Math Quotes - Page 35

A generating function is a clothesline on which we hang up a sequence of numbers for display.

How is error possible in mathematics?

If we have no idea why a statement is true, we can still prove it by induction.

Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.

Young men should prove theorems, old men should write books.

In my experience most mathematicians are intellectually lazy.

Why don't we teach sex the way we teach math or history? It is such a deeply crucial and healing part of life and we offer no road map. I think it is core to ending violence.

[A mathematician is a] scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.

Perhaps the most surprising thing about mathematics is that it is so surprising.

What mathematics are to matter and force, occult science is to life and consciousness.

USA Today has come out with a new survey - apparently, three out of every four people make up 75% of the population.

Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.

Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.

Every culture has contributed to maths just as it has contributed to literature. It's a universal language; numbers belong to everyone.

In some ways, I never outgrew my adolescence. I wake up in the morning and think, 'Oh my God, I'm late for a math test!' But then I say, 'Wait a minute. I'm 40.

Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding.

Math is my favorite subject. It's the universal language. I like the fact that wherever you go in the whole world, two plus two will still be four.

Even in pure mathematics they can't remove all paradox, and the rest of us should also recognize we are going to have to endure a lot of paradox, like it or not.

Mathematics is purely hypothetical: it produces nothing but conditional propositions.

Mathematics seems to endow one with something like a new sense.

There is a mathematical formula to why you got famous. It isn’t some magical thing that just started happening.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

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.

Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth.

The sole cause of man's unhappiness is that he does not know how to stay quietly in his room.