Martin Gardner tweet

Water is densest at 4°C. This property is the reason why lakes freeze from the top down. 💧 water at 4°C is denser than water at both lower and higher temperatures ❄️ as water cools from room temperature toward 4°C, it becomes denser and sinks but as it cools further from 4°C toward 0°C, it becomes less dense and rises 🧊 at 0°C liquid water turns to ice, which is less dense, which is why it floats So in a cooling lake, the sequence is: warmer water cools and sinks until it reaches 4°C, then the coldest water (approaching 0°C) actually rises to the surface where it can freeze. The 4°C water, being densest, settles at the bottom.

Principia Mathematica takes over 360 pages to prove 1+1=2. It's not because the authors were unsure of the answer, but because they were trying to prove that all of mathematics could be built from the ground up using nothing but pure logic.

In 1808, the French mathematician Christian Kramp introduced the "!" as the factorial symbol as a convenience to the printer. Before him, Euler, Stirling, and others, used more verbose notations like 𝑛⋅(𝑛−1)⋅(𝑛−2)⋯1