Visual guide to the Quantum Fourier Transform: from binary numbers and roots of unity to the QFT circuit, with comparisons to classical DFT and implications for Shor's algorithm.

From 1/x to the Schwarzschild radius: what singularities mean in analysis and general relativity, and whether they correspond to anything physically real.

A minimum working example comparing Newtonian and Einsteinian gravity using Mars' orbit — starting from the Schwarzschild metric and solving the resulting differential equations numerically.