The Potato Paradox is a really weird mathematical paradox that I found in Alexander Kruel's newsletter [https://axisofordinary.substack.com/p/the-most-counterintuitive-facts-in]. Here's the description of the paradox from Wikipedia [https://en.wikipedia.org/wiki/Potato_paradox]: > Fred brings

Via [https://fermatslibrary.com/s/pick-the-largest-number]the Fermat's Library, a paper that describes a really strange mathematical result: * Write two distinct numbers on slips of paper and give them face down to a friend. * Your friend chooses one slip at random and

A good introduction to Bayes' theorem:

One of the things I enjoy reading about is the intuitions of experts in cold, hard, logical fields like mathematics and physics. Years ago I assumed that a breakthrough in such a field must require a similar thought process – rigid, methodological, with no room

The Mathematics YouTube channel 3Blue1Brown has a video [https://www.youtube.com/watch?v=Kas0tIxDvrg] on how exponential growth works, particularly in the context of COVID-19. Worth watching.

Zipf's law is the observation that the frequency of words in almost all known texts in any language follow a power law. This video [https://www.youtube.com/watch?v=fCn8zs912OE] starts by exploring Zipf's law but quickly expands its

This article [https://www.americanscientist.org/article/knowing-when-to-stop] from the American Scientist gives a good overview of optimal stopping problems – a field of mathematics that has surprisingly practical applications in daily life.

This simulation [https://ciechanow.ski/tesseract/] demonstrates the tesseract, which is roughly speaking a four dimensional cube. i.e., just as a cube (a three dimensional object) is made of six equally sized squares (two dimensional object), the tesseract is an object in four

Here's [https://www.cut-the-knot.org/Curriculum/Geometry/RABH.shtml] a really elegant proof for the area of a circle. We assume the circle is made up of an infinite number of circular lines. We then straighten the lines out and stack them

We all love to make predictions, but how good are we really at making them? The Brier score [https://en.wikipedia.org/wiki/Brier_score] is an easy way to quantify the accuracy of your decisions. It's quite simple to calculate: BS

Compound interest and exponential growth in general can be difficult to understand intuitively. This [https://wealth.visualcapitalist.com/visualizing-power-compound-interest/] infographic helps visualize what it looks like.

About 2400 years ago Euclid found an incredibly elegant proof [https://www-users.cs.york.ac.uk/susan/cyc/p/primeprf.htm] that there were an infinite number of primes.