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
Day 12
Logic & Proof
propositional logic · predicate logic · Gödel's incompleteness · formalization
Day 13
Information Theory
Shannon entropy · mutual information · channel capacity · cross-entropy & neural nets
Day 14
Optimization
gradient descent · convexity · Lagrange multipliers · stochastic gradient descent
Day 15
Discrete Mathematics
induction · recursion & recurrence · Big-O complexity · discrete probability
Day 16
Dynamical Systems
fixed points · Lorenz attractor · chaos & determinism · double pendulum
Day 17
Fractals & Self-Similarity
self-similarity · fractal dimension · Mandelbrot set · fractals in nature
Day 18
Symmetry & Noether's Theorem
symmetry as invariance · groups · least action · Noether's theorem
Day 19
Category Theory
categories · functors · natural transformations · monads & Curry-Howard
Day 20
Group Theory
group = reversible actions · symmetric group Sₙ · Lagrange's theorem · action & representation
Day 21
Measure Theory & Foundations of Probability
σ-algebra · measure & null sets · Lebesgue integration · probability as measure
Day 22
Differential Equations
ODEs & population · heat equation · wave equation · numerical methods
Day 23
The Arc of Mathematical History
Greek geometry → Arabic algebra → Newton & Leibniz → Hilbert's 23 problems
Day 24
Gödel, Turing, Church
computability & provability · the halting problem · λ-calculus
Day 25
Mathematics & Art
wallpaper groups · projective perspective · the golden ratio, critiqued · Bézier curves
Day 26
Mathematics & Music
harmonics · equal vs just temperament · Fourier analysis · why music pleases
Day 27
Probability Paradoxes
Monty Hall · birthday · two envelopes · Bertrand · Simpson
Day 28
How to Solve It (Pólya)
understand · plan · execute · review · invariants · the extremal principle
Day 29
Frontiers of Pure Mathematics
Fermat & modularity · Poincaré & Ricci flow · Zhang & prime gaps · Langlands
Day 30
The Mathematics of AI
backpropagation · attention · nets as function approximation · the manifold hypothesis
Day 31
The Mathematics of Game Theory
Nash equilibrium · the Shapley value · mechanism design · evolutionary games
Day 32
The Mathematics of Cryptography
modular arithmetic & RSA · elliptic curves · post-quantum lattices · zero-knowledge proofs
Day 33
Coding & Error Correction
the Shannon limit · Hamming codes · Reed–Solomon · how QR codes work
Day 34
The Traps of Statistical Inference
p-value misuse · multiple comparisons · effect size & the winner's curse · Bayesian vs frequentist
Day 35
Operations Research
LP & duality · max-flow min-cut · queueing theory · scheduling
Day 36
Computational Complexity
P vs NP · reductions · NP-completeness · quantum complexity
Day 37
The Mathematics of Randomness
random walks · martingales · Brownian motion · random matrices
Day 38
Discrete Geometry & Packing
Kepler's conjecture · tilings & quasicrystals · Voronoi diagrams · convex hulls
Day 39
Complex Analysis
holomorphic functions · the residue theorem · conformal maps · Riemann surfaces
Day 40
Fourier Analysis
the frequency domain · the FFT · wavelets · transform coding & sparsity
Day 41
Probabilistic Graphical Models
Bayesian networks · Markov chains · hidden Markov models · inference as message passing
Day 42
The Impossible in Mathematics
squaring the circle · the quintic (Galois) · the parallel postulate · uncertainty
Day 43
Combinatorial Optimization
the traveling salesman · approximation algorithms · matching theory · matroids
Day 44
Functional Analysis
functions as vectors · Hilbert space & projection · operators & spectrum · the math of QM
Day 45
Mathematics & Biology
population dynamics · Turing patterns · phylogenetic trees · protein folding
Day 46
Mathematics & Economics
fixed-point theorems · general equilibrium · Black–Scholes · Arrow's theorem
Day 47
Model Theory & Foundations
first-order logic & completeness · compactness · non-standard analysis · decidability
Day 48
Spectral Graph Theory & Networks
graph Laplacian · random-graph transition · Cheeger's inequality · GNNs
Day 49
Applied Topology
homology & the shape of data · persistent homology · knot invariants · braiding as computation
Day 50
Number Theory Applied
congruences & calendars · primality testing · tuning & ratios · continued fractions
Day 51
Visual Thinking in Mathematics
high-dimensional intuition · projection & dimensionality reduction · continuous deformation · visual encoding
Day 52
Differential Geometry
geodesics · the Gauss–Bonnet theorem · fiber bundles · gauge theory
Day 53
The Philosophy of Mathematics
Platonism · formalism & intuitionism · unreasonable effectiveness · independence of CH
Day 54
The Mathematics of Decisions & Gambling
expected utility · coherent risk measures · the Kelly criterion · multi-armed bandits
Day 55
Mathematics & Music, Deeper
scales as Diophantine approximation · rhythm as group theory · time–frequency uncertainty · algorithmic composition
Day 56
The Riemann Hypothesis & Primes
PNT as a zero-free line · the explicit formula · L-functions & GRH · the Langlands program
Day 57
The Mathematics of Fair Design
envy-free division · Arrow's impossibility · VCG & revenue equivalence · stable matching
Day 58
The World of Differential Equations
predictability horizon · solitons · Fisher–KPP fronts · CFL & neural operators
Day 59
The Competition Mindset
invariants · the extremal principle · coloring arguments · construction & counterexample
Day 60
The Frontier of Mathematics
the abc conjecture · machine-assisted proof · experimental math · the future
Day 61
Statistical Learning Theory
PAC learning · VC dimension · generalization bounds · why deep nets shouldn't generalize but do
Day 62
Numerical Analysis & Floating Point
IEEE 754 & rounding · condition number & stability · catastrophic cancellation · from LU to low precision