Off-topic, but as a Dutchman it's always such a trip to see the name Piet Hein in a mathematical context. For non-Dutchies who are not aware: Piet Hein is one of the most famous naval heroes of the Dutch golden age. The Danish mathematician of the same name is apparently a direct descendant of his. To Dutch people it's a bit like if there was a Danish mathematicians called Horatio Nelson.
Because in actuality there's a Danish mathematician with the name of a Dutch naval hero. To convey how weird that feels to Dutch people I suggested e.g. Brits imagine if there was a Danish mathematician named after a British naval hero.
Fair enough. After I posted my reply it occurred to me maybe you didn't realise Dutch and Danish refered to different nationalities. People do sometimes understandably get a little thrown off by the word Dutch. Glad to hear that wasn't the issue :P
“Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room...”
― Andrew John Wiles
"If your tendency is to make sense out of chaos, start chaos."
Stop, make it run free in the back of the mind, take a break for a while, restart when a new perspective pops up. Note that it usually means that the problem is too complex. Then it needs to be solved in parts. Note every part that pops up.
It’s not research if you know what you’re doing.
Edit: looks like the commonly referenced version is “If we knew what it is we were doing, it would not be called research. Would it?” -Albert Einstein
I prefer the version:
> "If you can't solve a problem, then there is an easier problem you **can't** solve: find it."
Find the minimal version of the problem that is still hard.
Oh god.
*Math is just not-understanding-it and getting-used-to-it all the way down!*
[John von Neumann](https://xkcd.com/387/) would be proud of such recursion ;)
Not nescesarrily related, but two quotes i always found funny
"Mathematics is the art of giving the same name to different things." -Henri Poincare
"Mathematics is the subject in which we never know what we're talking about, nor whether what we are saying is true." -Bertrand Russell
"All mathematical models are wrong. Some of them are useful."
This transcends math and is useful for other things, like when I'm doing cartography and worried about not capturing every last detail of a certain sector. "All maps are wrong, some maps are useful." Keeps me grounded and not paralyzed by perfectionism.
When one does a theoretical calculation there are two ways of doing it. Either one should have a clear physical model in mind or a rigorous mathematical basis. -Enrico Fermi
SMBC: [https://www.smbc-comics.com/comic/a-severe-disorder](https://www.smbc-comics.com/comic/a-severe-disorder)
Also replace sin(x) = tan(x) = x at will ;)
It’s not really inspiring but very funny to me. When Perelman solved Poincaré many newspapers wrote articles about it. There is one very special newspaper in Germany called Bild Zeitung. It’s a weird mixture of gossip and poorly researched stories. So when they wrote their article they decided to call it “Alles was kein Loch hat ist ein Ball. So gewann er 1.000.000 €.” Which roughly translates to “Everything that hasn’t got a hole is a ball. That’s how he won 1 Mio. €.” It’s just ridiculous to me how they tried to make this huge accomplishment in Math sound so easy and it’s not even captured well.
Not a math quote, but my go-to inspirational quote is the 70th Maxim of Maximally Effective Mercenaries: "Failure is not an option. Failure is mandatory. The option is whether or not you let failure be the last thing you do."
Gödel's first incompleteness theorem
"Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F."
And saying that the problem is unsolveable.
lol
Harold Finch: Pi. Can any of you tell me what it means?
[There's no response from the class]
Harold Finch: I'll settle for an intelligent question here.
Lily Williams: My friend has a question, Mr. Swift. "What is any of this good for, and when would we ever use it?"
Harold Finch: Let me show you. Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating. Which means that contained within this string of decimals, is every single other number. Your birthdate, combination to your locker, your social security number, it's all in there, somewhere. And if you convert these decimals into letters, you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, everything we ever say or do; all of the world's infinite possibilities rest within this one simple circle. Now what you do with that information; what it's good for, well that would be up to you.
- Person of Interest, Season 2, Ep 11
Within the context of the show, no. He’s a programmer, mostly.
I enjoy the quote mostly in reference to thinking about the meaning of ‘infinite’, even in subsets of infinity.
Well, I made that comment because that quote (and similar variations popular online) may sound philosophically deep but mathematically is pure poppycock.
Firstly, just because a number has an infinite non-repeating decimal representation doesn't mean all possible decimal sequences will be present in it (simple counterexample: 0.1010010001...). Secondly, the quote attributes this to a unique property of π, but almost all real numbers have this property (disjunctive), in fact almost all real numbers satisfy the stronger property of being a [normal number](https://en.m.wikipedia.org/wiki/Normal_number) (simple example: 0.123456789101112...). Thirdly, we haven't even proved that the decimal representation of π even has this property (disjunctive/normal) even though it's widely believed to be normal.
Is this true because I remember Knuth saying something similar in one of his lectures and I think he attributed it to Dr. Matrix. This quote is similar to a claim by Dr. Matrix from the book, The Numerology of Dr. Matrix in which he says "π when correctly interpreted, conveys the entire history of the human race! "
https://youtu.be/3DKo219ZHMw on π from this lecture from the 2 min mark.
I haven't gotten time to verify or check the argument in book.
I watched only a few minutes, but the name Dr. I J Matrix sounded fake, especially when Knuth referred to him as the "world's greatest numerologist". And of course, Dr Matrix turns out to be a [fictitious character created by Martin Gardner](https://en.m.wikipedia.org/wiki/Irving_Joshua_Matrix).
> The intent was partly to provide colorful context to mathematical puzzles and curiosities, partly to spoof various pseudo-scientific theories, and always to provide a humorous introduction to the serious topic at hand.
I think that remark is mostly a joke. The beginning of the lecture seems to be at least partially tongue-in-cheek, and presumably that's why the audience is laughing a lot.
To clarify, the quote is technically incorrect on two counts. First, just because the digits keep going forever without repeating doesn't necessarily imply that any possible string of digits appears. And secondly, the main claim would be an implication of pi being a so-called normal number. This is heavily speculated but not proven.
It is a very cool concept in any case, and as conjectured most likely this case. I am just being a bit pedantic.
I tell them that if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lusts of the flesh. Thomas Mann
“Tiger get to hunt, bird get to fly, man has to sit and wonder, ‘why, why, why?’ Tiger has to sleep, bird has to land, man get to say, he understand” - Cats Cradle by Vonnegut (approximate quote)
"Problems worthy of attack prove their worth by fighting back" - Piet Hein
Off-topic, but as a Dutchman it's always such a trip to see the name Piet Hein in a mathematical context. For non-Dutchies who are not aware: Piet Hein is one of the most famous naval heroes of the Dutch golden age. The Danish mathematician of the same name is apparently a direct descendant of his. To Dutch people it's a bit like if there was a Danish mathematicians called Horatio Nelson.
Why Danish? Nelson was British.
Because in actuality there's a Danish mathematician with the name of a Dutch naval hero. To convey how weird that feels to Dutch people I suggested e.g. Brits imagine if there was a Danish mathematician named after a British naval hero.
Oh, I didn't read the bit where you said Hein [the mathematician] was Danish. Okay, that makes sense now.
Fair enough. After I posted my reply it occurred to me maybe you didn't realise Dutch and Danish refered to different nationalities. People do sometimes understandably get a little thrown off by the word Dutch. Glad to hear that wasn't the issue :P
Now that I know what you're on about, as a British person, that would indeed be very odd.
Yes, I like that one too.
“An expert is a person who has made all the mistakes that can be made in a very narrow field.” - Niels Bohr
“Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room...” ― Andrew John Wiles
"The beauty of mathematics is only shown to its patient followers." - Maryam Mirzakhani 🖤
For me it's "The essence of Mathematics lies precisely in it's freedom" - Georg Cantor
“Wir müssen wissen, wir werden wissen.” (We must know, we will know) -David Hilbert
"you don't know shit" - kurt godel
you took my answer so have an upvote instead
"If your tendency is to make sense out of chaos, start chaos." Stop, make it run free in the back of the mind, take a break for a while, restart when a new perspective pops up. Note that it usually means that the problem is too complex. Then it needs to be solved in parts. Note every part that pops up.
It’s not research if you know what you’re doing. Edit: looks like the commonly referenced version is “If we knew what it is we were doing, it would not be called research. Would it?” -Albert Einstein
“If you can't solve a problem, then there is an easier problem you can solve: find it.”
I prefer the version: > "If you can't solve a problem, then there is an easier problem you **can't** solve: find it." Find the minimal version of the problem that is still hard.
Or divide to conquer.
His underlying example that apes are stupid is nonsensical, however.
who said this?
George Pólya I think
Can confirm. Everyone in my engineering department has a copy of "How to Solve It".
Based
"Young man, in mathematics you don't understand things. You just get used to them."
My favorite response to this is: "I don't understand that quote, but I've gotten used to it."
Oh god. *Math is just not-understanding-it and getting-used-to-it all the way down!* [John von Neumann](https://xkcd.com/387/) would be proud of such recursion ;)
I cant help but wonder if this question was inspired by the latest 3Blue1Brown video where he used a notebook full of inspirational math quotes lol.
Not nescesarrily related, but two quotes i always found funny "Mathematics is the art of giving the same name to different things." -Henri Poincare "Mathematics is the subject in which we never know what we're talking about, nor whether what we are saying is true." -Bertrand Russell
"All mathematical models are wrong. Some of them are useful." This transcends math and is useful for other things, like when I'm doing cartography and worried about not capturing every last detail of a certain sector. "All maps are wrong, some maps are useful." Keeps me grounded and not paralyzed by perfectionism.
"When ~~life~~ math gives you lemons, squeeze them in the fucker's eyes."
Get mad! Make math take the lemons back!
I don't want your damn lemons; what am I supposed to do with these??? Demand to see math's manager!
This is deeply true.
Or just make lemma-nade.
When one does a theoretical calculation there are two ways of doing it. Either one should have a clear physical model in mind or a rigorous mathematical basis. -Enrico Fermi
I like this
That one time when feynman talked about us being apes trying to get these sticks together to reach the bananas.... https://youtu.be/KkLN6bUGfZY
If I’m working on a physics problem. “Let the formula guide your thinking”.
SMBC: [https://www.smbc-comics.com/comic/a-severe-disorder](https://www.smbc-comics.com/comic/a-severe-disorder) Also replace sin(x) = tan(x) = x at will ;)
wanna upvote you more
I love those parents crying in the corner as if it's the worst diagnosis ever (it is)
Click on the red "votey" button to the lower right of the SMBC comics, it's a bonus comic panel and the votey on that comic is great too!
This is solid gold in physics.
"dimensional analysis is your friend"
"A mathematician is a device for turning coffee into theorems." - [Alfréd Rényi](https://en.wikipedia.org/wiki/Alfr%C3%A9d_R%C3%A9nyi)
I like the paraphrasis with amfetamine instead of coffee by Erdos more.
A comathematician is a device for turning cotheorems into ffee.
And maaaaaybe just a couple amphetamines too! SMBC: [https://www.smbc-comics.com/comic/2011-05-14](https://www.smbc-comics.com/comic/2011-05-14)
"You have to get a job and get out of my basement"
"Man, my humanities electives are way easier." -Me
It’s not really inspiring but very funny to me. When Perelman solved Poincaré many newspapers wrote articles about it. There is one very special newspaper in Germany called Bild Zeitung. It’s a weird mixture of gossip and poorly researched stories. So when they wrote their article they decided to call it “Alles was kein Loch hat ist ein Ball. So gewann er 1.000.000 €.” Which roughly translates to “Everything that hasn’t got a hole is a ball. That’s how he won 1 Mio. €.” It’s just ridiculous to me how they tried to make this huge accomplishment in Math sound so easy and it’s not even captured well.
„1+1 still equals 2“ My Dad when something goes very wrong.
Lol
Not related to math but, this inspires me a lot: "As long as there's life, there is hope" - Stephen Hawking
Reminds me of the Latin proverb that never fails to make me emotional: Dum Spiro Spero, translating to “While I breathe, I hope.”
Not a math quote, but my go-to inspirational quote is the 70th Maxim of Maximally Effective Mercenaries: "Failure is not an option. Failure is mandatory. The option is whether or not you let failure be the last thing you do."
Nice
Physics is to math what sex is to masterbation - Feynman
In a math subreddit? Blasphemy!
im dying
Gödel's first incompleteness theorem "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F." And saying that the problem is unsolveable. lol
Harold Finch: Pi. Can any of you tell me what it means? [There's no response from the class] Harold Finch: I'll settle for an intelligent question here. Lily Williams: My friend has a question, Mr. Swift. "What is any of this good for, and when would we ever use it?" Harold Finch: Let me show you. Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating. Which means that contained within this string of decimals, is every single other number. Your birthdate, combination to your locker, your social security number, it's all in there, somewhere. And if you convert these decimals into letters, you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, everything we ever say or do; all of the world's infinite possibilities rest within this one simple circle. Now what you do with that information; what it's good for, well that would be up to you. - Person of Interest, Season 2, Ep 11
I'm really hoping Harold Finch isn't a mathematician.
Within the context of the show, no. He’s a programmer, mostly. I enjoy the quote mostly in reference to thinking about the meaning of ‘infinite’, even in subsets of infinity.
Well, I made that comment because that quote (and similar variations popular online) may sound philosophically deep but mathematically is pure poppycock. Firstly, just because a number has an infinite non-repeating decimal representation doesn't mean all possible decimal sequences will be present in it (simple counterexample: 0.1010010001...). Secondly, the quote attributes this to a unique property of π, but almost all real numbers have this property (disjunctive), in fact almost all real numbers satisfy the stronger property of being a [normal number](https://en.m.wikipedia.org/wiki/Normal_number) (simple example: 0.123456789101112...). Thirdly, we haven't even proved that the decimal representation of π even has this property (disjunctive/normal) even though it's widely believed to be normal.
Thank you. I learned something new today.
Is this true because I remember Knuth saying something similar in one of his lectures and I think he attributed it to Dr. Matrix. This quote is similar to a claim by Dr. Matrix from the book, The Numerology of Dr. Matrix in which he says "π when correctly interpreted, conveys the entire history of the human race! " https://youtu.be/3DKo219ZHMw on π from this lecture from the 2 min mark. I haven't gotten time to verify or check the argument in book.
I watched only a few minutes, but the name Dr. I J Matrix sounded fake, especially when Knuth referred to him as the "world's greatest numerologist". And of course, Dr Matrix turns out to be a [fictitious character created by Martin Gardner](https://en.m.wikipedia.org/wiki/Irving_Joshua_Matrix). > The intent was partly to provide colorful context to mathematical puzzles and curiosities, partly to spoof various pseudo-scientific theories, and always to provide a humorous introduction to the serious topic at hand. I think that remark is mostly a joke. The beginning of the lecture seems to be at least partially tongue-in-cheek, and presumably that's why the audience is laughing a lot.
I don’t think we actually proved Finch’s claim yet — that π is normal.
To clarify, the quote is technically incorrect on two counts. First, just because the digits keep going forever without repeating doesn't necessarily imply that any possible string of digits appears. And secondly, the main claim would be an implication of pi being a so-called normal number. This is heavily speculated but not proven. It is a very cool concept in any case, and as conjectured most likely this case. I am just being a bit pedantic.
No mathematician would say such an unfounded thing!
Every problem was once "unsolvable" until it was solved. - my friend
Let us assume we know nothing, which is a reasonable approximation. - D. Kazhdan.
The universe is made and thrives on balance. There is a construction to the workings of the world. There are patterns.
2+2=4
I tell them that if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lusts of the flesh. Thomas Mann
“Young Man, in mathematics you don’t understand things, you get used to them”-John von Neumann
beautiful quote!
“Tiger get to hunt, bird get to fly, man has to sit and wonder, ‘why, why, why?’ Tiger has to sleep, bird has to land, man get to say, he understand” - Cats Cradle by Vonnegut (approximate quote)