Mathematics 4 You

Perfect numbers like perfect men are very rare. ~Rene Descartes

I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. -Isaac Newton

Calculus has it's limits -Anonymous

I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go. -Sir Winston Churchill (1874-1965)

There are 10 kinds of people, those who can count in binary and those who can't -Anonymous

I want to know God's thoughts; the rest are details. -Albert Einstein

As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality. -Albert Einstein

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater. -Albert Einstein

Not everything that counts can be counted, and not everything that can be counted counts. (Sign hanging in Einstein's office at Princeton)

Education is what remains after one has forgotten everything he learned in school. -Albert Einstein

There is nothing strange in the circle being the origin of any and every marvel. -Aristotle

One geometry cannot be more true than another; it can only be more convenient. -Henri Poincare

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful. -George Boole

There are three kinds of people, those who can count and those who can't -Anonymous

Mathematics is the most under-appreciated of the fine arts. -Harry Shenk

Perfect numbers like perfect men are very rare. -Rene Descartes

Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore. -Albert Einstein

If I have been able to see further, it was only because I stood on the shoulders of giants. -Sir Isaac Newton

To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it. -Pierre de Fermat (side note in the narrow margin of his textbook)

On two occasions I have been asked [by members of Parliament], Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out? I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. -Charles Babbage

I have had my results for a long time: but I do not yet know how I am to arrive at them. -Carl Freidrich Gauss

Either mathematics is too big for the human mind or the human mind is more than a machine. -Kurt Godel

Order is not sufficient. What is required, is something much more complex. It is order entering upon novelty; so that the massiveness of order does not degenerate into mere repetition; and so that the novelty is always reflected upon a background of system. -Alfred North Whitehead

Nature is an infinite sphere of which the center is everywhere and the circumference nowhere. -Blaise Pascal

It is not certain that everything is uncertain -Blaise Pascal

I have made this letter longer than usual, because I lack the time to make it short. -Blaise Pascal

The shortest path between two truths in the real domain passes through the complex domain. -Jacqes Salomon Hadamard

No one will expel us from this paradise Cantor has created for us. -David Hilbert

If only I had the theorems! Then I should find the proofs easily enough. -Bernard Riemann

The infinite! No other question has ever moved so profoundly the spirit of man. -David Hilbert

When you can measure what you are talking about and express it in numbers, you know something about it. -Lord William Thomson Kelvin

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts. -Andrien-Marie Legendre (1752-1833) (All of Fermat's theorems have now been proven.)

What we know is not much. What we do not know is immense. -Pierre-Simon Laplace

One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them. -Heinrich Hertz

The essential fact is simply that all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures... the Great Architect of the universe now begins to appear as a pure mathematician. -Sir James Jeans.

A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction. ― Leo Tolstoy