The Mathematician

Bourbaki: Self-Generated and Goal-Conditioned MDPs for Theorem Proving (arxiv:cs). Bourbaki utilizes self-generated goal-conditioned MDPs and MCTS to enhance automated theorem proving, achieving state-of-the-art results on PutnamBench

Faber polynomials in a deltoid region and power iteration momentum methods (arxiv:cs). Faber polynomials in deltoid regions enable polynomial approximations, enhancing power iteration methods for matrices with complex eigenvalues

The pure condition for incidence geometries (arxiv:math). Introduces a pure condition for parallel redrawings of incidence geometries using bracket polynomials, extending White and Whiteley's framework for distinct point realizations

On Iterated Lorenz Curves with Applications: The Bivariate Case (arxiv:math). Generalizes Lorenz curves to bivariate case, proving uniform convergence to power-law distributions and independence of marginals under certain conditions

Inequalities in Fourier analysis on binary cubes (arxiv:math). Explores Hausdorff-Young and Young's inequalities on binary cubes, providing bounds on energies, entropic uncertainty, and Fourier restriction estimates

Decision algorithms for fragments of real analysis. III: A theory of differentiable functions with (semi-)open intervals (arxiv:cs). Enrichment of satisfiability tests for unary real functions with continuous derivatives, extending Tarski's algebra for differentiable functions over (semi-)open intervals

Schauder-type estimates and applications (arxiv:math). Schauder estimates provide Holder regularity for elliptic PDEs, influencing various fields, with proofs of essential theorems for practical applications detailed

Happy Birthday Saharon Shelah and Yuri Gurevich! (gilkalai​.wordpress​.com). Celebrating Saharon Shelah and Yuri Gurevich's birthdays with conferences covering model theory, combinatorics, quantum computing, and their collaborative contributions

Travels, 11 (cameroncounts​.wordpress​.com). Workshop on the Road Closure Problem with Peter Cameron and Cheryl Praeger in Serpa, Portugal, exploring permutation groups and their properties

Thank you, JoAnne Growney (cameroncounts​.wordpress​.com). Peter Cameron reflects on mathematics and poetry, expressing gratitude to JoAnne Growney for her contributions, including her poem in a conference gift

Some Events (gilkalai​.wordpress​.com). Annual meeting of the Israeli Mathematical Union features key speakers including Elon Lindenstrauss, Amnon Shashua, and Erdos Prize recipients; student talks on July 6-7, 2025

MSc in Theoretical Physics & Mathematics at Maynooth (telescoper​.blog). MSc in Theoretical Physics & Mathematics at Maynooth University opens applications for September 2025, blending Physics and Mathematics curricula

Inquiries-Week 3: Reflect and Rotate (fractalkitty​.com). Explore polygon reflection and rotation through interactive activities, conjectures, and proofs focusing on triangles and squares with engaging educational tools

Explainable Minesweeper and solvable nonograms (quuxplusone​.github​.io). Exploring explainable Minesweeper and solvable nonograms, including techniques for generating levels and solving using specific tactics

Literary genres as equations. (mathwithbaddrawings​.com). Exploring literary genres through equations, highlighting connections between narrative conventions and mathematical concepts like exponentiation and mystery

Reservoir Sampling, or How to Sample Sets of Unknown Size (hackaday​.com). Reservoir sampling explained with interactive guides, solving the challenge of sampling unknown dataset sizes using a fair selection method illustrated by Sam Rose

A retrospective on my first published scientific paper (skullsinthestars​.com). Retrospective insights on a first paper in optics, exploring nonradiating sources, coherence theory, and mentorship from Emil Wolf in scientific publishing

Mathematicians interact with AI, July 2025 update (math​.columbia​.edu). Mathematicians interact with AI at Epoch AI symposium, exploring reasoning models, mathematical problem creation, and implications for future research in mathematics

Slides from a talk at LuCaNT (davidlowryduda​.com). Explorations in math and programming by David Lowry-Duda presented at LuCaNT, featuring interactive commenting and mathematical formatting

Mathematics linked to Water (poetrywithmathematics​.blogspot​.com). Explore the intersection of poetry and mathematics through Donald Illich's work, particularly the poem 'Water Mathematics', highlighting themes of water's mathematical representation

Double Maths First Thing: Issue 2B (aperiodical​.com). Colin Beveridge discusses reflections and rotations, TMiP animation challenge, Simon Tatham's puzzles, monostable tetrahedron, and upcoming events in the maths community

Hannah Cairo has solved the Mizohata-Takeuchi conjecture (english​.elpais​.com). Hannah Cairo, a 17-year-old, refutes the 40-year-old Mizohata-Takeuchi conjecture in harmonic analysis, utilizing fractals and counterexamples during her studies at UC Berkeley

Benjamin Franklin and Exponential Growth (sharonlohr​.com). Benjamin Franklin's insights on exponential growth, including population dynamics, compound interest, and the implications of resource constraints in America

From τὰ φυσικά (ta physika) to physics – XLVII (thonyc​.wordpress​.com). Explores the evolution of inertia from Aristotle to Newton, highlighting key figures like Galileo, Descartes, and Beeckman in the development of motion theory

July 5, 1687: When Newton Explained Why You Don’t Float Away (multiverseemployeehandbook​.com). Isaac Newton's 1687 Principia explains gravity, planetary motion, and foundational physics still used by NASA and today’s scientific endeavors

Dentist may have solved 500-year-old mystery in da Vinci's iconic Vitruvian Man (phys​.org). Rory Mac Sweeney uncovers geometric principles in da Vinci's Vitruvian Man, relating it to natural design through dental anatomy's Bonwill triangle

July 5, 1687: Newton’s Principia is published (astronomy​.com). Isaac Newton's Principia Mathematica, a foundational text in physics outlining the laws of motion and gravity, is published on July 5, 1687

Stability Regions for Mihelčić's Formulas (eklausmeier​.goip​.de). Exploration of stability regions for Mihelčić's cyclic multistep methods, QZ algorithm, and program tools for analyzing stiff differential equations

Bayes Theorem, Pearl Harbor, and the Niihau Incident (themultidisciplinarian​.com). Bayesian reasoning applied to the Niihau Incident illustrates decision-making under uncertainty, revealing shifts in residents' beliefs about Japanese pilot Nishikaichi's intentions

New Sphere-Packing Record Stems From an Unexpected Source (quantamagazine​.org). Boaz Klartag achieves a significant breakthrough in sphere packing using convex geometry, surpassing previous records in high-dimensional spaces

Breakthrough on 125 Year-Old Physics Problem (backreaction​.blogspot​.com). Sabine Hossenfelder explores a significant advancement in solving a long-standing physics issue, highlighting mathematics, quantum gravity, and implications for particle physics

Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory (arxiv​.org). Exploration of Hilbert's sixth problem, focusing on the derivation of fluid equations using Boltzmann's kinetic theory within the context of applied mathematics

The Broken Mirror: What Generative Models Still Don’t Understand About Symmetry (riccardo-disipio​.medium​.com). Exploring generative models and their struggles with mirror symmetry, highlighting insights from physics and the role of Emmy Noether's theorem in understanding structure

The Clifford group as a permutation group (stylewarning​.com). Exploration of the Clifford group in quantum computing, its computational aspects, and utilizing algorithms like Todd–Coxeter and Schreier–Sims for group theory analysis

Inverse Triangle Inequality (matklad​.github​.io). Exploring the Inverse Triangle Inequality's role in mathematics and software engineering, emphasizing smaller commits, refactors, releases, and the benefits of thorough problem exploration

Weierstrass Factorization Theorem (kuniga​.me). Explore the Weierstrass Factorization Theorem, entire and meromorphic functions, and their zeros with concepts like infinite products and canonical products

How to Count n-Ary Trees (golem​.ph​.utexas​.edu). Counting rooted planar n-ary trees using generating functions and Lagrange inversion, exploring Catalan numbers and Bell polynomials

Notes on even and odd functions (eli​.thegreenplace​.net). Overview of even and odd functions, their properties, examples, sums, products, integrals over symmetric intervals, and representation as sums of odd and even functions

Turnabout (futilitycloset​.com). Triangle geometry, parallel lines, and a theorem by James Clerk Maxwell illustrating a unique intersection concept

Expanding Knowledge (futilitycloset​.com). Socrates' dialogue on square areas illustrates the pursuit of knowledge and highlights the importance of inquiry in understanding mathematical concepts

Autoformalization of mathematical theorems? No shit! (freedommathdance​.blogspot​.com). Discussion on autoformalization in mathematics, challenges with proof assistants, and skepticism towards AI-driven methods and tools like Trinity from Morph Labs

Busy Beaver Backwards (nickdrozd​.github​.io). Exploring the Busy Beaver problem using backward reasoning to refute haltingness in Turing machine programs with various states and colors

Proof-Search Friendly Non-Equality Proofs (stranger​.systems). Exploring proof-search for non-equality in programming, emphasizing auto implicit proofs and unique value representation in lists

The Tree Borrows paper is finally published (ralfj​.de). Tree Borrows paper presented at PLDI 2025; awarded distinguished paper for formal proofs, optimizations, and extensive evaluation on 30,000 crates

The New Lower Bound on Busy Beaver of 6. (blog​.computationalcomplexity​.org). New advancements in lower bounds for the Busy Beaver function BB(6) are discussed, with historical comparisons and implications for computational complexity

Matrix Inverse Using Cayley-Hamilton from Scratch Python (jamesmccaffrey​.wordpress​.com). Use Cayley-Hamilton theorem for matrix inversion in Python with NumPy, explaining characteristics, implementations, and a demo with a 5x5 matrix

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