Mathematics
BigCat's Mathematical Lens
Probability · Calculus · Linear Algebra · Topology · Information Theory · Mathematical Beauty
Day 1
The Beauty of Mathematics
Euler's identity · golden ratio · symmetry · the beauty of proof
Day 2
Probability and Uncertainty
Bayes' theorem · Monte Carlo · expected value · law of large numbers
Day 3
The Essence of Calculus
limits · derivatives · integrals · fundamental theorem
Day 4
The Essence of Linear Algebra
vectors · matrices as transformations · eigenvectors · determinants
Day 5
Complex Numbers & Geometry
the complex plane · Euler's formula · multiplication as rotation · why QM needs complex numbers
Day 6
The Beauty of Number Theory
prime distribution · Riemann hypothesis · RSA · Fermat's Last Theorem
Day 7
Combinatorics
permutations & combinations · pigeonhole · inclusion–exclusion · generating functions
Day 8
Graph Theory
nodes & edges · the Königsberg bridges · Dijkstra · network effects
Day 9
Intuitive Topology
homotopy · Möbius strip · high-dimensional spheres · topological data analysis
Day 10
Geometry & Curvature
non-Euclidean geometry · curvature · Theorema Egregium · gravity as curvature
Day 11
Set Theory & Infinity
bijection · Cantor diagonal · Russell's paradox · ZFC axioms