Posts

• Sun 19 October 2025 - Cauchy Products Encode Convolution [mathematics] [generating functions] [recurrences] [Lagrange inversion]
• Thu 16 October 2025 - The Circle Has Fundamental Group Z by Winding Number [mathematics] [fundamental groups] [covering spaces] [van Kampen theorem]
• Wed 04 May 2022 - A Rational Function Has a Principal Divisor [mathematics] [algebraic curves] [divisors] [Riemann--Roch] - updated: Wed 15 October 2025
• Tue 30 April 2024 - The Argument Principle Counts Zeros Minus Poles [mathematics] [complex analysis] [contour integration] [residues] - updated: Sat 04 October 2025
• Sun 19 March 2023 - The Regular Representation Contains Every Irreducible [mathematics] [representation theory] [characters] [group algebras] - updated: Fri 03 October 2025
• Wed 01 October 2025 - Factorisation Modulo p Reveals Cycle Types [mathematics] [polynomials] [discriminants] [Galois groups]
• Mon 01 September 2025 - Integrality Is Equivalent to a Finite Stable Module [mathematics] [integral extensions] [normalization] [spectra]
• Fri 08 August 2025 - Transfinite Induction Follows the Well-Ordering of Ordinals [mathematics] [set theory] [cardinals] [choice]
• Wed 19 July 2017 - Yoneda Identifies an Object through All Maps into It [mathematics] [category theory] [functors] [adjunctions] - updated: Thu 31 July 2025
• Fri 23 June 2017 - q-Cyclotomic Cosets Factor Roots of Unity over Finite Fields [mathematics] [finite fields] [Frobenius] [normal bases] - updated: Sun 27 July 2025
• Sun 08 November 2020 - The Riemann Tensor Is a Commutator Corrected by the Lie Bracket [mathematics] [curvature] [Gauss--Bonnet] [Jacobi fields] - updated: Mon 14 July 2025
• Mon 16 June 2025 - The Tutte Polynomial Is a Rank-Nullity Sum [mathematics] [graph enumeration] [chromatic polynomials] [matroids]
• Sun 26 July 2020 - A Splitting Field Is Generated by Every Root [mathematics] [splitting fields] [separability] [Galois theory] - updated: Sun 18 May 2025
• Mon 21 March 2022 - The Riemann--Roch Space Bounds Allowed Poles [mathematics] [algebraic curves] [divisors] [Riemann--Roch] - updated: Thu 08 May 2025
• Mon 28 April 2025 - Binomial Inversion Undoes a Subset Sum [mathematics] [enumeration] [binomial identities] [inclusion-exclusion]
• Tue 22 April 2025 - Morse Critical Points Have a Quadratic Normal Form [mathematics] [symplectic geometry] [Hamiltonian systems] [Morse theory]
• Mon 21 April 2025 - Cohen--Macaulay Rings Have No Depth Defect [mathematics] [flatness] [regular sequences] [depth]
• Sat 26 November 2022 - The Cup Product Is Graded-Commutative [mathematics] [cohomology] [cup products] [Poincare duality] - updated: Thu 17 April 2025
• Thu 12 December 2024 - The Recursion Theorem Gives Programs Access to Their Own Description [mathematics] [computability] [incompleteness] [Turing machines] - updated: Mon 07 April 2025
• Fri 23 February 2024 - The Derivative Decides Local Fixed-Point Stability [mathematics] [dynamical systems] [chaos] [Lyapunov exponents] - updated: Wed 12 March 2025