Riemann – Cantor's Archive

Series

The Mind-Boggling Properties of the Alternating Harmonic Series

Riemann’s simple algorithm to approximate computationally any real number

Philosophy

The Demons of the Mathematicians

There is a rich history of mathematicians, philosophers, and other thinkers invoking demons (real or imaginary) in their reasonings. The tradition goes back at least to the iconic ancient Greek philosopher Socrates.

Topology

The Hardest Math Problems

Six Difficult Ways of Becoming a Millionaire

Complex Analysis

A Gentle Introduction to Analytic Continuation

How to Extend the Domain of Analytic Functions

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.

Physics

Extending Einstein’s Field Equations

Wave Properties of Matter in Gravitational Fields