Analysis
Mathematical Induction: The Domino Effect in Natural Numbers
We discuss the concept of mathematical induction on the natural numbers and give some examples.
Latest
Quantum Electrodynamics
The Strange Theory of Light and Matter
The Nobel Prize in Physics 1965: Sin-Itiro Tomonaga, Julian Schwinger, and Richard P. Feynman
Prime Numbers
Discovering Zero Among the Prime Numbers
It was a big surprise discovering zero when I was really looking for prime numbers. Back in 1992, I had a simple computer at my disposal …
Ramsey Theory
The Erdős–Szekeres Theorem
Monotonicity will prevail
Relativity
Thinking Relativistically
Problem-solving in special relativity.
von Neumann
John von Neumann’s 1935 letter to Oswald Veblen
Mathematical Gossip
Harmonic Analysis
Discrete and Fast Fourier Transforms
Visually and mathematically
Number Theory
Faltings’s Theorem and the Mordell Conjecture
On the number of rational solutions to polynomials.
Prime Numbers
The Infinity of Primes
We present two proofs of one of the great theorems in number theory, namely that there are infinitely many primes.
Calculus
Another Proof Of Zero Equals One
The first experience with calculus is usually quite memorable for most of us. For some it introduces a tool of immense beauty and…
Prime Numbers
The Twin Prime Conjecture
Are there infinitely many primes p such that p + 2 is prime?
Astrophysics
Black Hole Entropy and the Laws of Thermodynamics
The Remarkable Similarities Between the Black Holes Mechanics and Laws of Thermodynamics