The Mathematician: 22nd July 2025

Twenty years of blogging (11011110​.github​.io). Reflecting on two decades of blogging, covering technical topics, pseudonymous user policies, movement between platforms like LiveJournal and GitHub Pages, and significant mathematical discussions

Profile on COMAP (mrhonner​.com). COMAP blog features Mr. Honner's mathematical modeling group, highlighting student contributions and the role of organizations in applied mathematics education

Jumping Kangaroos (futilitycloset​.com). Kandice the Kangaroo must rescue Joey from a number line while avoiding guards positioned at cubic numbers

Going for Gold: Henri Poincaré and Solar System Stability (thatsmaths​.com). Henri Poincaré's work on the three-body problem advanced mathematics and physics, influencing chaos theory and the stability of the solar system

Turing, Wagner, Ruth (blog​.computationalcomplexity​.org). Exploring the intersections of computation, music, and sport through Turing's theories, Wagner's operas, and Ruth's baseball legacy, highlighting complexity and beauty

2015 Documentary Film -- Calculating Ada (poetrywithmathematics​.blogspot​.com). Explores Ada Lovelace's contributions to computing through the lens of poetry, featuring the documentary 'Calculating Ada' and a poem by Harriet Zinnes

His life depended on the outcome of a game of chess (mathewingram​.com). Ossip Bernstein, a notable chess master, narrowly escaped execution after winning a game against a firing squad officer during the Red Terror in 1917

How to reason from first principles (caseyhandmer​.wordpress​.com). Exploration of reasoning from first principles in AI modeling, emphasizing the seven Ds method: Diagram, Directions, Definitions, Diagnosis, Derivation, Determination, Dimensions, Substitution

Asymmetry of verification and verifier’s law (jasonwei​.net). Explores asymmetry of verification and verifier's law in AI, emphasizing ease of verifying tasks like Sudoku, coding, and scientific hypotheses in reinforcement learning

OpenAI claims gold-medal performance at IMO 2025 (greyenlightenment​.com). OpenAI's LLM achieved gold medal-level performance at the International Math Olympiad, showcasing advanced reasoning and challenge-solving capabilities in mathematics

Will LLMs get us the Missing Data for Solving Physics? (economistwritingeveryday​.com). Explores AI's potential to solve physics mysteries, with insights on LLM limitations, string theory, and future mathematical advancements

Quoting Daniel Litt (simonwillison​.net). Daniel Litt discusses AI's impressive capabilities in mathematics and cautions against viewing recent advancements as a signal of 'solved' mathematical problems

A human metaphor for evaluating AI capability (mathstodon​.xyz). AI capability is not singular; human mathematical competition illustrates diverse potential based on resources and conditions

Revisiting scaling laws via the z-transform (francisbach​.com). Explores scaling laws in machine learning using z-transform, discussing asymptotic behavior, gradient descent, Nesterov acceleration, and convergence rates

All Truth in Truthtables! (paddy3118​.blogspot​.com). Exploration of Boolean expressions, truth tables, and Python coding for electronic design automation and logic operations

[Reading log] “Polymorphic functions with set-theoretic types” parts 1 and 2 (dcreager​.net). Exploring set-theoretic types through Castagna's papers on polymorphic functions, unification solvers, and type variable specialization methods

Cauchy coup (leancrew​.com). Bruce Ediger's numerical experiments on the Cauchy distribution reveal insights into quotients of normal variables and their distribution characteristics

TIL #126 – Hash of infinity (mathspp​.com). Discover the unique Python Easter Egg revealing the hashes of infinity, linked to the mathematical constant π during EuroPython 2025

Graphics & geometry: the orth function in 3D (hunsley​.io). Explores the orth function in 3D graphics, utilizing cross products, 2D orth concepts, and coding solutions in Swift for vector generation

Double Bubble Problem (samjshah​.com). Exploration of the Double Bubble Problem involving intersecting circles forming angles, using law of sines, cosines, and geometric configurations

Area-Perimeter Problem (samjshah​.com). Explores maximizing and minimizing perimeters relative to area using geometric configurations, presenting formulas and insights from computational verification methods like Desmos

Brain Busting Apple Interview Puzzle Paths On Grid (mindyourdecisions​.com). Explore a combinatorial puzzle involving paths on a grid, showcasing techniques with binomial coefficients and the historical context of mathematical discoveries

A New Geometry for Einstein’s Theory of Relativity (quantamagazine​.org). Vienna mathematicians develop alternative mathematical methods to extend general relativity, addressing singularities and curvature in non-smooth space-times

Opening a Six-Lock Safe With One Key Using Brunnian Links (hackaday​.com). Brunnian links enable a unique six-lock safe design, allowing each padlock to independently unlock the enclosure while promoting learning in knot theory

When .999… Isn’t 1 (mathenchant​.wordpress​.com). Exploration of .999… equating to 1 through limits, q-deformation concepts by Morier-Genoud and Ovsienko, and rational functions in unique number systems

Multiples and powers mod 1 (johndcook​.com). Explores the distribution of multiples and powers mod 1, focusing on rational versus irrational numbers and their uniform distribution properties

Powers of 3 + √2 (johndcook​.com). Numerical calculations for large powers of 3 + √2 using bc and Mathematica, examining asymptotic behavior and integer-irrational parts

2025-07-21 Math finds (alexschroeder​.ch). Moessner's theorem illustrates the connection between skipping natural numbers and forming partial sums to discover nth powers like squares and cubes

Is 0.999… = 1? (larspsyll​.wordpress​.com). Explores the mathematical debate over the equality of 0.999... and 1, addressing limits, ontological perspectives, and implications for economics

Free Things Are Complicated (Especially the Sphere Spectrum!) (grossack​.site). Exploration of complexities in free constructions, Sphere Spectrum, noncommutative geometry, and category theory through personal insights and discussions with experts like Clark Barwick

2011 N1 = 2024 A2 (blog​.evanchen​.cc). Evan Chen emphasizes the importance of well-written mathematical solutions through comparison of problems from 2011 N1 and 2024 A2 shortlist

Joram’s seminar 2025: Hypercontractivity, Groups and Representations (gilkalai​.wordpress​.com). Summary of Joram's seminar 2025 featuring talks on hypercontractivity, groups, representations, product mixing, CSPs, and their implications in quantum communication and combinatorics

When is a group not a group? (cameroncounts​.wordpress​.com). Exploration of group theory, endomorphisms, and GAP in constructing and analyzing groups through a computational approach using Cayley's theorem

The computable surreal numbers, Fudan University, July 2025 (jdh​.hamkins​.org). Exploring computable surreal numbers, their properties, and real-closed fields; highlighting hyperarithmetic reals and contributions from Dan Turetsky and Jacob Lurie

Landmark Langlands Proof Advances Grand Unified Theory of Math (cosmicmeta​.io). 800-page proof of geometric Langlands conjecture connects number theory and geometry, advancing a grand unified theory of mathematics led by Gaitsgory and Raskin

Extension of a complete monotonicity theorem with applications (arxiv:math). Extension of complete monotonicity theorem; applications to Hurwitz zeta function, hypergeometric function, and Turán type inequalities

LISA -- A Modern Proof System (arxiv:cs). LISA proof system for constructing proofs in first-order logic, set theory, polynomial-time proof checking, and ortholattices, featuring proof tactics and Cantor's theorem formalization

FormulaOne: Measuring the Depth of Algorithmic Reasoning Beyond Competitive Programming (arxiv:cs). FormulaOne benchmark evaluates AI model capabilities in solving complex real-life problems in graph theory, logic, and algorithms, revealing significant performance gaps

Generalized Jensen's inequality motivated from thermodynamics (arxiv:math). Generalized Jensen's inequality inspired by thermodynamics, proving uniqueness of equilibrium temperature and spontaneous equilibration in diverse systems using real analysis

Characterizing p-Simulation Between Theories (arxiv:math). Characterizes p-simulation between axiomatic theories, efficient interpretations, and implications for computational complexity including Feige's Hypothesis and circuit lower bounds

Density of solutions for systems of forms (arxiv:math). Establishes an effective bound for the density of rational solutions to systems of forms, generalizing Schmidt's result and linking to Hardy-Littlewood asymptotics

Equivariant Borel liftings in complex analysis and PDE (arxiv:math). Borel equivariant analogues of classical theorems in complex analysis, including entire functions, Laplacian, heat operator, and Borel liftings

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