Quotes on Math

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.

Our greatest pretenses are built up not to hide the evil and the ugly in us, but our emptiness. The hardest thing to hide is something that is not there.

Cultivate solitude and quiet and a few sincere friends, rather than mob merriment, noise and thousands of nodding acquaintances.

When I was a boy I was called a nerd all the time — because I didn’t like sports, I loved to read, I liked math and science, I thought school was really cool — and it hurt a lot. Because it’s never ok when a person makes fun of you for something you didn’t choose. You know, we don’t choose to be nerds. We can’t help it that we like these things — and we shouldn’t apologize for liking these things.

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.

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.

Most students who take math classes aren't going to be mathematicians. They're going to be engineers, statisticians - in many ways, that's the more important mission of math education.

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.

There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.

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.

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.

All human states are organic brain states - happiness, sadness, fear, lust, dreaming, doing math problems and writing novels - and our brains are not static.

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.

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.

Children are coming to school with trauma, everyday trauma, that they live under: violence in the homes, alcoholism in the community, unemployment thats 80 percent, not just during the recession. We need to help treat that before they can even go sit in a class and learn about math.

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

We all know that there are these exemplars who can take the toughest students, and they'll teach them two-and-a-half years of math in a single year.

In a way, math isn't the art of answering mathematical questions, it is the art of asking the right questions, the questions that give you insight, the ones that lead you in interesting directions, the ones that connect with lots of other interesting questions -the ones with beautiful answers.