Fermat's Library

Stefan Banach was born exactly 133 years ago. Here’s an interesting instance of the Banach fixed-point theorem

"It is through logic that we prove, but through intuition that we discover" - Poincaré

"There are two possible outcomes: if the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery" - Enrico Fermi

In 1633, Descartes shelved "The World" after learning Galileo had been condemned for Heliocentrism. He feared the Church. Ironically, he still hoped his physics would be taught in Catholic schools someday.

Paul Erd?s was born exactly 112 years ago. "A mathematician is a machine for turning coffee into theorems"

This handwritten letter featuring the famous E=mc2 was sold for $1.2M. In this week's paper, Ryan Dahn explores what Einstein’s handwriting tells us about the man himself. Here's the annotated paper: https://lnkd.in/d3n5E-b5

Joseph Liouville was born exactly 216 years ago. In 1844, he became the first person to prove the existence of transcendental numbers — numbers that are not roots of any non-zero polynomial equation with integer coefficients — and provided the first explicit decimal examples, such as the Liouville constant.

A beautiful plot created by Jahnke and Emde in 1933, before the advent of computers, featured in their book Tables of Functions with Formulae and Curves.

Here's an example when scientists were wrong - and the outsider was right In Gulliver’s Travels (1726), Jonathan Swift mocked British scientists for failing to solve the Longitude Problem: how to track your east-west position within a mile after crossing the Atlantic. It was the great scientific challenge of the 18th century. Parliament offered ￡20,000 - worth millions today - for a solution, entrusting the Royal Observatory to award the prize. In 1731, a self-taught clockmaker, John Harrison, cracked it. The astronomers didn’t believe him. For 40 years, Harrison refined his invention while the Observatory stonewalled. Only in 1773 - by act of Parliament - did he finally receive the prize and east-west navigation could be made safe.

That’s how close a human once came to Mars on August 2003 — the closest in 60,000 years. Closer than the Apollo astronauts. This was due to a rare alignment between Earth and Mars known as perihelic opposition - we won't get this close again until 2287.