Pierre de Fermat

The purpose of life is not to be happy. It is to be useful, to be honorable, to be compassionate, to have it make some difference that you have lived and lived well.

Challenges are what make life interesting and overcoming them is what makes life meaningful.

The only way to escape the corruptible effect of praise is to go on working.

I could not, however, make use of the method of descent, which I have often employed with success, because the problem is of a different nature.

I have found a very great number of beautiful theorems of arithmetic. I will send you some of them if you wish.

Every number which is not a prime, and which is not a power of a prime, is the sum of two squares.

If a prime number P divides a number A, then P also divides A to the power of P minus one, minus one.

The area of a right-angled triangle whose sides are integers can never be a square number.

I have discovered a method for finding the maxima and minima of curves, and for drawing tangents to them, which is not inferior to that of Descartes.

The shortest path between two points is a straight line.

I have found a method for finding the center of gravity of any solid, which is more general than that of Archimedes.

I have discovered a method for finding the area of any curve, which is more general than that of Archimedes.

I have discovered a method for finding the volume of any solid, which is more general than that of Archimedes.

I have discovered a method for finding the length of any curve, which is more general than that of Archimedes.

I have discovered a method for finding the tangent to any curve, which is more general than that of Archimedes.

I have discovered a method for finding the maximum and minimum of any function, which is more general than that of Archimedes.

I have discovered a method for solving all problems of geometry by means of algebra, which is more general than that of Vieta.

I have discovered a method for solving all problems of arithmetic by means of algebra, which is more general than that of Diophantus.

I have discovered a method for solving all problems of optics by means of algebra, which is more general than that of Kepler.

I have discovered a method for solving all problems of mechanics by means of algebra, which is more general than that of Galileo.