With all the greats from Cantor to Gauss, from Plato all the way to Marcus du Sautoy, not to mention Albert Einstein and Bertrand Russell, and even members of our own society, here are 60 of the greatest, most inspirational, or just plain funny mathematical quotes.
1
“Pure mathematics, is, in its way, the poetry of logical ideas.”
Albert Einstein
2
“In mathematics, the art of proposing a question must be held of higher value than solving it.”
Georg Cantor
3
“It is not knowledge, but the act of learning, not possession, but the act of getting there, which grants the greatest enjoyment.”
Carl Friedrich Gauss
4
“Do not worry about your difficulties in mathematics, I can assure you mine are far greater.”
Albert Einstein
5
“Not everything that can be counted counts, and not everything that counts can be counted.”
Albert Einstein
6
“In math, you’re either right or you’re wrong.”
Katherine Johnson
7
“The only way to learn mathematics is to do mathematics.”
Paul Halmos
8
“A mathematician is a machine for turning coffee into theorems.”
Alfred Rényi
9
“A topologist is someone who doesn’t know the difference between a doughnut and a coffee cup.”
John Kelley
10
“Mathematicians stand on each other’s shoulders.”
Carl Friedrich Gauss
11
“Beauty is the first test: there is no permanent place in the world for ugly mathematics.”
Godfrey Harold Hardy
12
“Math is the language of the universe. So, the more equations you know, the more you can converse with the cosmos.”
Neil deGrasse Tyson
13
“To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.”
Pierre de Fermat
14
“Prediction is very difficult, especially if it’s about the future.”
Niels Bohr
15
“Politicians use statistics as a drunken man uses lamp-posts – for support rather than illumination.”
Andrew Lang
16
“If P = NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in ‘creative leaps,’ no fundamental gap between solving a problem and recognising the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss…”
Scott Aaronson
17
“Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”
Bertrand Russell
18
“The essence of mathematics lies in its freedom.”
Georg Cantor
19
“Mathematics is the art of giving the same name to different things.”
Henri Poincaré
20
“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.”
David Hilbert
21
“Mathematics is the music of reason.”
James Joseph Sylvester
22
“Mathematics has beauty and romance. It’s not a boring place to be, the mathematical world. It’s an extraordinary place; it’s worth spending time there.”
Marcus du Sautoy
23
“Mathematics is not just a subject, it is a language that allows us to unlock the mysteries of the universe.”
Katherine Johnson
24
“The moving power of mathematical invention is not reasoning but imagination.”
Augustus de Morgan
25
“No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.”
George Boole
26
“The art of doing mathematics consists in finding that special case which contains all the germs of generality.”
David Hilbert
27
“In Mathematics, you don’t understand things, you just get used to them.”
John von Neumann
28
“The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.”
Charles Caleb Colton
29
“There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else – but persistent.”
Raoul Bott
30
“‘Obvious’ is the most dangerous word in mathematics.”
Eric Temple Bell
31
“An expert problem solver must be endowed with two incompatible quantities: a restless imagination and a patient pertinacity.”
Howard Eves
32
“The traditional mathematician recognises and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.”
Edsger Dijkstra
33
“Mathematics allows for no hypocrisy and no vagueness.”
Stendhal
34
“The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future.”
Eric Temple Bell
35
“An elegantly executed proof is a poem in all but the form in which it is written.”
Morris Kline
36
“Mathematicians aren’t people who find Maths easy. They’re people who enjoy how hard it is.”
Andrew Sainsbury
37
“The beauty of mathematics only shows itself to its more patient followers.”
Maryam Mirzakhani
38
“I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.”
Maryam Mirzakhani
39
“Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.”
Richard Courant
40
“Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they’re extremely hard to solve. There’s no reason why these problems shouldn’t be easy, and yet they turn out to be extremely intricate.”
Andrew Wiles
41
“I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.”
Pál Turán
42
“What we really need is a machine for turning some of those theorems back into coffee.”
AJ Tolland
43
“Arithmetic is being able to count to twenty without taking off your shoes.”
Mickey Mouse
44
“I love maths because it is the unending, eternally beautiful and simple fabric that links all of life and existence… and studying it is brilliant fun!”
Charlton C
45
“I love maths because you can transpose everything in the world into maths, therefore logicising and simplifying what is so chaotic. It puts the world into order.”
Emily B
46
“STEP questions lure you in. The first part will ask ‘if I have a fair coin what is the probability it comes up heads’? The second bit will say: ‘if I have 5 biased coins and am blindfolded what is the probability it was raining last Tuesday?’”
Ed Tansley
47
“In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for re-election.”
Hugo Rossi
48
“He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its sides.”
Plato
49
“Medicine makes people ill, mathematics makes them sad, and theology makes them sinful.”
Martin Luther
50
“Good! He did not have enough imagination to become a mathematician.”
David Hilbert (on hearing that a student has dropped maths to study poetry instead)
51
“Understand well as I may, my comprehension can only be an infinitesimal fraction of all I want to understand.”
Ada Lovelace
52
“Consequently he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics.”
Maimonides
53
“An interesting theorem of mathematics differs from interesting results in other fields because over and above the surprise and beauty of what it says, it has as ‘aspect of eternity’; it is always part of an infinite chain of results.”
Leo Zippin
54
“Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.”
Yuri Manin
55
“A theory has the alternative of being right or wrong. A model has the third possibility; it may be right but irrelevant.”
Manfred Eigen
56
“I have had my results for a long time, but I do not yet know how I am to arrive at them.”
Carl Friedrich Gauss
57
“Music is the pleasure the human mind experiences from counting without being aware that it is counting.”
Gottfried Leibniz
58
“To be a good general you must know mathematics, it serves to direct your thinking in a thousand circumstances.”
Napoleon Bonaparte
59
“We all make mistakes. Relentlessly. And that is nothing to be feared.”
Matt Parker
60
“Number rules the universe.”
Pythagoras
We will continue to expand this list of maths quotes. Please contact us with any suggestions.