About A Once-in-a-Century Proof: The Kakeya Conjecture

Wavelet Analysis and Universality in Stochastic Parabolic PDEs The Langlands Program: Connecting Number Theory and Harmonic Analysis The Geometric Langlands Conjecture: Sheaves and Representation Duality Geometry of Numbers: Analogues of Gauss Composition in Quadratic Expressions Tensor Decomposition for Optimizing Matrix Multiplication Algorithms Convergence from Newtonian Dynamics to the Boltzmann Equation (Hilbert's Sixth Problem) Empathy and the Curse of Knowledge in Mathematics Communication Competition Math Problems as Training for Creative Logical Reasoning Quantum-Entangled Interactive Proof Systems and the Limits of Verification (MIP* = RE) The 17 Wallpaper Groups: Symmetry Classification of Repeating Patterns Infinite-Width Neural Networks as Kernel Machines, the Continuum Hypothesis, and Liouville Quantum Gravity High-Dimensional Sphere Packing via Graph-Theoretic Independent Sets The Four Color Theorem and Computer-Assisted Proof Order vs. Randomness: Ramsey Numbers, Aperiodic Tilings, and Arithmetic Progressions The Unique Games Conjecture and Hardness of Approximation Carmichael Numbers and the Distribution of Pseudoprimes Cantor's Diagonal Argument for Uncountable Infinity Eclipse Prediction Using Saros Cycles and Newtonian Three-Body Mechanics Geometric Structures on Surfaces and Moduli Space Deformations Frequency Shredding Operators for Global Parameter-Space Analysis in Polygonal Billiards Exotic Smooth Structures on Four-Manifolds The Riemann Hypothesis and the Distribution of Prime Numbers Quantum Field Theory as a Non-Rigorous Source of New Mathematics Game Trees as Geometric Structures for Deriving Perfect Strategies Formal Proof Verification and Proof Assistants (Lean) in Mathematics The Mandelbrot Set via Iterated Quadratic Maps Discovery-Based Problem Solving and Productive Discomfort in Learning Universality in Random Matrix Theory and Physical Systems The Interpolation Problem, Standard Bubble Clusters, and the Expectation Threshold Conjecture