The Mathematician: 5th August 2025

AI at IMO 2025: a round-up (xenaproject​.wordpress​.com). AI technologies like OpenAI's and DeepMind's claim achievements at IMO 2025, raising questions about methods and validation in mathematics competitions

IMO 2024 and 2025 (blog​.evanchen​.cc). Insights on coordination processes and problem-solving for the IMO 2024 and 2025, featuring Turbo the Snail and Bonza Functions

Russian Teacher Tricks American Students (mindyourdecisions​.com). Russian teacher puzzles American students with a triangle question, revealing a deeper lesson on critical thinking and problem-solving beyond standard testing environments

At 17, Hannah Cairo Solved a Major Math Mystery (quantamagazine​.org). At 17, Hannah Cairo disproved the 40-year-old Mizohata-Takeuchi conjecture using graduate-level math, showcasing extraordinary talent from her homeschooling background

My academic publications (sylviawenmackers​.be). A comprehensive list of Sylvia Wenmackers' academic publications, covering fields from philosophy and probability to the impact of AI on scientific literature

Quantum Complexity Theory Student Project Showcase #5 (2025 Edition)! (scottaaronson​.blog). Scott Aaronson showcases student projects on Quantum Complexity Theory, exploring topics like zero-knowledge protocols, quantum search, and the Hermite transform

Some thoughts on journals, refereeing, and the P vs NP problem (blog​.computationalcomplexity​.org). Eric Allender critiques the flawed peer-review process of a P vs NP paper published in Frontiers of Computer Science, highlighting its inadequacies

Brain Baking Impact (brainbaking​.com). Explores the h-index concept, Brain Baking Impact map, and the influence of blogging on academic work through visualizations and community interactions

Carja Receives NSF CAREER Award for Evolutionary Dynamics Research (cs​.cmu​.edu). Oana Carja receives NSF CAREER Award for innovative research on spatial structure's impact on evolutionary dynamics across biological systems

Archiving Links from 21st Century Math (samjshah​.com). Math teacher professional development highlights from 2025, tools like LaTeX, resources for number theory, and engaging mathematical communities shared among participants

On Teaching Mathematics (scientificgems​.wordpress​.com). Critique of mathematics education, emphasizing experiential learning, recreational mathematics, and the importance of mathematical literacy for future careers and informed citizenship

Direction for Solving the Millennium Prize Problem of Turbulence (trevornestor​.com). Exploration of the Navier-Stokes problem in turbulence, connecting it to quantum gravity, Kolmogorov scaling, and holography in physics

Beam deflections by the moment-area method (leancrew​.com). Moment-area method for beam deflections simplifies complex differential equations into geometric calculations, focusing on curvature and bending moments in structural engineering

The Holey Monster (numberphile​.com). Richard Elwes explores polyhedra, toroids, and the intriguing Holey Monster using Stella software, alongside additional resources and related mathematical discoveries

Exploring the Immaterial Aspects of Thought and Understanding (mindmatters​.ai). Dr. Selmer Bringsjord discusses mathematical objects' immateriality and its implications for human understanding with guest host Pat Flynn

Slow (michaelnotebook​.com). Explores long-term human projects like Fermat's Last Theorem, Sagrada Familia, and LIGO, highlighting their significance and impact over time

From τὰ φυσικά (ta physika) to physics – L (thonyc​.wordpress​.com). Exploration of optics from ancient theories to the sine law of refraction, highlighting contributions from Euclid, Ptolemaeus, Ibn al-Haytham, and Descartes

Kai Bird & Martin J Sherwin - American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer (resolutereader​.blogspot​.com). Explores J. Robert Oppenheimer's life, his role in the Manhattan Project, and the impact of anti-communist sentiments on his legacy

Lawvere’s Work on Arms Control (johncarlosbaez​.wordpress​.com). Lawvere's classified arms control work in the 1960s involved probabilistic mappings and verification protocols for treaty support between superpowers amid Cold War tensions

Odd analysis in an old book (leancrew​.com). Retired engineer explores 1940 textbook's odd differential equation solving methods, including catenary analysis and unconventional trigonometric identities

Goodbye, Tom Lehrer (deeshaa​.org). Tom Lehrer, the satirical musician and mathematician, passed away at 97, remembered for his unique wit and impactful songs

Jack Morava (golem​.ph​.utexas​.edu). Jack Morava's recent passing, shared by David Benson, shocks the mathematical community, highlighting his recent engagement with the n-Category Café

[Repost] Citing Lobachevsky (danq​.me). Tom Lehrer hid an Easter Egg in his 1957 NSA paper, unnoticed for nearly 60 years, blending humor with bureaucratic subversion

Toroidally Progressive Stratified Sampling in 1D (blog​.demofox​.org). Explores toroidally progressive stratified sampling in 1D for Monte Carlo integration, highlighting sampling techniques like golden ratio and standard stratification

Twentyseven 1.0.0 (blog​.poisson​.chat). Twentyseven 1.0.0 is a Haskell-based Rubik's cube solver, using IDA* for optimal solving; a commemorative release after twelve years of development

A focus week (blog​.mitrichev​.ch). Petr Mitrichev explores algorithms involving dynamic programming, greedy approaches, and problem-solving strategies for movie scheduling and card games in competitive programming

Superimposed codes, take three (blog​.sesse​.net). Steinar H. Gunderson discusses optimizations in computing superimposed codes, achieving a(13) = 26 with significant speed and performance enhancements

Semantic Refinement/Dependent Typing for Knuckledragger/SMTLIB Pt 1 (philipzucker​.com). Exploring dependent types in Knuckledragger using SMTLIB for functional programming and verification enhancements

Circle STARKs: Part III, Circle FFT (blog​.zksecurity​.xyz). Circle STARKs implement Circle FFT to interpolate polynomials over twin-cosets using efficient algorithms like Cooley-Tukey for cryptographic applications

The Math Is Haunted (overreacted​.io). Explores Lean, a programming language for formalizing mathematics, providing examples of theorems, proofs, and the implications of axioms within mathematical frameworks

Harmonic Functions (kuniga​.me). Explores harmonic functions, their historical context, mathematical definitions, relations to holomorphic functions, and properties like the Maximum Principle and Poisson Kernel

Moessner’s Magic (johndcook​.com). Moessner's Magic generalizes an ancient theorem about summing odd numbers and deriving powers using iterative sums and removal processes

Counting sums of squares (johndcook​.com). Exploration of the Landau-Ramanujan theorem on sums of squares and comparison of predicted versus exact proportions using computational methods

Two for One (futilitycloset​.com). Exploration of twin primes and prime magic squares by mathematician Leo Moser, featuring smaller and larger prime pair configurations

Thinking Machines: Mathematical Reasoning in the Age of LLMs (arxiv:cs). Explores LLMs in mathematics, focusing on coding strength, formal theorem proving challenges, reasoning mechanisms, training domain trade-offs, and logical state representation

Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving (arxiv:cs). Seed-Prover employs Lean for automated theorem proving, achieving high success rates on IMO problems with a novel geometry reasoning engine, Seed-Geometry

Math Natural Language Inference: this should be easy! (arxiv:cs). Investigation of LLMs' capabilities in mathematical natural language inference, with experimental corpus and findings on premium human vs. LLM hypothesis results

Smoothness of extremizers for certain inequalities of the Radon transform (arxiv:math). Smoothness of extremizers for Radon transform inequalities; critical points are infinitely differentiable when associated exponents are integers, adapted from Christ and Xue's method

Zeroing Diagonals, Conjugate Hollowization, and Characterizing Nondefinite Operators (arxiv:cs). Proves Damm and Fassbender's conjecture on orthogonal transformations of traceless matrices, involving hollow and almost hollow matrices, and characterizes nondefinite operators

Generalized Multiple Operator Integrals and Perturbation Theory for Operators with Continuous Spectra (arxiv:math). Advancements in generalized multiple operator integrals for non-selfadjoint operators with continuous spectra, including algebraic structure and perturbation formulas

A strong height gap theorem for $PGL_2$ (arxiv:math). Height gap theorem improved for matrices generating Zariski dense subgroups in $PGL_2$ with bounds linked to covolume of maximal arithmetic subgroups

Exponential Lower Bounds on the Size of ResLin Proofs of Nearly Quadratic Depth (arxiv:cs). Proves exponential lower bounds on size of Res(⊕) proofs with specific depth limitations using Tseitin formulas and small correlation gadgets

Ordinal Folding Index: A Computable Metric for Self-Referential Semantics (arxiv:cs). Ordinal Folding Index measures self-reference in statements, linking fixed-point logics, infinite parity games, and formal theories; opens new research areas in logic and game theory

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