Posts

• Fri 14 February 2025 - Dihedral Groups Are Semidirect Products [mathematics] [semidirect products] [presentations] [extensions] - updated: Wed 01 April 2026
• Wed 25 March 2026 - Cholesky Factorization Characterizes Positive Definiteness [mathematics] [inner products] [spectral theorem] [quadratic forms]
• Tue 24 March 2026 - Universal Machines Encode Programs as Data [mathematics] [computability] [incompleteness] [Turing machines]
• Wed 18 March 2026 - Seifert--van Kampen Builds a Fundamental Group from an Open Cover [mathematics] [fundamental groups] [covering spaces] [van Kampen theorem]
• Thu 10 February 2022 - The Torus Fundamental Group Has One Commutator Relation [mathematics] [fundamental groups] [covering spaces] [van Kampen theorem] - updated: Tue 17 March 2026
• Thu 21 November 2024 - Baker--Campbell--Hausdorff Corrects Noncommutative Addition [mathematics] [Lie algebras] [brackets] [matrix groups] - updated: Sun 15 March 2026
• Thu 12 March 2026 - The sl2 Commutation Relations Fit in Three Generators [mathematics] [Lie algebras] [brackets] [matrix groups]
• Mon 02 March 2026 - The Prime Number Theorem Is a Statement about Chebyshev's Function [mathematics] [analytic number theory] [zeta functions] [Dirichlet characters]
• Thu 19 February 2026 - Linearized Polynomials Encode F_q-Linear Maps [mathematics] [finite fields] [Frobenius] [normal bases]
• Mon 08 September 2025 - Bézout Counts Plane Intersections with Multiplicity [mathematics] [projective geometry] [Proj] [Hilbert polynomials] - updated: Mon 16 February 2026
• Sat 07 February 2026 - A Short Exact Sequence Is an Extension [mathematics] [modules] [exact sequences] [homological algebra]
• Sat 30 August 2025 - Sobolev Norms Penalize High Frequencies [mathematics] [Fourier analysis] [convolution] [Sobolev spaces] - updated: Wed 21 January 2026
• Mon 19 January 2026 - The Cycle Index Averages Monomials of Cycle Counts [mathematics] [Polya enumeration] [combinatorial species] [symmetry]
• Sat 17 January 2026 - Cantor's Theorem Makes Every Power Set Larger [mathematics] [set theory] [cardinals] [choice]
• Thu 29 December 2022 - Tilde Turns Modules into Quasi-Coherent Sheaves [mathematics] [sheaves] [quasi-coherent sheaves] [differentials] - updated: Sun 11 January 2026
• Mon 05 January 2026 - Combinatorial Species Turn Constructions into Series [mathematics] [Polya enumeration] [combinatorial species] [symmetry]
• Tue 08 October 2024 - Odd p-Adic Squares Are Detected Modulo p [mathematics] [p-adic numbers] [valuations] [Hensel lemma] - updated: Wed 17 December 2025
• Mon 15 December 2025 - Faithfully Flat Base Change Detects Vanishing [mathematics] [flatness] [regular sequences] [depth]
• Thu 20 November 2025 - Singular Value Decomposition Works for Every Matrix [mathematics] [matrix factorizations] [least squares] [positive matrices]
• Mon 27 October 2025 - Beta Is a Quotient of Three Gamma Values [mathematics] [special functions] [asymptotic analysis] [distributions]