Here's an even more expansive iceberg of math theorems, with 100 entries categorized by difficulty: Above Water: 1. Pythagorean Theorem 2. Arithmetic Mean-Geometric Mean Inequality 3. Fundamental Theorem of Arithmetic 4. Euclidean Algorithm 5. Euler's Formula for Polyhedra 6. Thales' Theorem 7. Triangle Inequality 8. Binomial Theorem 9. Cramer's Rule 10. Descartes' Rule of Signs 11. Vieta's Formulas 12. Fundamental Theorem of Calculus 13. Rolle's Theorem 14. Intermediate Value Theorem 15. Squeeze Theorem Just Below the Surface: 16. Fermat's Little Theorem 17. Lagrange's Theorem (Group Theory) 18. Fundamental Theorem of Algebra 19. Divergence Theorem 20. Green's Theorem 21. Cauchy's Integral Formula 22. Cayley-Hamilton Theorem 23. Fundamental Theorem of Galois Theory 24. Picard-Lindelöf Theorem 25. Cantor's Theorem 26. Liouville's Theorem 27. Rouché's Theorem 28. Gauss-Bonnet Theorem 29. Poincaré-Bendixson Theorem 30. Dirichlet's Theorem on Arithmetic Progressions Getting Deeper: 31. Cauchy-Schwarz Inequality 32. Bezout's Theorem 33. Sylow Theorems 34. Spectral Theorem 35. Brouwer Fixed Point Theorem 36. Nakayama's Lemma 37. Artin-Wedderburn Theorem 38. Stone-Weierstrass Theorem 39. Tychonoff's Theorem 40. Hilbert's Nullstellensatz 41. Heine-Borel Theorem 42. Baire Category Theorem 43. Urysohn's Lemma 44. Lefschetz Fixed-Point Theorem 45. Krein-Milman Theorem Deep Waters: 46. Zorn's Lemma 47. Hahn-Banach Theorem 48. Snake Lemma 49. Atiyah-Singer Index Theorem 50. Gödel's Incompleteness Theorems 51. Riemann-Roch Theorem 52. Serre Duality 53. Quillen-Suslin Theorem 54. Mostow Rigidity Theorem 55. Feit-Thompson Theorem 56. Deligne's Theorem on Weil Conjectures 57. Szemeredi's Theorem 58. Mirzakhani's Theorem on Riemann Surfaces 59. Ax-Grothendieck Theorem 60. Borel Determinacy Theorem The Abyss: 61. Yoneda Lemma 62. Grothendieck-Riemann-Roch Theorem 63. Langlands Correspondence 64. Monstrous Moonshine 65. abc Conjecture 66. Hodge Conjecture 67. Bloch-Kato Conjecture 68. Baum-Connes Conjecture 69. Standard Conjectures on Algebraic Cycles 70. Riemann Hypothesis 71. Tate Conjecture 72. Milnor Conjecture 73. Manin Conjecture 74. Sato-Tate Conjecture 75. Erdős-Gyárfás Conjecture Mariana Trench: 76. Birch and Swinnerton-Dyer Conjecture 77. Novikov Conjecture 78. Thurston's Geometrization Conjecture (Perelman's Proof) 79. Navier-Stokes Existence and Smoothness 80. P versus NP Problem 81. Jacobian Conjecture 82. Hadamard-Nelson Problem 83. Collatz Conjecture 84. Goldbach's Conjecture 85. Twin Prime Conjecture Challenger Deep: 86. Kissing Number Problem 87. Busemann-Petty Problem 88. Kakeya Conjecture 89. Whitehead Conjecture 90. Kaplansky's Conjectures 91. Hilbert's 16th Problem 92. Hilbert-Smith Conjecture 93. Zimmer's Conjecture 94. Bombieri-Lang Conjecture 95. Ramanujan-Petersson Conjecture Unknowable Depths: 96. Continuum Hypothesis 97. Axiom of Choice 98. Large Cardinal Axioms 99. Determinacy Axioms 100. Woodin's Ω-Conjecture This list delves into even more advanced and specialized areas of mathematics, including some of the most challenging open problems and foundational questions in set theory and logic. The "Unknowable Depths" section includes statements that are independent of ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice), meaning they cannot be proven or disproven within the standard axioms of mathematics. Please note that the difficulty rankings become increasingly subjective and debatable at the deeper levels, as many of these problems are still open and actively researched by mathematicians worldwide. AI pipeline that creates video lecture series from books The most general notion of intelligence: ability to find a solution in a certain set of domains, none or many Weak general intelligence: ability to find solutions in multiple domains Strong general intelligence: ability to generalize from one domain to previously unseen ones Exploring hyper abstract math is lovely, but now I'm trying to ground myself with concrete math predicting our physical universe as concretely as possible Everything around you works because of math, everything around you is math There is no "I", there is only math Infinitely meta nested conditional probabilities of probabilities encoded by ∞-categories Living systems maybe optimize for structural and functional stability across scales, maybe that's what we need to encode into our AI systems as an objective function <3 My Effective Omni is all about bringing the nerd tribes together by their common ground https://x.com/burny_tech/status/1801954086503252368?t=V-e7Nae3ObmmEDy5tR_Cow&s=19 Applied theoretics Theoretical applicatics [Mind mapper: MIT's new tech shows whole brain hemispheres in 3D detail](https://interestingengineering.com/science/mit-innovation-brain-hemispheres-mapping) Mind upload with all hardware implementation details soon? Do you abide in hedonium or hellium or voidium or exotic nonlinear combinations? Thousands brains theory model in the form of quantum machine learning algorithm running on topological quantum computers [Introducing Lamini Memory Tuning: 95% LLM Accuracy, 10x Fewer Hallucinations | Lamini - Enterprise LLM Platform](https://www.lamini.ai/blog/lamini-memory-tuning) [GitHub - timescale/pgvectorscale: A complement to pgvector for high performance, cost efficient vector search on large workloads.](https://github.com/timescale/pgvectorscale) [Sara Walker: Physics of Life, Time, Complexity, and Aliens | Lex Fridman Podcast #433 - YouTube](https://www.youtube.com/watch?v=wwhTfyX9J34) [Making Our Own Working Neuron Arrays! | DOOM Neurons Part 2 - YouTube](https://www.youtube.com/watch?v=c-pWliufu6U) [Topological game - Wikipedia](https://en.wikipedia.org/wiki/Topological_game) In mathematics, a topological game is an infinite game of perfect information played between two players on a topological space. Players choose objects with topological properties such as points, open sets, closed sets and open coverings. Time is generally discrete, but the plays may have transfinite lengths, and extensions to continuum time have been put forth. The conditions for a player to win can involve notions like topological closure and convergence. Too many AI people put current AI systems and brains into equivalence. There are many shared mathematical patterns, but the systems are still different in many ways! We need decentralization of power acceleration! https://x.com/jam3scampbell/status/1801843133124383010?t=iASZlVRuD3k-reGwgR_XJg&s=19