Quotes on Mathematics

A few honest men are better than numbers.

Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.

Physics is an otherworld thing, it requires a taste for things unseen, even unheard of- a high degree of abstraction... These faculties die off somehow when you grow up... profound curiosity happens when children are young. I think physicists are the Peter Pans of the human race... Once you are sophisticated, you know too much- far too much. Pauli once said to me, "I know a great deal. I know too much. I am a quantum ancient.".

Mathematics brought rigor to Economics. Unfortunately, it also brought mortis.

I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.

But however measurable, there is much more life in music than mathematics or logic ever dreamed of.

Thou shalt not answer questionnaires Or quizzes upon world affairs, Nor with compliance Take any test. Thou shalt not sit with statisticians nor commit A social science.

I set out to show that there exists single creative activity,which is displayed alike in the arts and in the sciences.It is wrong to think of science as a mechanical record of facts, and it is wrong to think of the arts as remote and private fancies. What makes each human, what makes them universal, is the stamp of the creative mind.

Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950]

Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful._x000D_ If you don’t see why, someone can’t tell you. I know numbers are beautiful._x000D_ If they aren’t beautiful, nothing is.

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

In a lot of scientists, the ratio of wonder to skepticism declines in time. That may be connected with the fact that in some fields-mathematics, physics, some others-the great discoveries are almost entirely made by youngsters.

One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

Look somewhere else for someone who can follow you in your researches about numbers. For my part, I confess that they are far beyond me, and I am competent only to admire them.

One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.

Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him.

After years of finding mathematics easy, I finally reached integral calculus and came up against a barrier. I realized that this was as far as I could go, and to this day I have never successfully gone beyond it in any but the most superficial way.