Shatranj Ke Khilari
Premchand's chess players, Zermelo, and the difference between playing a game well and playing the right game at all.
Blog
Interesting Number Plates
Taxicab numbers, Carmichael liars, Kaprekar attractors, Wieferich primes, and Grothendieck's 57.
Ham Sandwich Theorem
One plane that bisects three objects at once: the intermediate value theorem meets Borsuk–Ulam.
Jordan Curve Theorem
Every simple closed curve splits the plane into inside and outside, and why proving it is hard.
Quaternions
From Broom Bridge to modern attitude control: smooth 3D rotations without gimbal lock.
How Many Times Do You Need to Shuffle a Deck of Cards Before It Is Truly Random?
Diaconis, riffle shuffles, and the cutoff phenomenon behind the famous threshold of seven.
Bounded Gaps Between Primes
Unbounded prime gaps, bounded liminf, and how Zhang, Maynard, and Polymath pushed the frontier.
Dirac Delta Function
A perfectly sharp tap, its sifting property, and why its Fourier transform is constant.
Quantum Zeno Effect
Frequent measurement that freezes decay, and the intermediate-rate anti-Zeno acceleration.
The Lady, or the Tiger?
Ill-posed inverse problems and why one bit of information cannot justify the ending.
Lie Groups
Symmetries that vary smoothly: groups like rotations, and their infinitesimal Lie algebras.
Green's Functions
How systems react to a single point poke, and why that response gives the solution to any forcing.
Fourier Series
Turning jagged periodic patterns into weighted sums of smooth waves, and what happens near jumps.
Gödel's Proof of the Existence of God
Gödel, modal logic, and the ontological argument: formal assumptions that force a conclusion.
Arnold's Cat Map
Stretching and folding a square: a perfectly deterministic transformation that looks, for all practical purposes, like chaos.
Isospectral Shapes
Drums that sound the same: isospectral polygons and the transplantation idea that preserves spectra.
On Recording Patterns
Mathematics is not an artistic overlay placed upon reality, but the grammar through which reality permits itself to be analysed at all.