The Mathematician: 13th May 2025

Sepehr Assadi and international collaborators receive STOC 2025 Best Paper Award (uwaterloo.ca, 2025-05-12). Sepehr Assadi and collaborators won the STOC 2025 Best Paper Award for their randomized algorithm achieving a near-optimal (∆ + 1)-edge coloring in O(m log ∆) time, advancing graph theory solutions

Seminar on “Hyper – Catalan series solution to polynomial equations” Tuesday May 13 UNSW (njwildberger.com, 2025-05-07). A seminar on solving polynomial equations using Hyper-Catalan series, featuring a novel approach that connects combinatorics and algebra without radicals, presented by njwildberger and Dean Rubine at UNSW on May 13

Skolem’s paradox and the countable transitive submodel theorem, Leeds Set Theory Seminar, May 2025 (jdh.hamkins.org, 2025-05-12). Joel David Hamkins discusses Skolem's paradox and the countable transitive submodel theorem, demonstrating the complexities of transitive models in set theory and their relation to large cardinal principles

The Fastest Way Yet to Color Graphs (quantamagazine.org, 2025-05-12). Researchers have developed a nearly optimal edge-coloring algorithm for graphs, improving efficiency by focusing on lines rather than points, achieving near-linear time complexity through innovative randomization techniques

My Graduate Career in Math (jeremykun.com, 2025-05-12). A personal account of transitioning from computer science to mathematics at Cal Poly, navigating graduate studies, tackling complex topics like algebraic topology and computational geometry, and blogging to synthesize learning experiences

High finance and higher education the legacy of Thomas Gresham (thonyc.wordpress.com, 2025-05-07). The legacy of Thomas Gresham includes establishing Gresham College in London, introducing disciplines like geometry and astronomy, and advocating for English language lectures to enhance mathematical education for merchants and mariners

The Joys and Sorrows of the Matthew Effect (thereader.mitpress.mit.edu, 2025-05-12). The Matthew Effect highlights how recognition boosts visibility and opportunities for scientists, as seen with Nobel laureates like Harold Kroto, whose fame opened doors and affected their career trajectories significantly

Quote Origin: The Fear of Infinity Is a Form of Myopia. The Infinite in Its Highest Form Created Us (quoteinvestigator.com, 2025-05-11). The quote about the fear of infinity, attributed to Georg Cantor, emphasizes myopia as a barrier to understanding the actual infinite, noted in works by Cantor, Rudy Rucker, and David Foster Wallace

Julia Parsons, "Code Girl", 1921-2025 (rdvlivefromtokyo.blogspot.com, 2025-05-06). Julia Parsons, a key figure in WWII codebreaking, passed away at 104. She deciphered Enigma messages using the Navy Bombe, contributing significantly to Allied efforts against German U-boats

Product Packaging (futilitycloset.com, 2025-05-10). German mathematician August Leopold Crelle introduced a multiplication method using 3-digit chunks, allowing complex calculations with manageable sizes, aided by historical methods documented in his book and later exploration by R.P. Boas

Are We Serious About Using TLA+ For Statistical Properties? (emptysqua.re, 2025-05-10). Exploring potential enhancements to TLA+ for performance modeling, this discussion focuses on queueing theory, Monte Carlo simulations, and limitations including statistical properties and randomization in TLA+ specifications

A tool to verify estimates, II: a flexible proof assistant (terrytao.wordpress.com, 2025-05-10). Terence Tao updates on his flexible proof assistant, utilizing Python's sympy for symbolic algebra and focusing on semi-automated proofs, with features for asymptotic estimates and linear arithmetic verification

How to (actually) prove it – New Frontiers of Mathematics and Computing in Lean (kirancodes.me, 2025-05-09). The Lean Theorem prover revolutionizes mathematics by allowing mathematicians to formalize proofs, with tools like Lean Blueprints providing insights into their proof processes and collaboration through machine-checked results

Cosine in the BEST LANGUAGE EVER (unnamed.website, 2025-05-09). Learn to implement lazy infinite power series using Lean, a powerful proof assistant and programming language that combines features from Haskell, Rust, and more, while exploring lazy lists and mathematical operations

Analytic Combinatorics Redux (grossack.site, 2025-05-09). Explores counting rooted ordered ternary trees using complex analysis, demonstrating geometric approach to singularities and generating functions through implicit function theorem

Brute Force E-Graphs Modulo Theories via SMT (philipzucker.com, 2025-05-12). Exploring the integration of brute-force E-graphs and specialized theories via SMT solving, utilizing Z3 for term manipulation and equalities to enhance equational reasoning

Learn you Galois Fields for Great Good (11): Reed-Solomon as Linear Algebra (xorvoid.com, 2025-05-10). Explore Reed-Solomon Erasure Codes through polynomial evaluation, interpolation, and linear algebra techniques like Vandermonde matrices, matrix multiplication, and LU factorization

Learn you Galois Fields for Great Good (10): Reed-Solomon as Polynomial Representation (xorvoid.com, 2025-05-08). Explores Reed-Solomon Erasure Codes and their polynomial evaluation and interpolation methods. Discusses encoding, decoding, and implementing Reed-Solomon using GF(256) to achieve error correction in data transmission

Tensor Calculus Layout Conventions (leimao.github.io, 2025-05-08). Tensor calculus layout conventions explored through numerator and denominator layouts, detailing derivative calculations for scalars, vectors, and matrices using systematic unrolling techniques

Converting between quaternions and rotation matrices (johndcook.com, 2025-05-07). Explore quaternion representation for rotations and conversion techniques to rotation matrices using Python code with emphasis on numerical algorithms, double covers, and generating random test data

Composing rotations using quaternions (johndcook.com, 2025-05-07). Quaternions simplify the composition of 3D rotations, as demonstrated by Euler's rotation theorem. A rotation quaternion relates to an axis and angle, facilitating easy multiplication for combined rotations

SDFs and the Fast sweeping algorithm in Jax (rohangautam.github.io, 2025-05-08). Explore the Fast Sweeping Method for solving Eikonal equations efficiently with JAX, including concepts like level sets, signed distance functions, and the approach to interface evolution in computational simulations

Notes on the phi-4-reasoning Technical Paper (nishtahir.com, 2025-05-10). Phi-4 reasoning, a 14B parameter model by Microsoft, utilizes supervised fine-tuning and synthetic dataset curation, outperforming larger models. The approach emphasizes careful dataset curation and challenging examples for enhanced reasoning performance

Combinatorial Proofs: Counting the Same Thing in Two Different Ways (themathdoctors.org, 2025-05-09). The discussion centers on combinatorial proofs for the identity C(n,r)C(r,k) = C(n,k)C(n-k,r-k), emphasizing counting techniques and interpretations of combinations

A note on closed addition chains and complete numbers (eprint.iacr.org, 2025-05-09). Investigates novel closed addition chains, proves optimality for certain numbers by connecting to Scholz conjecture using inequality ι(2^n-1) ≤ n-1+ι(n) for cryptographic number theory research

APOLLO: Automated LLM and Lean Collaboration for Advanced Formal Reasoning (arxiv:cs, 2025-05-09). APOLLO combines LLMs with Lean compiler for automated theorem proving, achieving 75% accuracy on miniF2F benchmark with low sampling, and demonstrates significant improvements in efficiency and correctness in formal proofs

Beyond Theorem Proving: Formulation, Framework and Benchmark for Formal Problem-Solving (arxiv:cs, 2025-05-07). Problem-solving is formulated as a deterministic Markov decision process with the FPS framework utilizing FTP environments. Benchmarks like FormalMath500 and verification via RPE yield varied success rates among tested models

$n$-Valued Groups, Kronecker Sums, and Wendt's $(x, y, z)$-Matrices (arxiv:math, 2025-05-07). Explores n-valued groups through Kronecker sums, Wendt matrices, and polynomials, revealing multiplication laws and group structures across different symmetric algebraic group classes

Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields, II (arxiv:math, 2025-05-07). Proves Van Lint-MacWilliams' conjecture by extending results on Cayley graphs over finite fields using a novel approach avoiding complex number theory techniques

Some Observations about the "Generalized Abundancy Index" (arxiv:math, 2025-05-11). The generalized abundancy index is explored through combinatorial numbers, with results showing that the limit of scaled sums equals the product of zeta functions, leading to conjectured asymptotics for specific cases

Some variants of the periodic tiling conjecture (arxiv:math, 2025-05-10). Establishes three variants of the periodic tiling conjecture, including multi-tilings in G=ℤ², and demonstrates the decidability of constant-level integer tilings in any finitely generated Abelian group

New Taylor and Laurent series of axially harmonic, Fueter regular and polyanalytic functions (arxiv:math, 2025-05-10). Comprehensive investigation of series expansions for axially harmonic, Fueter regular, and axially polyanalytic functions in the quaternionic framework, establishing representation formulas and exploring applications in operator theory

Existence of Bianchi-Egnell stability extremizer for the Hardy-Sobolev inequality (arxiv:math, 2025-05-11). Proves the best Bianchi-Egnell constant for the Hardy-Sobolev inequality, demonstrating existence of an extremizer under certain conditions, addressing challenges with eigenspaces and weak limits, and improving previous results in the field