Number Theory – Cantor's Archive

Kronecker

Kronecker, God and the Integers

Natural numbers were created by God, everything else is the work of men — Kronecker (1823–1891).

Number Theory

Perfect Numbers

An ancient riddle

Prime Numbers

The Goldbach Conjecture

An Equivalent Formulation of an Unsolved Mystery

Number Theory

The Euler Totient Function

A Probabilistic Approach

Number Theory

Transcendental Numbers

Into the Unknown

Riemann Hypothesis

A Fun Proof of the Riemann Hypothesis

Real math about a fictional object.

Number Theory

The Euler-Mascheroni Constant

Remember the harmonic series? More often than not, it serves as one’s first encounter with a series wherein individual terms diminish successively yet the series diverges to infinity. The below quote nicely sums the up notoriousness of the harmonic series: Today I said to my calculus students, “I know,

Euler

The Most Beautiful Equation in the World

And the Geometry of Numbers

Philosophy

Professor E. Brian Davies’s Mathematical Empiricism

This commentary is on the relevant parts of Davies’s book, Science in the Looking Glass. The following is not a book review.

Babylonian

A Modern Look at Square Roots in the Babylonian Way

Revisiting the Babylonian method for square roots: why and how does it work?

Ramanujan

It’s Time for a Breakdown (of Numbers)

Now it’s time for a breakdown… (cue En Vogue’s My Lovin’ (You’re Never Gonna Get It)) In particular, a breakdown of numbers!

Pi

A slice of π

π is ubiquitous both in mathematics and physics. Its appearance in some contexts are intuitive to grasp. Others require intellectual contortion, a mind-bending that defies all intuition.