"mathematics is" quotes...

[ajschumacher]

"Mathematics is the art of explanation." (page 29, , Lockhart, A Mathematician's Lament)

"Mathematics is about problems, and problems must be made the focus of a student’s mathematical life." (pages 60-61, Lockhart, A Mathematician's Lament)

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Mathematics is the study of things that come out a certain way because there is no other way they could possibly be." (page 12, , Ellenberg, in How Not to Be Wrong)

(that one is maybe in conflict, or at least not clearly resolved) with a view that doing math includes making choices about how things should be defined, etc.)

"Mathematics is the extension of common sense by other means." (page 13, Ellenberg, in How Not to Be Wrong)

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“Mathematics is the language in which God has written the universe” is attributed to Galileo, but I can't find a reference for it...

[ajschumacher]

"... mathematics is not an empirical science ..."

John von Neumann, The Mathematician

• https://mathshistory.st-andrews.ac.uk/Extras/Von_Neumann_Part_1/
• https://mathshistory.st-andrews.ac.uk/Extras/Von_Neumann_Part_2/

[ajschumacher]

"... mathematics is the science of skillful operations with concepts and rules invented just for this purpose."

Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences

• https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

[ajschumacher]

"Mathematics is not settled." (page 14, Ellenberg, in How Not to Be Wrong)

[ajschumacher]

"Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite." (page 223, Ellenberg)

[ajschumacher]

Doesn't fit perfectly here, but this is interesting on physics/metaphor being used in number theory: https://getpocket.com/explore/item/secret-link-uncovered-between-pure-math-and-physics

[ajschumacher]

https://math.ucsd.edu/~harel/What%20Is%20Mathematics.pdf Guershon Harel

more in #185

[ajschumacher]

"This is how I think about math: It’s about how things fit together." (Bryna Kra)

https://www.youtube.com/watch?v=mZaEVoH9Z4k&ab_channel=QuantaMagazine

Go ahead and resolve the pronoun:

"Mathematics is about how things fit together." (Bryna Kra)

[ajschumacher]

"Mathematics is interesting in so far as it occupies our reasoning and inventive powers." (Polya)

https://planspace.org/2013/09/28/polyas-how-to-solve-it-quotes-and-comments/

[ajschumacher]

When interviewed several years ago, he [Halmos] was asked: What is mathematics to you? He responded: "It is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing — one great, glorious thing." A few years later, he was asked about the best part of being a mathematician. He said: "I'm not a religious man, but it's almost like being in touch with God when you're thinking about mathematics."

From the MAA obit: https://www.maa.org/news/paul-halmos-a-life-in-mathematics (Could probably find that interview too.)

[ajschumacher]

As recommended by Japheth:

"Wiles’s incredible journey is too long to even begin to explore on this page, but it is best summarised by the following quote by Andrew Wiles, which draws an analogy between doing mathematics and exploring a dark mansion:

"“You enter the first room of the mansion and it’s completely dark. You stumble around bumping into the furniture but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are the culmination of, and couldn’t exist without, the many months of stumbling around in the dark that precede them.”"

From https://simonsingh.net/books/fermats-last-theorem/who-is-andrew-wiles/

[ajschumacher]

"Mathematics is prestidigitation."

Carl E. Linderholm, Mathematics Made Difficult, page 10

[ajschumacher]

"Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does, but it is different in its degree of precision and information. Possibly philosophers would look on us mathematicians the same way as we look on the technicians, if they dared." (page 321, Halmos, I want to be a mathematician)

comparing to von Neumann's "not an empirical science" above, it's interesting... many people describe the doing of mathematics as having an empirical feel... it's the subject itself that isn't empirical, in the sense of physically existing, maybe...

[ajschumacher]

doesn't quite follow the pattern, but:

"... what I believe is the true purpose of maths: making complicated, seemingly impenetrable things intuitive and simple."

https://graphicallinearalgebra.net/2016/08/26/30-the-essence-of-graphical-linear-algebra/ Pawel Sobocinski

[ajschumacher]

my thought today: mathematics is about equality

[ajschumacher]

"Mathematics is the art of giving the same name to different things." (Henri Poincaré)

http://www.nieuwarchief.nl/serie5/pdf/naw5-2012-13-3-154.pdf

I think here he's talking about equality, as I was thinking... Here's some context:

[The styles and methods of proofs in mathematics have evolved since your time. With the enormous growth of both pure and applied mathematics there is now an abundance of mathematical styles,there are even computerassisted proofs. Does it make sense to distinguish between beautiful and ugly mathematics, between elegant and graceless reasoning?]

Question: Mathematicians attach a great importance to the elegance of their methods and of their results, and this is not mere dilettantism. What is it that gives us the feeling of elegance in a solution or proof? [3, essay ‘L’avenir des mathematiques’] ´

Answer: It is the harmony of the different parts, their symmetry, and their happy adjustment; it is, in a word, all that introduces order, all that gives them unity, that enables us to obtain a clear comprehension of the whole as well as of the parts. Elegance may result from the feeling of surprise caused by the unlooked-for occurrence of objects not habitually associated. In this, again, it is fruitful, since it discloses thus relations that were until then unrecognized. Mathematics is the art of giving the same names to different things.

The original source ("3") then is Henri Poincare,´Science et Methode´, Flammarion, Paris, 1908.

Ooh this is good too:

The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious. It is through it that the mathematical world remains in touch with the real world.

[ajschumacher]

"Math is never just numbers. In the wrong hands, it’s a weapon. In the right hands, deliverance." (Hari Seldon)

"Math is never just numbers. When words fail us, we use math to describe the inexpressible. The things that terrify us most. The vastness of space, the shape of time, the weight and worth of a human soul." (Gaal Dornick)

from the first two episodes of the Foundation TV show

[ajschumacher]

"mathematics cannot amount to anything more than an immense tautology"

Henri Poincaré in his 1902 book, Science and Hypothesis - and not really agreeing with this sentiment; see http://planspace.org/20230116-ten_equations_that_rule_the_world/

[ajschumacher]

math teaches us to be surprised: even tautologies can be, often are surprising

[ajschumacher]

Pure mathematics is, in its way, the poetry of logical ideas. (Einstein)