Explore Quotes on Mathematics

Mathematics is a language. We want scientists to be able to read it, speak it, and write it. But we are are not training them to be grammarians.

My basic idea is that programming is the most powerful medium of developing the sophisticated and rigorous thinking needed for mathematics, for grammar, for physics, for statistics, for all the "hard" subjects.... In short, I believe more than ever that programming should be a key part of the intellectual development of people growing up.

This attitude [the abstract method in mathematics] can be encapsulated in the following slogan: a mathematical object is what it does.

Yes, I share your concern: how to program well -though a teachable topic- is hardly taught. The situation is similar to that in mathematics, where the explicit curriculum is confined to mathematical results; how to do mathematics is something the student must absorb by osmosis, so to speak. One reason for preferring symbol-manipulating, calculating arguments is that their design is much better teachable than the design of verbal/pictorial arguments. Large-scale introduction of courses on such calculational methodology, however, would encounter unsurmoutable political problems.

If all art aspires to the condition of music, all the sciences aspire to the condition of mathematics.

How is error possible in mathematics?

I protest against the use of infinite magnitude ..., which is never permissible in mathematics.

With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.

Numbers are intellectual witnesses that belong only to mankind.

I don't agree with mathematics; the sum total of zeros is a frightening figure.

The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry.

The understanding of mathematics is necessary for a sound grasp of ethics.

When I entered graduate school I had carried out the instructions given to me by my father and had knocked on both Murray Gell-Mann's and Feynman's doors and asked them what they were currently doing. Murray wrote down the partition function for the three-dimensional Ising model and said it would be nice if I could solve it (at least that is how I remember the conversation). Feynman's answer was 'nothing'.

But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.

In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.

The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?

We've taught you that the earth is round, That red and white make pink, And something else that matters more - We've taught you how to think.

It strikes me that mathematical writing is similar to using a language. To be understood you have to follow some grammatical rules. However, in our case, nobody has taken the trouble of writing down the grammar; we get it as a baby does from parents, by imitation of others. Some mathematicians have a good ear; some not (and some prefer the slangy expressions such as 'iff'). That's life.

Serious numbers will speak to us always.

If you think it's simple, then you have misunderstood the problem.

The very term 'combinatorial methods' has an oxymoronic character.