Infinity
Problems with infinity*
I had the pleasure of witnessing this interaction the other day: two kids were locked in a battle of wits to see who could think of the…
Mathematics
Mathematics
Proving Arrow’s Impossibility Theorem
Let’s prove the result behind why group decisions, from democracy to take-away choice, are always flawed.
History
The Mathematical Center of the Universe
The inception of quantum mechanics can essentially be traced back to a single “Golden Age” in the mid-1920s at one university: the Georg-August University of Göttingen, in the city of Göttingen in Germany.
Group Theory
The Rubik’s Icosahedron and the Mathieu Group M12
Modeling this construction using GAP
Mathematics
1988 IMO Question Six
Solving the Hardest Problem on the Hardest Test
Feynman
Richard Feynman on the Differences between Mathematics and Physics
“I would like to make a number of remarks on the relation of mathematics and physics”
Number Theory
The History of Euler’s Number (e)
From Napier Table’s To Bernoulli’s Compounding Interest
Mathematics
The Besicovitch 1/2 Conjecture
Unsolved weirdness in 1-dimension
Mathematics
Understanding Exponents
Countering Our Limited Intuition Towards Exponential Functions
Mathematics
The Geometry of Pitch Class Sets
Strange Spaces in Music Theory
Mathematics
A Computability Proof of Gödel’s First Incompleteness Theorem
A computability proof of Gödel’s incompleteness theorem equally as strong as Gödel’s version, but much easier to deduce
Mathematics
The Envy-Free Cake-Cutting Procedure
How to Ensure Fairness as a Mechanistic Outcome. Implications for policy?