Is maths beautiful?

Question

I've often heard mathematicians say that there is beauty in the purity and logic of mathematics. I'm quite numerate, (I'm an accountant with stats and calculus in my degree) but I don't get this "beauty". Can anyone please explain. PS If I want humour I'll buy a comic and get it from a professional writer

Answer 1

Is Mathematics Beautiful?

1. Bertrand Russell

It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect but true.
2. Bertrand Russell (1872-1970), The Study of Mathematics

Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
3. Aristotle
Beauty depends on size as well as symmetry.
4. J.H.Poincare
The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.
5. J.Bronowski,
Mathematics in this sense is a form of poetry, which has the same relation to the prose of practical mathematics as poetry has to prose in any other language. The element of poetry, the delight of exploring the medium for its own sake, is an essential ingredient in the creative process.
6. J.W.N.Sullivan

Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of Mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.
7. G. H. Hardy
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.
8. Lawrence University catalog, Cited in Essays in Humanistic Mathematics, A
Born of man's primitive urge to seek order in his world, mathematics is an ever-evolving language for the study of structure and pattern. Grounded in and renewed by physical reality, mathematics rises through sheer intellectual curiosity to levels of abstraction and generality where unexpected, beautiful, and often extremely useful connections and patterns emerge. Mathematics is the natural home of both abstract thought and the laws of nature. It is at once pure logic and creative art.
9. I.Newton,

I can hardly tell with what pleasure I have read the letters of those very distinguished men Leibniz and Tschirnhaus. Leibniz's method for obtaining convergent series is certainly very elegant...
10. Jane Muir, Of
Gauss: You have no idea how much poetry there is in the calculation of a table of logarithms!
11. F.Dyson,

Characteristic of Weyl was an aesthetic sense which dominated his thinking on all subjects. He once said to me, half-joking, "My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful." (Herman Weyl (1885-1955))
12. O. Spengler, in J. Newman, The World of Mathematics, Simon & Schuster,
To Goethe again we owe the profound saying: "the mathematician is only complete in so far as he feels within himself the beauty of the true."
13. O. Spengler, in J. Newman, The World of Mathematics,

"A mathematician," said old Weierstrass, "who is not at the same time a bit of a poet will never be a full mathematician."
14. Jakob Bernoulli, Tractatus de Seriebus Infinitis, 1689
So the soul of immensity dwells in minutia.
And in narrowest limits no limits inhere.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!
15. S.Lang, The Beauty of Doing Mathematics,

Last time, I asked: "What does mathematics mean to you?" And some people answered: "The manipulation of numbers, the manipulation of structures." And if I had asked what music means to you, would you have answered: "The manipulation of notes?"

Answer 2

In my view many people find beauty in expressions of the human mind. Indeed, that ability to express thoughts is a very human trait. Expression takes several obvious forms - art, sculpture, music, literature etc. All, in their own characteristic way, are expressing very powerful thoughts. They are attempting to convey and explain to others. That is exactly what maths does. It is the ultimate explanation, not just of the physical world but sometimes of the more traditional art forms. It captures and defines, so people look at a formula or equation and see as much beauty as Michelangelo's sublime Pieta. Furthermore. mathematical proofs transcend the proofs of all other disciplines. The latter can be disproved in the light of further knowledge but an established mathematical lasts forever.

Answer 3

I am sure that, as you are an Accountant, that you realise there is a difference between Applied Mathematics, which is what you do - using arithmetical calculations to achieve a result, and Pure Mathematics, in which the discipline exists to prove and improve itself. The best reading, for an appreciation of the relationship between Pure Mathematics, and the intellectual process, is Wittgenstein. Arthur Koestler, too, is worthy of prolonged study.

There is a beauty in Applied Mathematics. It is similar to the beauty found in music - I do not include most pf the 'pop' genre herein. Music, being, essentially, composed from the relationships of quantifiable intervals between combinations of notes (harmony), the equally quantifiable element of pulse (rhythm), and the devices of melody (even if the melody does not meet with the common appreciation of 'tune'). also attempts to embrace the reluctant partner of Pure Mathemics, even though the embrace is reluctantly eschewed. Think on this!

Answer 4

Hi:

Math is everywhere in Nature, man things,the process of life, in the flowers art,music,games But for something to help you see the beautiful of Mathematics get the show entitled " Donald Duck in Mathamagic Land" by Walt Disney it on VHS tape It shows you what we people who love math see what is so wonderful about Mathematics, The book Mathematics in the Making by Lancelot Hogben tell the history and story of mathematics from the Greeks,Egyptian,Babylonian, Chinese, and English to the 20th century. How men have struggled with it for thousands of years and explained how somed succeeded and how others failed and what was learned from it - it is a good book to read

To start you on a mathematical advendure of your own. Read the following books and tapes that listed in the "Sources"

Answer 5

Ever seen fractals? Not quite what you ask about, but these beautiful pictures are created mathematically, and many naturally occuring things of beauty like seeds in a sunflower, sand dunes and waves can be explained and regenerated through maths.

Answer 6

I have dyscalculia (like dyslexia but with numbers) and I just don't see maths at all! Sometimes I can't even understand what the clock is saying, but you give me fractions or percentages or anything else and I'm lost! I barely know my times tables, however my boyfriend is a scientist, he studies extended mathematics at university and he loves it, I see a beauty in words, in music, in art, but his passion is the way the numbers have no complications and are all black and white, I guess a person who has a passion for it will see it, but personally - it's my worst nightmare.

Answer 7

I'm not good at maths in fact I'm useless, however I can understand that the beauty is because it's a exact science. For those who are good at maths it must be great to know that once you have worked out the answer to a problem, no one can say it wrong, if you know what I mean !

Answer 8

I don't know if you've heard of Euler's equation, but here it is:

e^(pi*i) + 1 = 0

This is said to be beautiful because it encompasses the eight basic principles of mathematics (e, pi, i, 1, 0, +, =, power). It serves no use in the real world, but it shows how nicely everything ties together.

Answer 9

maths is beautiful.... because it has an order, a method and an indisputable system... everything - numbers, alphabets, shapes, musical notes, colors in paintings, motions of objects, design of clothes etc etc - whatever you take - all fall into place in the cradle of maths...

if music is lovely, it has an underlying maths... (and some physics too...); if computers work the way they do, there is enormous maths behind them...(and some electronics too...)...

"beauty" itself exists because of some mathematical relationships...is not that beautiful?

see http://www.cut-the-knot.org/manifesto/beauty.shtml for much more deliberations and ideas....

Answer 10

I'd have to say yes. Many people point to the how mathematics is a universal language, as stated in the film contact.

Answer 11

The Golden Ratio and the Fibbonacci Sequence. If you see all the ways that these two aspects of mathematics apply in nature, you can only then realize its beauty.