The Mathematician: 14th October 2025

An enough week (blog​.mitrichev​.ch). Overview of F problem on sorted arrays, randomized vs deterministic splitting, and DP-based analysis on tree substructures

Researchers Discover the Optimal Way To Optimize (quantamagazine​.org). Dantzig’s simplex method improved by Bach and Huiberts via more randomness; polynomial-time guarantees for optimization under constraints

Rising on arXiv - 2025-10-10 (blog​.rinesi​.com). Overview of Lindbladians, zero-knowledge proofs, and the Algonauts 2025 Challenge with brain data and multimodal perception notes

Change ringing: extensions to place notation (hunsley​.io). Explores extending place notation with a new ; operator for rotational symmetry, plus examples in Bristol Major, Double Norwich CBM, and other double methods

Basketball trivia, editing distances, and derangement (leancrew​.com). Basketball trivia about retirements, edit distances (Hamming, Levenshtein, Damerau-Levenshtein), and derangements with Python and Mathematica code examples

Do Nothing (blog​.tanyakhovanova​.com). Creative interpretations of 8 + 8 = 91: flipping paper, modular arithmetic, bases, alien numerals, and classroom ideas

An NSA Puzzle (futilitycloset​.com). NSA puzzle on finding integers a,b,c,d,e,f,g >1 satisfying four equations and their product yields a unique solution 2,3,5,7,11,13,17

Book review: Science and Islam – A History by Ehsan Masood (ianhopkinson​.org​.uk). Science and Islam–A History by Ehsan Masood surveys Abbasid translation, astronomy, medicine, algebra, trigonometry, and Bijir ibn-Hayyan within the medieval Islamic empire

Academic chat: On PhD (muratbuffalo​.blogspot​.com). A reflection on PhD life: transformation, curiosity, mentorship, courage, and onboarding in CS, with personal anecdotes from Murat and Aleksey

Genius grant for Math-Woman (poetrywithmathematics​.blogspot​.com). MacArthur Fellow Lauren Williams highlighted for connections between algebraic combinatorics, math, and physics; includes Marion Cohen poetry excerpt

Oct. 9, 1873: The birth of Karl Schwarzschild (astronomy​.com). Karl Schwarzschild’s birth and his pioneering solutions to Einstein’s field equations underpinning black hole theory

AI Delivers an Unexpected Mathematical Proof (politicalcalculations​.blogspot​.com). AI GPT-5-Pro reportedly produced a new, verifiable mathematics proof improving a 1/L bound in convex optimization

Turing Test at 75 (markbernstein​.org). Turing Test at 75: a day-long symposium on the 75th anniversary of the Turing Test with talks and notes

AI as a Copilot for Mathematical Discovery (alexdong​.com). AI as a copilot for mathematical discovery; Ken Ono discusses AI's role, conjecture generation, and the future of math research

How AI Is Replacing Mathematicians (backreaction​.blogspot​.com). AI tools, search for proofs, and the future role of mathematicians in problem-solving and verification

Binomial proportion estimation with unknown and varying number of trials (possiblywrong​.wordpress​.com). Estimating a Bernoulli probability from paired daily hit counts with unknown daily trials, using a trick involving Paul and Quinn’s records

Notes on using LaTeX to generate formulae (eli​.thegreenplace​.net). LaTeX rendering tips: standalone formulae, pandoc conversions, dvisvgm/dvipng, TikZ, TeXstudio, and Docker-based workflows

How many valid UTF-8 (or UTF-16, or UTF-32) byte sequences are there? (qntm​.org). How many valid UTF-8, UTF-16, and UTF-32 byte sequences exist, with recurrences and eigenvalues discussed

Notes - NLA MT25, Courant-Fischer minmax theorem (ollybritton​.com). Courant-Fischer minmax theorem for symmetric matrices and its relation to singular values, subspace optimization, and Weyl’s inequality

Random samples from a tetrahedron (johndcook​.com). Uniform random sampling inside a tetrahedron using exponential variables; compare with uniform sampling and cube-in-tetrahedron testing

Notes - NLA MT25, Norms (ollybritton​.com). Three useful inequalities and alternative characterisations for matrix and vector norms in MT25 NLA notes

The Unknotting Number is Not Additive (divisbyzero​.com). Brittainham and Hermiller disprove additivity of unknotting number via connected sum, using torus (2,7) knot and its mirror with five-crossing projection changes

Monday Morning Math: Square Packing (threesixty360​.wordpress​.com). Explores packing unit squares into larger squares, with rotation effects and known results for 1–11 squares, citing Trump and others

Explicit Lossless Vertex Expanders! (gilkalai​.wordpress​.com). Explicit, constant-degree lossless vertex expanders via Ramanujan cubical complexes and base graphs, with group actions and LDPC-code implications

More on Carmichael (johndcook​.com). Generalizations of n and n^k ending in the same digit for base b, using φ(b)+1 and λ(b)+1; Euler's φ and Carmichael's λ functions with RSA context

Lattice path matroids (matroidunion​.org). Construction and properties of lattice path matroids via north/east lattice paths and duality

Formaising Domain Theory with Lean (anna-maths​.xyz). Formalising domain theory in Lean: Subset predicates, inSubset wrappers, directed sets, and dcpo proofs

Theorems for Free Redux (reasonablypolymorphic​.com). Explains Theorems for Free Redux: parametric polymorphism, free theorems, fmap, length, and examples like id and fromJust with type substitutions

ZF style set theory in Knuckledragger I (philipzucker​.com). ZF-style set theory in Knuckledragger I builds ZFSet, defines classes, Russell’s paradox, extensionality, empty set, picking, and unions

The Hurwitz problem for abelian differentials (arxiv:math). Introduces the Sobolev gap, a quantitative Casselman–Wallach invariant, and computes it for SL(2,ℝ), discrete and principal series. Provides uniform analytic bounds for automorphic functionals—key for representation theory

Bidifferentials, Lagrangian projections and the Virasoro extension (arxiv:math). Characterizes Lagrangian supplements of H^0(C,Ω_C) via symmetric bidifferentials and constructs a Virasoro extension of the local derivation algebra. Important for algebraic curves, de Rham cohomology and conformal structures

Lagrangian Dual Sections: A Topological Perspective on Hidden Convexity (arxiv:math). Introduces Lagrangian dual sections to expose hidden convexity via topological conditions, giving convex reformulations and algorithms for QCQPs and Stiefel-type problems. Bridges topology and optimization theory

Asymptotically large free semigroups in Zariski dense discrete subgroups of Lie groups (arxiv:math). Constructs Zariski-dense free subsemigroups in semisimple Lie group lattices whose critical exponents approach that of the ambient group, via ε-contracting elements. Significant for geometric group theory and dynamics

Motivic Homotopy Groups of Spheres and Free Summands of Stably Free Modules (arxiv:math). Shows motivic stable homotopy groups of the sphere can be recovered from p-completions and motivic cohomology, and applies this to realization/isomorphism results and free-summand questions for stably-free modules

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