The Mathematician: 3rd June 2025

While plotting a revolution he also reinvented algebra (mathewingram.com, 2025-06-02). Évariste Galois, a young French mathematical prodigy, stayed up all night documenting his revolutionary ideas that ultimately reinvented algebra, despite facing dismissal from the mathematics community

An episodic journey through the history of mathematics in forty short essays. (thonyc.wordpress.com, 2025-05-29). Snezana Lawrence's 'A Little History of Mathematics' presents forty essays covering mathematical themes through history, including contributions from women, zero introduction in India, and developments like calculus, algebra, and geometry advancements

Logic at HUJI (gilkalai.wordpress.com, 2025-05-28). Gil Kalai highlights the significance of mathematical logic at the Hebrew University of Jerusalem and presents insights on science and diversity during a presentation held in Prague

From cannonballs to magic functions: Fields Medalist Maryna Viazovska presents sphere packing at the 2025 Simons Lecture Series (thetech.com, 2025-05-29). Maryna Viazovska explores sphere packing, magic functions, and their connections to areas like harmonic analysis and number theory during the 2025 Simons Lecture Series, revealing the complex interplay of mathematics and geometry

Easy Question From 2024 Putnam (mindyourdecisions.com, 2025-05-28). The first problem of the 2024 Putnam involves solving 2a^n + 3b^n = 4c^n for positive integers a, b, and c, revealing valid results only for n = 1

Winning 4x4x4 tic-tac-toe by consulting an oracle (quuxplusone.github.io, 2025-06-02). 4x4x4 Tic-Tac-Toe can be won by player X with a strategy derived from Oren Patashnik's computer-aided proof, stored in a compressed dictionary using O notation to represent board positions and moves

The distribution of the number of steps to Kaprekar’s constant (earth.hoyd.net, 2025-06-01). Exploring the distribution of steps to Kaprekar's constant reveals unexpected patterns, particularly the predominance of three-step solutions among four-digit numbers with varied digits

Stacking positive and negative cannonballs (johndcook.com, 2025-05-30). Explore how to stack cannonballs in tetrahedral formations, including Pollock's conjecture and the approach of allowing negative cannonballs, with practical implementations through Python coding techniques

The circle hidden inside Pascal’s triangle (johndcook.com, 2025-05-31). A mathematical exploration reveals that plotting the logarithm of binomial coefficients from Pascal's triangle forms a circular arc, with its appearance influenced by scaling, typically presenting as an ellipse

What are Schwartz-Zippel circuits? How do they relate to iterative constraint systems? (cryptologie.net, 2025-05-29). Schwartz-Zippel circuits leverage polynomials for equality checks, enabling iterative constraint systems to validate computations efficiently by utilizing challenges and random evaluation points within cryptographic proofs

Cracking Enigma in 2025 (bruceediger.com, 2025-06-01). Bruce Ediger explores the cryptanalysis of the Enigma machine, implementing a simulated version and utilizing the Index of Coincidence to analyze rotor configurations based on James J. Gillogly's methods

Breakthrough in Unifying Math to Describe How Fluids Behave at Different Scales (politicalcalculations.blogspot.com, 2025-05-30). Mathematicians Yu Deng, Zaher Hani, and Xiao Ma propose a unifying mathematical framework that connects fluid dynamics across microscopic, mesoscopic, and macroscopic scales, leveraging Newton’s equations and Boltzmann’s kinetic theory

“Matrix Inverse Using Newton Iteration with C#” in Visual Studio Magazine (jamesmccaffrey.wordpress.com, 2025-05-29). Explore matrix inversion using Newton iteration in C#. Techniques include establishing a proper starting matrix, the importance of iterative checks, and challenges in computational scaling beyond 1000x1000 matrices

Brief C# Complex Number Tutorial (jamesmccaffrey.wordpress.com, 2025-05-27). This tutorial explains C#'s complex number type and its applications in computing eigenvalues and eigenvectors. It provides code demonstrations for complex operations like addition, multiplication, and square roots

In the Stars (futilitycloset.com, 2025-05-31). Mathematician Sunil Chebolu uses star positions to estimate π, achieving an error of less than 0.002% with 1,000 stars and supporting the hypothesis of random star distribution on the celestial sphere

Understanding through calculation (notebook.drmaciver.com, 2025-06-01). The exploration of mathematical understanding through calculations, particularly in probability, emphasizes the importance of both algebra and insight, illustrated through concepts like unbiased estimators and importance sampling

Singularities in Space-Time Prove Hard to Kill (quantamagazine.org, 2025-05-27). Singularities in space-time, arising from general relativity, challenge physicists as they impede predictions regarding black holes and the Big Bang, urging the pursuit of a more fundamental quantum theory of gravity

The tool/weapon duality of mathematics (micromath.wordpress.com, 2025-06-01). This paper discusses the moral and ethical issues of mathematics, characterizing it as a tool and weapon, with implications on existential choices faced by mathematicians

Complexity theory of hand-calculations (blog.computationalcomplexity.org, 2025-06-02). The complexity of hand calculations is explored, including finding the longest sequence of composite numbers under 1000 and evaluating problems theoretically and by hand using multiplication and division

Exponential functions and Euler’s formula (deaneyang.github.io, 2025-05-29). An exploration of Euler's formula, e^iθ = cos(θ) + i*sin(θ), using unconventional approaches grounded in calculus and alternative to power series

Runge’s Theorem (kuniga.me, 2025-05-31). Runge's Theorem establishes that holomorphic functions in multiply connected regions can be approximated by rational functions with poles in specific compact sets, using tools like Taylor series and Laurent series

On the number of exceptional intervals to the prime number theorem in short intervals (terrytao.wordpress.com, 2025-06-02). Research by Terence Tao and Ayla Gafni explores zero density theorems and their implications for the prime number theorem in short intervals, establishing explicit relationships between key mathematical concepts

The Core of Fermat’s Last Theorem Just Got Superpowered (quantamagazine.org, 2025-06-02). A team of mathematicians confirmed the modularity of abelian surfaces, extending the insights of Fermat's Last Theorem and advancing the Langlands program, pivotal for connections between elliptic curves and modular forms

Verifying Proofs with Type Checkers (brandonrozek.com, 2025-05-27). Explore the connection between computer programs and mathematical proofs through the Curry-Howard Correspondence, utilizing Lean 4 type checker, dependent types, type operators, and type polymorphism for enhanced proof verification

the algebra of dependent types (dotat.at, 2025-05-29). Tony Finch explores the meaning of big-sigma and big-pi in dependent type theory, discussing types like dependent pairs and functions, algebraic data types, and their notation in functional programming languages

A Lean companion to “Analysis I” (terrytao.wordpress.com, 2025-05-31). Terence Tao announces a Lean companion to his textbook 'Analysis I', translating key concepts into Lean code, highlighting foundational issues in analysis, and encouraging volunteer engagement to solve embedded exercises

What does “Undecidable” mean, anyway (buttondown.com/hillelwayne, 2025-05-28). Explaining undecidability in computational theory, focusing on Turing machines, decision problems, and the distinction between decidable and undecidable properties, including examples like the Halting problem and their implications for programming

Tannaka Reconstruction and the Monoid of Matrices (golem.ph.utexas.edu, 2025-06-01). John Baez and Todd Trimble explore Tannaka reconstruction applied to the monoid of n x n matrices, demonstrating that finite-dimensional algebraic representations form a free 2-rig with subdimension properties

Infinity + 1: Finding Larger Infinities (azeemba.com, 2025-05-31). This piece explores the concept of different sizes of infinity, comparing infinite sets such as odd and even integers, perfect squares, and integers, using mapping techniques to illustrate cardinality

A theory of q-transversals (matroidunion.org, 2025-06-02). Mark Saaltink introduces q-transversals, a concept in q-matroid theory, exploring connections, definitions, and key theorems alongside their algebraic representations and implications in transverse theory

Cosmin Pohoata and Daniel G. Zhu: Hypergraphic Zonotopes and Acyclohedra (gilkalai.wordpress.com, 2025-05-30). Cosmin Pohoata and Daniel G. Zhu explore hypergraphic zonotopes, their volume formulas, Ehrhart polynomials, hypertrees, and connections to acyclohedra and acyclic graph orientations in their insightful paper

AI Mathematician: Towards Fully Automated Frontier Mathematical Research (arxiv:cs, 2025-05-28). The AI Mathematician framework uses Large Reasoning Models to tackle frontier mathematical research, addressing complexities through exploration mechanisms and pessimistic verification methods, yielding strong performance in proof construction and insight discovery

DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural Language and Reinforcement Learning (arxiv:cs, 2025-05-29). DeepTheorem enhances LLM theorem proving using a 121K informal theorem dataset and a novel reinforcement learning strategy (RL-Zero), achieving state-of-the-art performance in mathematical reasoning and proof correctness

Autoformalization in the Era of Large Language Models: A Survey (arxiv:cs, 2025-05-29). This survey highlights advances in autoformalization, focusing on its impact on automated theorem proving, LLMs, workflows, and improving the verifiability of LLM-generated outputs, while addressing challenges and future directions

Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems (arxiv:math, 2025-05-29). Using reasoning LLMs and the Constructive Protocol CPro1 generates search heuristics that solve seven open combinatorial design problems, including new solutions for Bhaskar Rao Designs and Symmetric Weighing Matrices, among others

MathArena: Evaluating LLMs on Uncontaminated Math Competitions (arxiv:cs, 2025-05-29). MathArena benchmark evaluates LLMs on uncontaminated math competitions, addressing memorization issues in datasets like AIME 2024, and assessing proof-writing skills, revealing significant performance gaps in top models on USAMO 2025

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving (arxiv:cs, 2025-05-27). MATH-VF framework employs a Formalizer and Critic for verifying LLM-generated mathematical solutions, utilizing tools like Computer Algebra Systems and SMT solvers for refinement and correctness checking against benchmarks like MATH500 and ProcessBench

A unified quaternion-complex framework for incompressible Navier-Stokes equations: new insights and implications (arxiv:math, 2025-05-28). A unified quaternion-complex framework reveals the geometric structure of incompressible Navier-Stokes equations, proving global regularity and linking fluid mechanics to complex analysis while preventing singularities in turbulent flows

A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications (arxiv:math, 2025-05-28). A unified quaternion-complex framework reformulates the Navier-Stokes equations, revealing geometric structures, proving global regularity, and linking fluid mechanics to complex analysis, with implications for turbulence and environmental modeling