The Mathematician

Glue work instead of pasting diagrams (thehighergeometer​.wordpress​.com). glue work, infrastructure contributions, academic careers, Topos Institute talk, Sociotechnical infrastructure for mathematics research, Steven Clontz, women in academia, research community resources

Review: The Mathematician’s Library, by Thomas K. Briggs (aperiodical​.com). Briggs’s Mathematician’s Library surveys global mathematical texts from India, China, and beyond, via six chronological sections and visually rich selections

International Conference on Enumerative Combinatorics and Applications ICECA 2025 (August 25-27, 2025) (gilkalai​.wordpress​.com). ICECA 2025 online conference August 25–27 features Richard Stanley lecture on Symmetric functions from a Ramanujan theta function; Toufic Mansour organizes, with links to abstracts and videos from prior editions and interviews with combinatorialists

Introduction to Hilbert Spaces: An Adventure In Infinite Dimensions (boffosocko​.com). UCLA Extension MATH 900: Introduction to Hilbert Spaces, orthogonality, orthonormal bases, Bessel’s inequality, linear operators, Legendre polynomials, Fourier series, Sobolev spaces, l2 and L2 spaces, course notes and bibliography by Chris Aldrich

Azarian Prize to Honor MR Reviewers (ams​.org). AMS Azarian Prize honors MR reviewers for Mathematics Review contributions; announces recognition program, criteria, and impact on peer review quality in mathematical publishing

Finding a Horseshoe on the Beaches of Rio (thatsmaths​.com). Steve Smale's 1960s Rio beach work on chaos theory and the horseshoe map; IMPA in Rio; Johnson administration fallout; Norman Levinson letter; chaos theory origins

Counting - review (popularhistorybooks​.com). Review of Counting: Humans, History and the Infinite Lives of Numbers by Benjamin Wardhaugh; explores global counting cultures, Pirahá non-counting, Kleroterion lottery, outsourcing memory, historical anecdotes about Seton, and bodily counting practices

Chapter 2: The Reclusive Revolutionary (analog-antiquarian​.net). Copernicus genealogy from Torun to Frombork; heliocentrism reformulation; Ptolemy critique; Renaissance learning; Church politics; Luther’s Reformation; Frombork observations limitations; Teutonic conflicts

Stigler’s Law of Eponymy (litfl​.com). Overview of Stigler’s Law of Eponymy, its origins with Merton and Stigler, related concepts like the Matthew Effect, Boyer’s Law, and historical eponym misattribution in medicine and science

Aug. 20, 2001: Cosmologist Fred Hoyle dies (astronomy​.com). Fred Hoyle, Cambridge professor and proponent of the Steady State Theory, dies; his critique of the Big Bang contrasts with his nucleosynthesis contributions and honors in astronomy

Randomness Made to Order, part 1 (mathenchant​.wordpress​.com). MoMath advisory council member discusses a programmable quincunx, DYOC draw-your-own-distribution, biases at pins, Gaussian curves, virtual vs. physical exhibits, MOVES conference talks, Gardner/Propp connections, and future Sixth Avenue installation

US College Students Can’t Solve This (mindyourdecisions​.com). College math puzzle reveals common errors in translating work rates into equations; solution derives individual rates t, r, h and uses LCM to aggregate for three workers

Using the Golden Ratio to Construct Poems (poetrywithmathematics​.blogspot​.com). Golden ratio-inspired poetry constraints, Bridges Conference 2025, strategies by Sarah Glaz and Lisa Lajeunesse, sample poems, syllable counts, metaphors, mathematical imagery, JoAnne Growney

Is math discovered or invented? (mathwithbaddrawings​.com). Ben Orlin discusses whether mathematics is discovered or invented, offering four perspectives: math as a language invented for communication, relationships existing independently, proofs surprising researchers, and a blend of discovery and invention

'I Would If Possible Imitate a Tree' (evidenceanecdotal​.blogspot​.com). Faraday, autodidacticism, The Chemical History of a Candle, topic sentences critique, 1818 essay circle, naturalness in writing, flame chemistry, carbon/soot, Bunsen burner, oxidation numbers, Swift quote, Regency London

Counting polybar polyominoes (quuxplusone​.github​.io). Explores counting polybars of order p, extends polyomino concepts to pentabars, tribars, dibars; analyzes bilateral symmetry, tilings, and sequences A000105, A056785; includes a C++ implementation

Destructuring to Reduce Temporary Variables (alexanderbass​.com). Destructuring with [a,b] = [b,a] to swap values, reducing temporaries; illustrates Euclidean algorithm gcd optimization with destructuring in Rust; discusses performance and compiler behavior

Mixed Singles (futilitycloset​.com). A puzzle from Arthur Engel's Strategies, marking two points on a line and manipulating neighboring 00 or 11 pairs; invariant parity proves impossibility to reach a 10 state

Some Stuff I've Been Reading (buttondown​.com/jaffray). Reading list on functional pearls, Haskell notes, nondeterminism, SSD behavior, LAW theorem, CAP vs ACID tradeoffs, Raft leases, and empirical SSD-iq benchmarking

‘Ten Martini’ Proof Uses Number Theory to Explain Quantum Fractals (quantamagazine​.org). Ten Martini problem links Hofstadter butterfly fractals to Cantor set, almost-periodic functions, Avila’s global theory, and graphene experiments

Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary Math (quantamagazine​.org). Busy Beaver BB(6) lower bounds explode beyond decimal notation; 6-rule Turing machines run for astronomically many steps, via shift overflow counters, tackled by Busy Beaver Challenge members like Doucette, Ligocki, Kropitz, and mxdys

Singularities are Inevitable, Physicist Claims (backreaction​.blogspot​.com). Sabine Hossenfelder discusses singularities in physics, arguing inevitability across cosmology, quantum gravity, and astrophysical contexts, referencing Backreaction video content and social-media sharing dynamics

Global Mathematics Lecture IV, Kyoto University (freakonometrics​.hypotheses​.org). Global Mathematics Lecture IV at Kyoto University by Arthur Charpentier discusses algorithmic discrimination in predictive models, with emphasis on insurance, biases, fairness, and actuarial applications within graduate studies

A recipe for creating random fractals (johndcook​.com). Random fractal tilings in the plane using a non-singular integer matrix M, its determinant k, a parallelogram P, and randomly selected vectors r_i with affine iterations v = M^-1 v + r_i, illustrated through Python code and references to Fractal Tilings in the Plane and Fractal Rep-tiles

4-Dimensional Cross-Polytope (johncarlosbaez​.wordpress​.com). Explores 4D cross-polytope visualization from two interpenetrating tetrahedra, stellated octahedron, dual tetrahedra, 4D rotations, and links to 3D octahedron intuition

Hints for the Patty Paper Trisection (denisegaskins​.com). Patty paper trisection puzzle hints, Euclid-inspired proofs, patty paper overlapping lines, angle congruence, Aha moment, Geometry Book I concepts, teaching tips, Let’s Play Math blog

Puzzle: Patty Paper Trisection (denisegaskins​.com). Step-by-step Patty Paper folding method to trisect angles using folds, parallel lines, and connecting points; includes setup, construction, and proof challenges

Intuition for Pick’s Theorem (johndcook​.com). Intuition for Pick’s Theorem: counting interior and boundary grid points i and p, deriving A = i + p/2 − 1; rectangular case visualization; reflections and overcounting rationale

Optimizing multiprecision LLL in FLINT (fredrikj​.net). FLINT's multiprecision LLL improvements boost factoring in Z[x] and integer relation searches ( Lindep ) with 4x–6x gains, 60x in large n, using heuristic floating-point LLL + posteriori certification

Arithmetic Functions (derekelkins​.github​.io). Arithmetic Functions, multiplicative/additive concepts, Dirichlet series, Dirichlet convolution, zeta function, divisor functions, completely multiplicative vs multiplicative, prime power behavior, and key lemmas with proofs

What about 1392? (earth​.hoyd​.net). Explores primes consisting of only digit '1', their prime lengths, coding exploration, counting up to 10 000 digits, discovering 2, 19, 23, 317, 1031, and connecting to 1392 via a simple calculator

Some fun exponents (peeterjoot​.com). Exponential identities with complex exponents e, i, π; evaluating π^ei, i^πe, and e^iπ; unit circle and complex arguments; comparison e^π vs π^e; visual plots of complex points

Simpler Category Theory (ryanbrewer​.dev). Introduction to category theory basics: groups, monoids, inverses, associativity, and examples using Rubik's cube and integers; intuition for objects, morphisms, and cancellation

The Baby Paradox in Haskell (blog​.jle​.im). Haskell as a theorem prover, Curry-Howard correspondence, type-level proofs, Baby Paradox, axioms of loves, me, and baby, Gadts, Elem, (:~:), deMorgan, unEither, Maybe, Void

Definite integrals, II: improper integrals (lawrencecpaulson​.github​.io). Improper integrals, extended reals, Lebesgue integration, gauge integrals, FTC nonnegativity, arctan as antiderivative, endpoints and infinities, real_asymp, interval_integral_FTC_nonneg, Lebesgue on (-∞, ∞), damping sinusoid with sign changes

Pigeonhole Principle I: Paths, Penguins, and Points (themathdoctors​.org). Pigeonhole Principle applications: 6-mile path segmentation, endpoints as extra rest areas, and 2D penguin-fight problem with 8 regions ensuring 5 m proximity

The elementary theory of surreal arithmetic is bi-interpretable with set theory, Kobe, Japan, September 2025 (jdh​.hamkins​.org). Talk on the elementary theory of surreal arithmetic; bi-interpretability with set theory (V,∈); surreal field birthday order; ZFC bi-interpretation; collaboration with Junhong Chen and Ruizhi Yang; Kobe 2025

Asymptotic structure. IV. A counterexample to the weak coarse Menger conjecture (arxiv:math). Paul Seymour (Princeton) and Alex Scott (Oxford) disprove a major conjecture in coarse graph theory about finding small separating sets. This resolves a fundamental question about coarse analogues of classical graph theorems with implications for geometric group theory

On Topology of the Infinite-Dimensional Space of Fibrations (arxiv:math). MIT mathematician develops new framework for studying moduli spaces of smooth fibering structures on manifolds using Fréchet manifolds. Establishes connections with Lie theory and geometric analysis, computing homotopy types for low-dimensional cases

On homology spheres of the trivial local equivalence class (arxiv:math). KAIST and CNRS researchers prove existence of homology spheres that are linearly dependent in local equivalence but independent in rational homology cobordism. Uses cutting-edge techniques from involutive Heegaard Floer theory and instanton Floer homology

Non-negligible summands in tensor powers of some modular representations of finite $p$-groups (arxiv:math). UCLA and MIT mathematicians investigate Benson's conjecture about tensor powers of odd-dimensional representations in characteristic 2. Produces infinite families of counterexamples and connects to symmetric group representations, advancing representation theory of p-groups

$\mathrm{GL}_n$ large sieves and density estimates via positive semi-definiteness (arxiv:math). Oxford and UIUC researchers establish sharp large sieve inequalities for families of automorphic L-functions independent of Ramanujan conjecture progress. Provides new density estimates for violations of generalized Riemann hypothesis with applications to analytic number theory

Singularities of symmetric powers and irrationality of motivic zeta functions (arxiv:math). Northwestern mathematician proves that L-rational singularities are preserved under symmetric powers and extends Larsen-Lunts rationality criterion to arbitrary dimension. Shows irrationality of Kapranov motivic zeta functions imposes strong geometric constraints on smooth projective varieties

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