Math Quotes - Page 53

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.

We use only 10% of our brains... Imagine how smart we would be if we used the other 60%!

I can become very emotional about math, although I'm not that good at it.

Physics without mathematics is meaningless.

. . . we have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.

Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.

The testament of science is so continually in a flux that the heresy of yesterday is the gospel of today and the fundamentalism of tomorrow.

Perhaps the greatest paradox of all is that there are paradoxes in mathematics.

Mathematics is man's own handiwork, subject only to the limitations imposed by the laws of thought.

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.

It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.

There should be no such thing as boring mathematics.

Asked for a testimony to the effect that Emmy Noether was a great woman mathematician, he said: I can testify that she is a great mathematician, but that she is a woman, I cannot swear.

Die mathematische Forschung besteht aus 10% Intuition und 90% Arbeit.

To speak algebraically, Mr. M. is execrable, but Mr. G. is (x + 1)- ecrable.

We lay down a fundamental principle of generalization by abstraction: The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features.

Most people that derail as leaders in the corporate world, it's not because they couldn't do the math and calculate return on investment properly. The issues are communication and understanding. All of what typically would've been called the 'soft stuff.' You have to be authentic. You have to be dialed into the soft stuff.

One nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive.

Bistromathics itself is simply a revolutionary new way of understanding the behavior of numbers. Just as Einstein observed that space was not an absolute but depended on the observer's movement in space, and that time was not an absolute, but depended on the observer's movement in time, so it is now realized that numbers are not absolute, but depend on the observer's movement in restaurants.

The real work of us mathematicians, from now until, roughly, fifty years from now, when computers won't need us anymore, is to make the transition from human-centric math to machine-centric math as smooth and efficient as possible.

I've had to recover not only from a single well-publicized incident, but several years of press aftermath.

If a child is poor in math but good at tennis, most people would hire a math tutor. I would rather hire a tennis coach.