# Quantum Tunnel Podcast – E1

This episode is in English.

Pierre de Fermat

Pierre de Fermat who is said to be the greatest mathematician of the seventeenth Century.

In 1629 he invented analytic geometry, but most of the credit went to Descartes, who did publish his own similar ideas in 1637. At this time – 13 years before Newton was born – Fermat discovered a method for drawing tangents to curves and finding maxima and minima, which amounted to the elements of differential calculus.

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His discovery of the principle of least time and its connection with the refraction of light was the first step in the development of a coherent theory of optics. It was however in the theory of numbers that Fermat’s genius shone most brilliantly. Among his discoveries in this field, the most famous are:

• Fermat’s two square theorem: Every prime number of the form $4n+1$ can be written as the sum of two squares in one and only one way.
• Fermat’s theorem : If $p$ is any prime number and $n$ is any positive integer, then $p$ divides $np-n$.
• Fermat’s last theorem: If $n>2$, then the equation $x^n+y^n=z^n$ cannot be satisfied by any positive integers $x, y$ and $z$.

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