Topology
Two Compactification Theorems
A Brief History of Spread-out Spaces.
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Optimization
The Method of Lagrange Multipliers
How to solve constrained optimization problems.
Analysis
Cantor’s Diagonal Argument
“Diagonalization seems to show that there is an inexhaustibility phenomenon for definability similar to that for provability” — Franzén…
Geometry
Three Quick Math Problems
Can you solve all three?
Economics
Is Economics a Science?
A Debate on the Scientific or Ideological Nature of Economics
Geometry
How Aristarchus Estimated the Distance to the Sun
How far are you, my Sunshine?
Quantum Mechanics
How Quantum Mechanics Alters Reality
The double-slit experiment
Calculus
Trapezoidal Rule: A Method of Numerical Integration
The knowledge of which geometry aims is the knowledge of the eternal. — Plato
Analysis
Why is 1 + 2 + 4 + 8 + … = -1?
On calculating infinite divergent series sums
Ramsey Theory
Theorem on Friends and Strangers
A side step into Ramsey Theory and a big number
Relativity
Can Transatlantic Flight Paths explain General Relativity?
The Geometry of Great Circle Routes and the Curvature of Spacetime
Calculus
The Fundamental Theorem of Calculus
The beginner’s guide to proving the Fundamental Theorem of Calculus, with both a visual approach for those less keen on algebra, and an…