Poincaré on how the solution to mathematical problems can often be inspired by nature

Ship of Theseus

The Ship of Theseus is a thought experiment proposed by the ancient Greek philosopher Plutarch (1st-2nd century AD). The Ship of Theseus was preserved by the Athenians as a museum piece. Over time as its wooden parts decayed they were gradually replaced with new…

Schwinger limit

This is the weakest electric field you need to spontaneously create electron-positron pairs.

42 is the sum of 3 cubes.

Characterizing the numbers that can be expressed as a sum of 3 cubes of integers (x³+y³+z³=n) has been long-standing unsolved problem in number theory.

114 is now the smallest unsolved case.

Microbial Art

These beautiful structures illustrate the coping mechanism that bacteria have learned to employ as they adapt to hostile environments.

🦠 🖼️

Basel Problem: 1/1² + 1/2² + 1/3² + 1/4² + ... = ?

Some of the brightest mathematicians like Newton, Liebniz and Jakob Bernoulli struggled with this simple series.

It was only in 1734 that Euler - at the age of 27 - found that this infinite series converged to π²/6.

'The Uncanny Valley' published by Masahiro Mori in 1970 explores how our affinity for robots changes as they become more human-like.

This paper has had a big impact on human-computer interaction and is especially relevant today's AI landscape.

Read on: fermatslibrary.com/s/the-uncanny-…

The letter π was first introduced as a symbol for the ratio of the circumference of a circle to its diameter by the Welsh mathematician William Jones in 1706.

π is the first letter of the Greek word 'peripheria' (περιφέρεια), which means perimeter.

Here are the only temperatures that are prime integers in both Celsius and Fahrenheit

Here is the only number that cannot be written as x² + 2y² + 7z² + 11w²

'A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.' - Max Planck

11¹¹ = 285311670611 contains exactly two embedded elevens

The infinite gift 🎁 is an interesting object where the side of the nth box is 1/√n. As n→+∞, the gift has infinite surface area and length but finite volume!

This week's paper is 'What is good mathematics?' by Terence Tao.

Paper: fermatslibrary.com/s/what-is-good…

No century begins with a Tuesday, Thursday, or Sunday

Here's a curious fact about e and π

There's enough DNA in the body of a human to stretch from the Sun to Pluto and back 17 times.

The 'πᵗʰ root of 4' can be expressed as the following limit

Here are a few examples of anomalous cancellations: a particular kind of arithmetic procedural error that gives a numerically correct answer. Can you derive a few elementary properties of anomalous cancellations?

'Nobody else took what I was doing seriously, so nobody would want to work with me. I was thought to be a bit eccentric and maybe cranky'

Peter Higgs, the physicist who discovered the theoretical mechanism explaining the origin of mass in the universe, has passed away today.