Quotes About Mathematics

partial sum is correct within an error less than the first term neglected.

today they are usually called the Fresnel integrals. One does still see them also called the Euler integrals, however, and it was Euler who first evaluated them.

In particular, the three roots to a cubic polynomial either must all be real, or there must be one real root and one conjugate pair.

the quadrature problem is a measure of the greatest difficulty, since it was shown in 1882 to be impossible.

mean proportional, i.e., if b and c are two given positive numbers, then x is the mean proportional of b and c if it satisfies the statement "b is to x as x is to c." Or, in algebra which

That is, he would have started over from the beginning to solve with, again, both p and q non-negative. This is totally unnecessary, however, as at no place in the solution to x3 + px = q did he ever actually use the non-negativity of p and q. That is, such assumptions have no importance, and were explicitly made simply because of an unwarranted aversion by early mathematicians to negative numbers. This

the tangent function is periodic with period 180°,

for the irreducible case with all three roots real, there is just one positive root; that is, the root given by the Cardan formula

The breakthrough for came not from quadratic equations, but rather from cubics which clearly had real solutions but for which the Cardan formula produced formal answers with imaginary components.

the product of two sums of two squares of integers is always expressible, in two different ways, as the sum of two squares of integers.

been given the basic grounding for a new science which is at once simpler and more embracing than the mathematical monstrosity we have conjured up.

One of the things that ultimately led me to leave mathematics and go into political science was thinking I could prevent nuclear war.

The cosmos is the ordering of number. Perception is the imaging of form contained in the potential of number. Robert Lawlor

Why are you still a priest?" Eigen asked, not letting the subject go. "My dear girl," Karras said. "I remain a goddamn cleric because in this world one needs something to hide behind. I have chosen this fucking collar. You have chosen mathematics.

Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.

Blowing up a few buildings is a lot better than an exploding planet, but people aren't very interested in simple arithmetic when there's blame to assign.

Calabi-Yau manifold

Do you know what the mathematical expression is for longing? ... The negative numbers. The formalization of the feeling that you are missing something.

To Plato, God was a mathematician. To Kepler, too, and to Biehl and Fredhoj. I do not believe it was a coincidence that their main subjects were biology and mathematics. A purpose behind them, the purpose that steered both them and the school, had caused them to align their own fates as closely as possible with God.

Fermat wrote in the margin: "I've discovered a truly wonderful proof for this argument. Unfortunately, this margin is too narrow to contain it." Two

Bertrand Russell wrote that pure mathematics is the field in which we don't know what we're talking about or to what extent what we say is true or false.

You can explain coincidence to me in mathematics all you like, but it won't kill the magic or the mystery.