Archives
2026
August
- 2026-08-30 - A Tree Center Is One Vertex or One Edge
- 2026-08-17 - Euler's Pentagonal Theorem Expands the Partition Denominator
- 2026-08-08 - Artin--Schreier Extensions Are Additive
July
June
- 2026-06-17 - The Fixed Field of the Full Galois Group Is the Base
- 2026-06-11 - Gram--Schmidt Produces an Orthonormal Basis
May
- 2026-05-24 - Jacobi Fields Describe Infinitesimal Families of Geodesics - updated: Mon 22 June 2026
- 2026-05-08 - The Jacobian Criterion Detects Smooth Complete Intersections - updated: Mon 10 August 2026
- 2026-05-07 - Zero Divisors on a Finite Module Lie in Associated Primes - updated: Wed 22 July 2026
April
- 2026-04-04 - The Matrix Exponential Solves a Constant Linear System
- 2026-04-01 - Transcendence Degree Counts Algebraically Independent Parameters
March
- 2026-03-25 - Cholesky Factorization Characterizes Positive Definiteness
- 2026-03-24 - Universal Machines Encode Programs as Data
- 2026-03-18 - Seifert--van Kampen Builds a Fundamental Group from an Open Cover
- 2026-03-12 - The sl2 Commutation Relations Fit in Three Generators
- 2026-03-02 - The Prime Number Theorem Is a Statement about Chebyshev's Function
February
- 2026-02-19 - Linearized Polynomials Encode F_q-Linear Maps
- 2026-02-07 - A Short Exact Sequence Is an Extension
January
- 2026-01-19 - The Cycle Index Averages Monomials of Cycle Counts
- 2026-01-17 - Cantor's Theorem Makes Every Power Set Larger
- 2026-01-08 - Convex Hull Trick Minimizes a Family of Affine Functions - updated: Sun 28 June 2026
- 2026-01-05 - Combinatorial Species Turn Constructions into Series
2025
December
- 2025-12-15 - Faithfully Flat Base Change Detects Vanishing
November
- 2025-11-20 - Singular Value Decomposition Works for Every Matrix
October
- 2025-10-27 - Beta Is a Quotient of Three Gamma Values
- 2025-10-19 - Cauchy Products Encode Convolution
- 2025-10-16 - The Circle Has Fundamental Group Z by Winding Number
- 2025-10-01 - Factorisation Modulo p Reveals Cycle Types
September
- 2025-09-08 - Bézout Counts Plane Intersections with Multiplicity - updated: Mon 16 February 2026
- 2025-09-01 - Integrality Is Equivalent to a Finite Stable Module
August
- 2025-08-30 - Sobolev Norms Penalize High Frequencies - updated: Wed 21 January 2026
- 2025-08-08 - Transfinite Induction Follows the Well-Ordering of Ordinals
July
- 2025-07-29 - Euler's Formula Forces a Planar Edge Bound - updated: Fri 03 April 2026
- 2025-07-15 - Zorn's Lemma Converts Chain Bounds into a Maximal Element - updated: Mon 15 June 2026
June
- 2025-06-16 - The Tutte Polynomial Is a Rank-Nullity Sum
April
- 2025-04-30 - The Law of Total Expectation Averages Conditional Means - updated: Thu 02 April 2026
- 2025-04-28 - Binomial Inversion Undoes a Subset Sum
- 2025-04-22 - Morse Critical Points Have a Quadratic Normal Form
- 2025-04-21 - Cohen--Macaulay Rings Have No Depth Defect
February
- 2025-02-19 - A Short Exact Sequence of Complexes Produces a Long Exact Sequence
- 2025-02-14 - Dihedral Groups Are Semidirect Products - updated: Wed 01 April 2026
January
- 2025-01-12 - Normalization Repairs Missing Integral Functions
- 2025-01-12 - The Summatory Möbius Function Measures Cancellation
- 2025-01-04 - Kullback--Leibler Divergence Is Nonnegative
2024
December
- 2024-12-28 - Symplectic Euler Preserves Phase-Space Geometry Better than Energy - updated: Mon 18 May 2026
- 2024-12-12 - The Recursion Theorem Gives Programs Access to Their Own Description - updated: Mon 07 April 2025
November
- 2024-11-24 - Galois Correspondence Reverses Inclusion
- 2024-11-21 - Baker--Campbell--Hausdorff Corrects Noncommutative Addition - updated: Sun 15 March 2026
- 2024-11-20 - Gauss's Lemma Counts Sign Crossings
- 2024-11-13 - Annihilators Reverse Inclusion
October
- 2024-10-08 - Odd p-Adic Squares Are Detected Modulo p - updated: Wed 17 December 2025
September
- 2024-09-28 - Turán's Theorem Maximizes Edges without a Clique
- 2024-09-16 - The Dirac Delta Is a Distribution, Not an Ordinary Function
July
June
May
April
- 2024-04-30 - The Argument Principle Counts Zeros Minus Poles - updated: Sat 04 October 2025
March
- 2024-03-29 - The First-Moment Method Deletes All Bad Outcomes
- 2024-03-23 - A Pullback Is a Fibre Product of Morphisms - updated: Sun 17 May 2026
February
- 2024-02-28 - An Adjunction Is a Natural Hom-Set Bijection
- 2024-02-27 - A Prime Is a Sum of Two Squares Exactly in the Split Case
- 2024-02-23 - The Derivative Decides Local Fixed-Point Stability - updated: Wed 12 March 2025
January
- 2024-01-31 - Hoeffding Gives Subgaussian Tails for Bounded Sums
- 2024-01-26 - A DFS Tree Edge Is a Bridge When No Back Edge Escapes
- 2024-01-12 - The Killing Form Takes a Trace of Two Adjoint Maps
- 2024-01-05 - Rooted-Tree Subtree Sizes Obey a Bottom-Up Recurrence - updated: Thu 23 May 2024
2023
December
- 2023-12-23 - Dirichlet L-Functions Twist the Zeta Function - updated: Fri 12 July 2024
November
- 2023-11-02 - Maschke Averaging Produces an Invariant Projection
October
- 2023-10-23 - Newton's Method Is Tangent-Line Root Finding
- 2023-10-19 - Optional Stopping Preserves Expectation under Safe Hypotheses
September
- 2023-09-14 - Cyclotomic Polynomials Have Abelian Galois Groups
- 2023-09-09 - Naturality Is a Family of Commuting Squares
July
- 2023-07-17 - The Jacobi Identity Is a Cyclic Cancellation Law
June
- 2023-06-27 - Simple Random Walk Is Reversible with Degree Weights
- 2023-06-26 - The Wedge Product Is Alternating Multiplication of Forms - updated: Thu 14 September 2023
- 2023-06-25 - Poisson Brackets Differentiate Observables along Hamiltonian Flow - updated: Wed 05 August 2026
- 2023-06-20 - Lower Ramification Groups Measure How Nearly Automorphisms Fix Integers
May
- 2023-05-23 - Every Nontrivial Tree Has at Least Two Leaves
April
- 2023-04-10 - Character Inner Products Count Multiplicities
- 2023-04-04 - The Supplementary Laws Handle Minus One and Two
March
- 2023-03-26 - The Discriminant Changes by the Sign of a Root Permutation
- 2023-03-19 - The Regular Representation Contains Every Irreducible - updated: Fri 03 October 2025
- 2023-03-19 - Conjugacy Classes in S_n Are Indexed by Partitions
February
- 2023-02-28 - Algebraic Elements Form a Field
- 2023-02-28 - Planar Duality Exchanges Cycles and Cuts - updated: Wed 28 August 2024
- 2023-02-08 - Five Characterizations of a Tree Collapse to One Object
January
- 2023-01-17 - Kähler Differentials Represent Derivations - updated: Thu 20 February 2025
- 2023-01-14 - The Spectral Theorem Diagonalizes Self-Adjoint Operators - updated: Wed 04 December 2024
2022
December
- 2022-12-29 - Tilde Turns Modules into Quasi-Coherent Sheaves - updated: Sun 11 January 2026
November
- 2022-11-26 - The Cup Product Is Graded-Commutative - updated: Thu 17 April 2025
- 2022-11-21 - Connectedness Is the Absence of a Nontrivial Clopen Split
- 2022-11-14 - The Group Algebra Converts Representations into Modules
October
- 2022-10-23 - Morse Inequalities Compare Critical Points with Homology - updated: Sun 04 December 2022
September
August
- 2022-08-30 - The Legendre Family Displays a One-Parameter Moduli Coordinate - updated: Tue 11 June 2024
- 2022-08-23 - Backward Euler Is A-Stable on the Left Half-Plane - updated: Tue 16 April 2024
- 2022-08-20 - Direct Sums Are Unique Coordinate Decompositions - updated: Mon 28 August 2023
- 2022-08-09 - The Open Mapping Theorem Makes Surjective Operators Quantitatively Open
July
June
- 2022-06-26 - An Irreducible Cubic Has Galois Group A3 or S3
- 2022-06-23 - Cayley's Theorem Embeds Every Group into a Symmetric Group
- 2022-06-18 - Hilbert's Basis Theorem Adds One Polynomial Variable - updated: Mon 13 November 2023
- 2022-06-17 - The Modular Discriminant Defines Ramanujan's Tau Function
May
- 2022-05-24 - Orthogonal Projection Solves the Closest-Point Problem - updated: Tue 06 September 2022
- 2022-05-18 - A Noetherian Ring Need Not Be Artinian - updated: Wed 17 May 2023
- 2022-05-06 - Euler Trails Are Controlled by Vertex Parity
- 2022-05-04 - A Rational Function Has a Principal Divisor - updated: Wed 15 October 2025
April
- 2022-04-27 - Fatou's Lemma Gives the Safe Direction for liminf
March
- 2022-03-21 - The Riemann--Roch Space Bounds Allowed Poles - updated: Thu 08 May 2025
February
- 2022-02-17 - The Hockey-Stick Identity Adds a Final Chosen Element - updated: Mon 06 June 2022
- 2022-02-10 - The Torus Fundamental Group Has One Commutator Relation - updated: Tue 17 March 2026
2021
December
- 2021-12-07 - Cauchy's Integral Formula Reconstructs Interior Values - updated: Wed 26 February 2025
November
- 2021-11-11 - The Torsion Subgroup Is Functorial
- 2021-11-11 - Valuations Extend with Ramification Index - updated: Sun 19 December 2021
- 2021-11-01 - Riesz Representation Identifies Hilbert-Space Functionals - updated: Sat 24 June 2023
October
- 2021-10-27 - The Adjoint Representation Is Bracketing by an Element
- 2021-10-17 - A Basis Generates Open Sets by Unions
September
- 2021-09-19 - Order Ideals Form a Distributive Lattice - updated: Sun 02 April 2023
August
- 2021-08-07 - Full Digit DP Tracks Position, Tightness, and Automaton State
- 2021-08-04 - Gaussian Binomial Coefficients Count Finite Subspaces
- 2021-08-03 - Gaussian Curvature Is a Determinant of the Shape Operator
July
- 2021-07-26 - A Branching Process Goes Extinct at a Fixed Point
June
- 2021-06-19 - A Discrete Valuation Ring Has One Uniformizer - updated: Sun 01 May 2022
May
March
- 2021-03-20 - Stokes' Theorem Contains Several Integral Theorems at Once - updated: Sun 19 September 2021
- 2021-03-16 - Chebyshev Nodes Suppress Endpoint Oscillation
- 2021-03-11 - Dijkstra Finalizes the Smallest Tentative Distance - updated: Fri 10 December 2021
February
- 2021-02-23 - Associated Primes Are Annihilators of Elements
- 2021-02-09 - Linear-Programming Duality Prices Every Constraint - updated: Mon 15 January 2024
- 2021-02-04 - A Modular Form Has a Weighted Transformation Law - updated: Sat 02 May 2026
January
- 2021-01-20 - The Laplacian Quadratic Form Is an Edge-Energy Sum - updated: Tue 11 June 2024
- 2021-01-19 - Classical RK4 Blends Four Slopes
- 2021-01-04 - Chernoff Bounds Optimize an Exponential Moment
2020
December
- 2020-12-30 - Double Cosets Record Two-Sided Symmetry
- 2020-12-09 - Perron--Frobenius Gives a Positive Dominant Eigenvector
November
- 2020-11-28 - Rank--Nullity Splits the Dimension Budget
- 2020-11-08 - The Riemann Tensor Is a Commutator Corrected by the Lie Bracket - updated: Mon 14 July 2025
October
- 2020-10-04 - The Affine Group of a Field Is a Semidirect Product
September
- 2020-09-07 - Brouwer's Fixed-Point Theorem Forbids a Retraction
August
- 2020-08-21 - A Linear Recurrence Produces a Rational Generating Function
- 2020-08-20 - The Laplace--Beltrami Operator Includes the Volume Density
- 2020-08-03 - Uniform Order Statistics Have Beta Densities
July
- 2020-07-27 - Geodesics Have Zero Covariant Acceleration
- 2020-07-26 - A Splitting Field Is Generated by Every Root - updated: Sun 18 May 2025
- 2020-07-04 - The Tensor--Hom Adjunction Curries Bilinear Data
- 2020-07-02 - The Multiplication Law in a Semidirect Product
June
- 2020-06-23 - Nakayama's Lemma Removes Redundant Local Generators - updated: Fri 13 November 2020
- 2020-06-05 - Uniform Convergence Permits Termwise Integration
May
- 2020-05-30 - The Krull Topology Uses Finite Fixed Fields as Neighbourhoods
- 2020-05-20 - Gödel Completeness Identifies Semantic and Syntactic Consequence
April
- 2020-04-24 - Bellman--Ford Detects Reachable Negative Cycles - updated: Wed 20 November 2024
- 2020-04-14 - Prüfer Codes Count Labeled Trees
- 2020-04-07 - Strong Components Form an Acyclic Condensation
March
- 2020-03-29 - Étale Morphisms Are Algebraic Local Isomorphisms
January
- 2020-01-29 - A p-Adic Integer Is an Infinite Base-p Expansion
2019
December
- 2019-12-14 - Kernels Are Normal Because Conjugation Cannot Leave Zero
- 2019-12-05 - RSK Turns a Permutation into Two Tableaux of One Shape
November
- 2019-11-17 - Normal Extensions Contain Every Conjugate
October
- 2019-10-29 - Convergents Satisfy a Determinant Identity - updated: Sun 15 January 2023
- 2019-10-24 - Additive Hilbert 90 Describes Trace-Zero Elements
- 2019-10-22 - The Schur Complement Controls a Block Matrix - updated: Thu 26 November 2020
- 2019-10-17 - Trace and Norm Are Additive and Multiplicative Shadows
September
- 2019-09-29 - The Gradient Is Metric-Dual to the Differential
- 2019-09-24 - The Möbius Function Is the Convolution Inverse of One
- 2019-09-11 - Proj Glues Degree-Zero Localizations - updated: Wed 03 June 2026
August
- 2019-08-24 - Split Exact Sequences Produce Direct Sums - updated: Thu 18 August 2022
June
- 2019-06-25 - The Weierstrass M-Test Controls a Function Series
- 2019-06-06 - Levi--Civita Is the Unique Metric Torsion-Free Connection
May
- 2019-05-18 - The Picard Group Splits Divisors by Degree - updated: Tue 21 November 2023
- 2019-05-17 - S3 Is the Smallest Nonabelian Semidirect Product - updated: Wed 05 January 2022
April
- 2019-04-29 - A Generic Polynomial Can Have the Full Symmetric Group
- 2019-04-26 - Detailed Balance Makes a Chain Reversible - updated: Wed 22 June 2022
- 2019-04-11 - Riemann--Roch Balances a Divisor with Its Canonical Complement - updated: Fri 10 May 2019
March
- 2019-03-20 - The Sign of a Permutation Is the Parity of Its Inversions
- 2019-03-10 - The Logistic Map Changes Stability at r Equals Three
February
- 2019-02-22 - Frobenius Is a Linear Operator over the Base Field
January
- 2019-01-01 - The Order of a Power in a Cyclic Group
2018
December
- 2018-12-01 - Brownian Covariance Is the Minimum of Two Times
November
- 2018-11-26 - Closed Immersions Are Surjections of Coordinate Rings - updated: Fri 23 September 2022
- 2018-11-17 - Exponential Generating Functions Remember Labels
- 2018-11-11 - LTE Computes Valuations of Exponential Differences - updated: Mon 16 December 2019
October
- 2018-10-03 - Subset DP Makes the Chosen Set an Explicit Coordinate - updated: Fri 18 October 2019
September
- 2018-09-29 - The Hilbert Function Eventually Becomes a Polynomial - updated: Mon 09 December 2019
- 2018-09-04 - Hahn--Banach Extends a Bounded Functional without Growing Its Norm
August
- 2018-08-14 - FFT Splits a Polynomial into Even and Odd Coefficients
- 2018-08-08 - The Canonical Divisor Has Degree Two g Minus Two
- 2018-08-07 - Conditional Expectation Is an L2 Projection - updated: Sat 27 July 2019
July
- 2018-07-30 - I-Adic Completion Is an Inverse Limit
- 2018-07-24 - The Universal Property of a Group Quotient
June
- 2018-06-24 - Quadratic Irrationals Have Periodic Continued Fractions
- 2018-06-09 - Articulation Points Separate DFS Child Subtrees
- 2018-06-01 - Infinite Galois Groups Are Inverse Limits - updated: Sun 18 November 2018
May
- 2018-05-12 - The Torus Cohomology Ring Is an Exterior Algebra
April
- 2018-04-15 - The Weak Law Follows from Variance Decay
March
February
- 2018-02-20 - Löwenheim--Skolem Produces Smaller Elementary Models
January
- 2018-01-24 - The Poincaré Disk and Half-Plane Are Isometric
- 2018-01-05 - Möbius Inversion Extracts Primitive Necklaces - updated: Sun 30 April 2023
- 2018-01-03 - When a Direct Product of Cyclic Groups Is Cyclic
- 2018-01-03 - The First Isomorphism Theorem Turns Fibres into Cosets
2017
December
- 2017-12-21 - The Trace Pairing over a Finite Field Is Nondegenerate - updated: Tue 10 August 2021
- 2017-12-12 - Hall's Condition Is a Set-System Inequality
November
- 2017-11-17 - Burnside Averaging Counts Orbits from Fixed Points
- 2017-11-07 - Characteristic Functions Turn Sums into Products
October
- 2017-10-20 - Parseval Turns L2 Energy into Fourier Coefficients
- 2017-10-03 - Laplacian Nullity Counts Connected Components
September
- 2017-09-20 - The Derivative Detects Repeated Irreducible Factors
August
- 2017-08-25 - Forward Euler Uses One Tangent Step - updated: Fri 15 May 2020
- 2017-08-10 - Azuma--Hoeffding Controls Martingales with Bounded Differences
- 2017-08-03 - Legendre's Formula Counts p in a Factorial
July
- 2017-07-19 - Yoneda Identifies an Object through All Maps into It - updated: Thu 31 July 2025
June
- 2017-06-26 - Sylvester's Law of Inertia Classifies Real Quadratic Forms
- 2017-06-23 - q-Cyclotomic Cosets Factor Roots of Unity over Finite Fields - updated: Sun 27 July 2025
- 2017-06-14 - A Floor Sum Counts Divisors in a Hyperbola - updated: Sat 09 December 2017
May
- 2017-05-28 - Pullback Moves Covectors in the Opposite Direction
- 2017-05-25 - Homogenization Adds the Hyperplane at Infinity - updated: Wed 06 November 2019
- 2017-05-12 - Independence Factorizes Every Joint Event - updated: Wed 13 December 2023
April
- 2017-04-17 - Compactness Converts Open Covers into Finite Data - updated: Mon 30 August 2021
March
- 2017-03-26 - Kronecker Products Multiply Blockwise
- 2017-03-21 - Gauss--Bonnet Turns Total Curvature into Euler Characteristic
- 2017-03-17 - A Stationary Distribution Is a Left Eigenvector
February
- 2017-02-10 - The Zeta Euler Product Encodes Unique Factorization
2016
November
- 2016-11-19 - Least Squares Projects b onto the Column Space - updated: Sun 02 February 2025
- 2016-11-18 - Exponential Waiting Times Are Memoryless
- 2016-11-15 - Cellular Homology Uses One Generator per Cell - updated: Sat 01 May 2021
- 2016-11-05 - A Lyapunov Exponent Measures Exponential Separation
October
- 2016-10-19 - Schur's Lemma Makes Irreducible Endomorphisms Scalar - updated: Thu 26 August 2021
September
- 2016-09-13 - Divisor-Count and Divisor-Sum Functions Factor Prime by Prime - updated: Mon 03 January 2022
July
- 2016-07-26 - The Exponent of a Finite Abelian Group
June
- 2016-06-19 - A Random Coloring Gives an Exponential Ramsey Lower Bound
- 2016-06-17 - An Isogeny Is a Finite Group Morphism of Elliptic Curves
- 2016-06-08 - Gamma Extends the Factorial by an Integral
- 2016-06-06 - Chebyshev's Inequality Applies Markov to Squared Deviation
May
- 2016-05-31 - Effective Resistance Is a Laplacian Pseudoinverse Distance - updated: Sun 07 May 2023
- 2016-05-31 - Integral Elements Form a Subring - updated: Mon 23 September 2024
- 2016-05-02 - A Minimal Polynomial Is the Kernel of Evaluation - updated: Mon 02 March 2020
April
- 2016-04-30 - Complementary Slackness Identifies Which Constraints Bind
- 2016-04-15 - Pólya Substitution Counts Colorings up to Symmetry
- 2016-04-07 - A Knot Group Comes from the Complement
- 2016-04-02 - K5 and K3,3 Violate Planar Density in Different Ways - updated: Sun 15 September 2024
February
- 2016-02-17 - A Presentation Solves a Universal Mapping Problem
- 2016-02-06 - Doob's Maximal Inequality Controls a Submartingale Peak
January
- 2016-01-29 - The Associated Graded Ring Keeps Leading I-Adic Terms
- 2016-01-07 - Euler's Totient Counts the Units Modulo n - updated: Wed 24 August 2016
2015
December
- 2015-12-03 - Commutators Build the Largest Abelian Quotient - updated: Tue 15 June 2021
October
- 2015-10-25 - Trace Is Cyclic but Not Fully Commutative
- 2015-10-14 - Poisson Increments Depend Only on Interval Length
- 2015-10-13 - A Normal Basis Is One Frobenius Orbit - updated: Wed 10 October 2018
September
- 2015-09-21 - Hamilton's Equations Come from Contracting dH with omega - updated: Wed 23 August 2023
- 2015-09-17 - Regular Local Rings Match Dimension with Tangent Dimension - updated: Fri 25 December 2015
- 2015-09-17 - Dominated Convergence Uses One Integrable Envelope
August
- 2015-08-31 - A Durfee Square Decomposes a Partition into Three Pieces - updated: Sun 13 August 2023
- 2015-08-30 - Unit and Counit Encode the Triangle Identities
- 2015-08-21 - The Halting Problem Defeats a Diagonal Decider
- 2015-08-09 - A Scheme Point Carries a Residue Field
July
- 2015-07-27 - Many-One Reductions Transfer Undecidability
- 2015-07-23 - Exactness of Sheaves Can Be Checked on Stalks
June
- 2015-06-22 - NTT Performs the Fourier Transform inside a Finite Field
- 2015-06-07 - Kummer Extensions Come from Classes Modulo n-th Powers
May
- 2015-05-18 - The Tower Formula Multiplies Extension Degrees - updated: Sun 10 September 2023
- 2015-05-17 - Bayes' Formula Reverses a Conditional Direction
- 2015-05-07 - Rational Canonical Form Works without Splitting Polynomials
April
- 2015-04-08 - Bellman's Principle Replaces a Global Search by Optimal Suffixes - updated: Fri 19 August 2016
March
- 2015-03-09 - Multiplicative Order Divides Every Valid Exponent - updated: Mon 29 January 2024
February
- 2015-02-21 - Formal Power Series Complete a Polynomial Ring at x - updated: Fri 08 July 2022
- 2015-02-12 - Finitely Generated Modules over Noetherian Rings Are Noetherian
2014
November
- 2014-11-22 - The Matrix--Tree Theorem Uses a Laplacian Cofactor - updated: Thu 28 July 2016
- 2014-11-15 - Compactness Reduces Infinite Satisfiability to Finite Pieces
October
- 2014-10-14 - The Multinomial Coefficient Counts Ordered Blocks
- 2014-10-10 - Dilworth Decomposes a Poset by Its Width - updated: Mon 01 March 2021
September
- 2014-09-27 - Menger Equates Disjoint Paths with Minimum Separators - updated: Sat 11 February 2017
- 2014-09-17 - The Chinese Remainder Theorem Builds One Residue from Local Data
August
- 2014-08-17 - A Regular Sequence Uses Successive Non-Zero-Divisors
- 2014-08-16 - Uniform Limits of Continuous Functions Are Continuous
July
- 2014-07-19 - Discriminant and j-Invariant Separate Smoothness from Isomorphism - updated: Mon 15 July 2019
- 2014-07-07 - Eisenstein Series Turn Divisor Sums into Fourier Coefficients
May
- 2014-05-29 - Inclusion--Exclusion Counts Onto Functions
- 2014-05-15 - Arzelà--Ascoli Converts Equicontinuity into Compactness
- 2014-05-08 - A Symplectic Form Is Closed and Nondegenerate - updated: Thu 12 October 2017
April
- 2014-04-23 - Poisson Summation Relates a Lattice Sum to Its Dual - updated: Sun 19 July 2020
- 2014-04-15 - Completion of Finite Modules Is Tensoring with the Completed Ring
February
- 2014-02-26 - Frobenius Satisfies a Quadratic Equation on an Elliptic Curve
- 2014-02-25 - The Lovász Local Lemma Handles Sparse Dependence - updated: Wed 21 June 2017
- 2014-02-11 - Mayer--Vietoris Computes Homology from Two Pieces - updated: Sun 30 March 2014
- 2014-02-06 - Quadratic Reciprocity Turns One Odd Prime around Another
January
- 2014-01-09 - Banach's Fixed-Point Theorem Gives a Unique Contractive Fixed Point - updated: Thu 25 April 2019
- 2014-01-09 - Quasi-Coherent Sheaves on an Affine Scheme Recover Modules
- 2014-01-04 - The Functor of Points Tests a Scheme on Every Ring
2013
December
- 2013-12-24 - Stirling's Formula Is a Logarithmic Asymptotic Expansion - updated: Wed 08 November 2017
- 2013-12-24 - Cross Ratio Is the Projective Quantity Preserved by Möbius Maps - updated: Sat 21 July 2018
October
- 2013-10-23 - Poincaré Duality Pairs Complementary Degrees
- 2013-10-04 - The Differential Pushes Tangent Vectors Forward - updated: Thu 16 April 2015
August
- 2013-08-26 - Intersection Multiplicity Is a Local Algebra Length
- 2013-08-16 - Partitions of an Exponent Classify Abelian p-Groups
- 2013-08-10 - Uniform Boundedness Turns Pointwise Bounds into an Operator-Norm Bound - updated: Fri 28 February 2020
- 2013-08-08 - The Exponential Map Sends Lie Algebra Directions to One-Parameter Subgroups
July
- 2013-07-28 - The Degree of a Sphere Map Is Its Action on Top Homology - updated: Sat 01 March 2014
- 2013-07-25 - Triangle-Free Planar Graphs Have an Even Stronger Bound
- 2013-07-23 - Rook Polynomials Encode Nonattacking Placements
- 2013-07-19 - Dirichlet Convolution Multiplies over Divisor Splittings
- 2013-07-02 - Euler's Partition Product Is a q-Series Identity
May
- 2013-05-14 - Artinian Rings Have Krull Dimension Zero - updated: Tue 13 July 2021
- 2013-05-08 - Projective Modules Lift through Surjections
- 2013-05-02 - The Lifting Criterion Is a Subgroup Condition
April
- 2013-04-25 - A DFS Low-Link Value Detects Back Edges - updated: Thu 07 February 2019
- 2013-04-16 - Primary Decomposition Splits an Operator by Coprime Factors
March
- 2013-03-13 - Degree Is the Leading Coefficient of the Hilbert Polynomial
- 2013-03-04 - Primitive Roots Exist for a Very Specific List of Moduli - updated: Tue 03 March 2015
February
- 2013-02-03 - Line Bundles Form the Picard Group
January
- 2013-01-14 - Tonelli Integrates Nonnegative Functions in Either Order
- 2013-01-01 - Alteration Repairs a Random Structure after Sampling
2012
December
- 2012-12-31 - Möbius Inversion Recovers a Function from Its Divisor Sum
- 2012-12-15 - Fubini Requires Absolute Integrability
October
- 2012-10-25 - Convolution Becomes Multiplication after Fourier Transform
- 2012-10-14 - Choice, Well-Ordering, and Zorn Are Equivalent
- 2012-10-02 - Left Translation Identifies Every Tangent Space of a Lie Group - updated: Sun 03 February 2013
September
- 2012-09-01 - Conjugates Are Images under Field Embeddings - updated: Fri 29 May 2015
August
- 2012-08-24 - Dirichlet Characters Have Finite Fourier Orthogonality - updated: Tue 15 August 2017
- 2012-08-05 - Boundary of a Boundary Is Zero
July
- 2012-07-29 - Tensor Product Is Right Exact
- 2012-07-03 - The Minimal Polynomial Has the Largest Jordan Exponents - updated: Sun 25 April 2021
June
- 2012-06-13 - A Primary Decomposition Separates Radical Components
- 2012-06-13 - The Weil Pairing Detects Two-Dimensional Torsion
May
April
- 2012-04-29 - Tangent Vectors Are Derivations at a Point
- 2012-04-17 - Rouché's Theorem Preserves the Number of Zeros - updated: Mon 10 September 2012
- 2012-04-10 - Hom Is Left Exact
- 2012-04-03 - Fibre Products of Affine Schemes Are Tensor Products
February
- 2012-02-22 - The Correspondence Theorem Organises Subgroups above a Kernel
- 2012-02-14 - Cantor's Diagonal Argument Makes Binary Sequences Uncountable - updated: Fri 05 July 2019
- 2012-02-11 - Cheeger's Inequality Links Expansion to the Spectral Gap
January
- 2012-01-29 - Primary Ideals Have One Radical Prime - updated: Mon 06 April 2015
- 2012-01-02 - The Tent Map Is Coded by Binary Itineraries - updated: Tue 03 April 2012
2011
December
- 2011-12-28 - Carmichael's Function Gives the Exponent of the Unit Group
- 2011-12-27 - Normalization Separates the Two Branches of a Node
November
- 2011-11-26 - Slutsky's Theorem Combines Random and Deterministic Limits
- 2011-11-17 - The Dual Map Reverses a Linear Arrow
- 2011-11-14 - Minimal Generators Are a Basis Modulo the Maximal Ideal
October
- 2011-10-15 - The Fundamental Matrix Sums Visits before Absorption - updated: Wed 28 August 2013
- 2011-10-09 - Quotient Topology Makes a Surjection Final - updated: Fri 20 June 2014
- 2011-10-05 - The Zariski Tangent Space Is a Kernel of the Jacobian
September
- 2011-09-20 - The Chromatic Polynomial Satisfies Deletion--Contraction
- 2011-09-10 - Lagrange Interpolation Uses Cardinal Basis Polynomials - updated: Thu 01 January 2015
August
- 2011-08-29 - Łoś's Theorem Evaluates Formulas Coordinatewise in an Ultraproduct
- 2011-08-25 - Kőnig's Theorem Equates Matching and Vertex Cover in Bipartite Graphs
July
- 2011-07-12 - A Distribution Is the Pushforward of Probability
- 2011-07-10 - Krull's Intersection Theorem Separates I-Adic Orders - updated: Fri 06 April 2012
- 2011-07-03 - Coboundaries Reverse the Chain Direction
June
- 2011-06-26 - Sectional Curvature Assigns Curvature to a Two-Plane
- 2011-06-23 - Simple Roots Lift Uniquely by Hensel's Lemma
April
- 2011-04-19 - Pell Solutions Come from Convergents to a Square Root
- 2011-04-14 - The Five-Color Theorem Uses a Low-Degree Vertex
- 2011-04-10 - Laplace's Method Localizes an Integral near Its Maximum
March
- 2011-03-26 - Exterior Powers Record All Minors at Once - updated: Fri 17 March 2017
February
- 2011-02-22 - Euler Characteristic Alternates Cell Counts
2010
December
- 2010-12-19 - The Residue Theorem Sums Local Laurent Coefficients
- 2010-12-16 - A Quotient Space Removes a Subspace Direction
- 2010-12-12 - The Species of Sets of Nonempty Sets Gives Bell Numbers
November
- 2010-11-23 - The First Borel--Cantelli Lemma Needs No Independence
- 2010-11-14 - Interval DP Chooses the Last Split inside a Segment - updated: Thu 30 July 2015
October
- 2010-10-14 - Bisection Trades Speed for a Guaranteed Bracket
September
- 2010-09-23 - The Real Projective Plane Attaches a Two-Cell by Degree Two
- 2010-09-23 - Local Truncation Error Accumulates into Global Error - updated: Mon 22 August 2011
- 2010-09-13 - The Second Borel--Cantelli Lemma Uses Independence
August
- 2010-08-22 - Depth Is the Length of a Maximal Regular Sequence
July
- 2010-07-25 - A Centered Random Walk Is a Martingale - updated: Wed 19 November 2014
June
- 2010-06-26 - Semirings Explain Why One Graph Recurrence Solves Many Problems
- 2010-06-10 - The Rees Algebra Remembers an Entire Filtration
May
- 2010-05-25 - QR Iteration Reveals Eigenvalues without Forming a Polynomial - updated: Sun 14 August 2011
- 2010-05-18 - The Hook-Length Formula Counts Standard Young Tableaux - updated: Tue 13 July 2010
April
- 2010-04-23 - Conditional Probability Renormalizes an Event
March
- 2010-03-26 - Max-Flow Equals Min-Cut
- 2010-03-10 - Möbius Functions Invert Sums over Poset Intervals - updated: Wed 18 February 2015
February
- 2010-02-04 - Support Is the Closed Set Defined by an Annihilator
January
- 2010-01-23 - Flat Modules Preserve Short Exact Sequences
- 2010-01-22 - A Transfer Matrix Counts Objects with Finite Memory
- 2010-01-17 - Unramified Local Extensions Are Controlled by Residue Fields - updated: Mon 27 September 2010
2009
November
October
- 2009-10-31 - A Riemannian Metric Converts Velocity into Length
- 2009-10-21 - Monotone Convergence Interchanges an Increasing Limit and Integral
- 2009-10-20 - Reduced Homology Removes the Extra Connected Component
September
- 2009-09-24 - Gödel's First Incompleteness Theorem Produces an Undecidable Sentence
- 2009-09-18 - Soundness Says Formal Proofs Preserve Truth - updated: Tue 20 March 2018
- 2009-09-07 - The Gaussian Is an Eigenfunction of the Fourier Transform
August
- 2009-08-16 - Affine Morphisms Reverse Ring Maps
- 2009-08-02 - Gaussian Quadrature Is Exact through Degree Two n Minus One
July
- 2009-07-13 - Uniform Derivative Convergence Recovers a Differentiable Limit
- 2009-07-09 - Going Up Lifts Chains of Prime Ideals
- 2009-07-02 - Markov's Inequality Uses Only Nonnegativity
May
- 2009-05-21 - Tree Metrics Satisfy the Four-Point Condition
April
- 2009-04-29 - Chapman--Kolmogorov Is Matrix Multiplication
- 2009-04-05 - Cayley--Hamilton Substitutes a Matrix into Its Characteristic Polynomial
March
- 2009-03-25 - Gambler's Ruin Solves a Discrete Harmonic Equation
- 2009-03-06 - Lying Over Makes an Integral Map of Spectra Surjective - updated: Sun 17 July 2016
- 2009-03-01 - Loop Concatenation Defines the Fundamental Group
February
- 2009-02-20 - Product Topology Is the Smallest Topology Making Projections Continuous
- 2009-02-18 - Absolute Stability Is Tested on y Prime Equals lambda y
January
- 2009-01-26 - Homology Quotients Cycles by Boundaries
- 2009-01-21 - The Upper Half-Plane Metric Is Möbius Invariant
- 2009-01-07 - Ramanujan Congruences Hide in Partition Coefficients - updated: Tue 03 April 2012