Quotes on Mathematics

Those who are accustomed to judge by feeling do not understand the process of reasoning, because they want to comprehend at a glance and are not used to seeking for first principles. Those, on the other hand, who are accustomed to reason from first principles do not understand matters of feeling at all, because they look for first principles and are unable to comprehend at a glance.

[Mathematics] 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. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.

It will be another million years, at least, before we understand the primes.

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.

I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.

Mathematics is one of the deepest and most powerful expressions of pure human reason, and, at the same time, the most fundamental resource for description and analysis of the experiential world.

If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.

And silence. She liked the silence most of all. The silence in which the body, senses, the instincts, are more alert, more powerful, more sensitized, live a more richly perfumed and intoxication life, instead of transmuting into thoughts, words, into exquisite abstractions, mathematics of emotion in place of violent impact, the volcanic eruptions of fever, lust and delight.

For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art.

Grown-ups never understand anything for themselves, and it is tiresome for children to be always and forever explaining things to them.

Physicists are more like avant-garde composers, willing to bend traditional rules... Mathematicians are more like classical composers.

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.

My belief is that nothing that can be expressed by mathematics cannot be expressed by careful use of literary words.

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

Hardly a pure science, history is closer to animal husbandry than it is to mathematics in that it involves selective breeding. The principal difference between the husbandryman and the historian is that the former breeds sheep or cows or such and the latter breeds (assumed) facts. The husbandryman uses his skills to enrich the future, the historian uses his to enrich the past. Both are usually up to their ankles in bullshit.

The hardest arithmetic to master is that which enables us to count our blessings.

Men who are unhappy, like men who sleep badly, are always proud of the fact.

Mathematics can remove no prejudices and soften no obduracy. It has no influence in sweetening the bitter strife of parties, and in the moral world generally its action is perfectly null.

I think it is a peculiarity of myself that I like to play about with equations, just looking for beautiful mathematical relations which maybe don't have any physical meaning at all. Sometimes they do._x000D_ _x000D_ At age 60.

I could never have gone far in any science because on the path of every science the lion Mathematics lies in wait for you.

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.