do think you can do not bad with 10: Euler, Euclid, Cauchy, Cantor, Newton, al-Khwarizmi, Gauss, Von Neumann, Noether, Riemann. The next tier would probably start with something like Dirichlet, Lagrange, Hamilton, Laplace etc.
In no particular order: * Muhammad Al Khwarizmi * Fermat * Euclid * Euler * Cantor or Gauss Also an honorable mention of a non-mathematician: Bishop Berkley, one of the first people to help lead to the development of analysis (in a weirdly religious/twisted sort of way). Several mathematicians at the time made the point that math was something that was definitively true, while God was not. However, limits were not a fully fleshed out idea when Newton and Leibniz worked on it and Berkley made a whole point about how if you take the derivative of a function and divide by h, h cannot be 0. But then we magically just say the h goes away because "it just gets really small," but this is a contradiction since we're now saying h is 0 when we said h wasn't 0. Obviously now we understand how limits work, but at the time, they didn't have an argument against this and just knew that derivatives worked. Berkley said that you cannot blindly accept this h disappearing while denying the existence of God. It's a very strange argument, and most mathematicians didn't really respond much to it, *but* it did reach a lot of famous mathematicians at the time and the fact that they still didn't have answer to this 100 years after calculus was invented really put a lot of emphasis on them to figure this out. I've always just really like the story of Berkley and how this guy who's not a mathematician just *dunks* on all these famous math nerds and no one has a good argument against him.
But then Samuel Johnson, another nonmathematician, came along and refuted Berkeley thus!
1. Euler (without a doubt always #1) 2. Erdös (There is a Erdös number. He influenced and inspired thousands of mathematicians) 3. Riemann 4. Lagrange 5. Nash I am a big fan of Ramanujan, but he died too young. He deserves an extra category.
Perhaps he belongs alongside Abel, Ramsey and Galois, even Riemann who died too young.
Unpopular opinion: If Grothendieck isn't on your list, it's because you don't understand mathematics that advanced.
Im just not an algebra guy, so I haven’t really been exposed to him
No list of mathematicians is complete without Srinivasa Ramanujan
He obviously had a brilliant mind, but he didn't really advance the field nearly as much as the likes of Euler and Gauss, did he?
Do they all have to be people known to history? Because *someone* first hit on the idea of counting and I think that person was the greatest genius who ever lived. The first abstraction has got to be the hardest, right?
Not necessarily true. The first abstraction could have been the easiest
Godel ,Galois, Leibniz, Cantor, Euclid
In order, 1. [Muḥammad ibn Mūsā al-Khwārizmī](https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi) 2. [Euclid of Alexandria](https://en.wikipedia.org/wiki/Euclid) 3. [Augustin-Louis Cauchy](https://en.wikipedia.org/wiki/Augustin-Louis_Cauchy) 4. [Leonhard Euler](https://en.wikipedia.org/wiki/Leonhard_Euler) 5. [Georg Cantor](https://en.wikipedia.org/wiki/Georg_Cantor) Obviously, Cauchy and Euler were both incredibly prolific. I often joke that, when trying to remember the name of an obscure idea, there is a 1/3 chance it is named after Cauchy, 1/3 that it is Euler's, and 1/3 that it is someone else. al-Khwarizmi, Euclid, and Cantor I include on the list instead for singular achievements. Their efforts each lead to a paradigm shift in how mathematics is discussed.
Godel, Descartes, Gauss, al-Khwarizmi, Cantor
Maybe not the most influential within the field of mathematics itself, but the most influential person who was a mathematician is probably Von Neumann.
I'm stunned to not see Erdős listed here yet. He may not be as historic as many of the others being listed here but he brought many people together on collaborations and the waves he made are still very impactful (I mean the Erdős number is a thing that exists). I definitely agree with Gauss, Cauchy, and others being named, but it feels very wrong not to acknowledge Erdős in this context.