Matthew Ward – Cantor's Archive
Discrete Mathematics
How Many Distances Must Be Made from N Points?
My most striking contribution to geometry is, no doubt, my problem on the number of distinct distances. This can be found in many of my papers on combinatorial and geometric problems. -Paul Erdős, On Some of My Favorite Theorems, 1996. Erdős is one of the greatest mathematicians from history, and
Riemann Hypothesis
A Fun Proof of the Riemann Hypothesis
Real math about a fictional object.
Abstract Algebra
How Many Number Fields Are There?
Modern results on a problem from the 1800s.
Probability Theory
What is the Probabilistic Method?
On proving that things exist without constructing them
Topology
Two Compactification Theorems
A Brief History of Spread-out Spaces.
Number Theory
Euler’s Odd Perfect Numbers Theorem
An ancient proof to give insight into an unsolved problem.
Bayesian Statistics
What is Bayesian Statistics?
A single, basic example: fully explained.
Arithmetic
Multiplication is Repeated Addition
The strange debate and controversy in K-12 math education
Number Theory
Faltings’s Theorem and the Mordell Conjecture
On the number of rational solutions to polynomials.
Quantum Physics
Mathematical Uncertainty Principles
How to understand a core idea from Quantum Mechanics.
Bayesian Statistics
The Carter Catastrophe
A Bayesian argument for why humans will soon be extinct
Topology
The Hodge Conjecture
Get $1 million if you solve this math problem.