The Mathematician

Souvenirs from Waterloo (noncommutativeanalysis.wordpress.com, 2025-06-08). The Canadian Operator Algebras Symposium 2025 honored Ken Davidson, showcasing contributions to operator algebras, including dilation theory, NC majorization, and RFD algebras, with highlights from several prominent speakers

From τὰ φυσικά (ta physika) to physics – XLV (thonyc.wordpress.com, 2025-06-04). Evangelista Torricelli's contributions to mathematics and physics include the invention of the barometer, advancements in projectile motion, and the use of Cavalieri's method of indivisibles to reformulate geometric principles

Travels, 5 (cameroncounts.wordpress.com, 2025-06-06). Peter Cameron shares his experiences from Kochi, including meetings with mathematicians, explorations of the Kerala Museum, and discussions about graphs, groups, and potential collaborative research on finite simple groups

June 5, 1819: The birth of John C. Adams (astronomy.com, 2025-06-05). John C. Adams, born on June 5, 1819, is renowned for predicting Neptune's existence and analyzing Uranus's motion, though his findings were overshadowed by Le Verrier's official discovery in 1846

Biography (pgadey.ca, 2025-06-04). Parker Glynn-Adey, a friendly geek and Assistant Professor, specializes in high-dimensional manifold geometry, emphasizing approachable mathematics education while balancing family activities and hobbies like juggling and magic

bab=aaa, bbb=bb (re.factorcode.org, 2025-06-04). Exploring finitely-presented monoids through Factor code, utilizing algorithms like Knuth-Bendix and interactive state transitions using rules like 'bab=aaa' and 'bbb=bb' in a creative gameplay context

Dodecagon star puzzle (leancrew.com, 2025-06-08). Explores the dodecagon star puzzle using brute force techniques to calculate the area by leveraging the regular polygon area formula and the half-angle formulas for tangent

The New Godel Prize Winner Tastes Great and is Less Filling (blog.computationalcomplexity.org, 2025-06-09). Bill Gasarch and Lance Fortnow discuss Eshan Chattopadhyay's work on probabilistic methods, particularly its applications to constructive Ramsey theory and the extraction of random bits from low min-entropy sources

Rules vs Standards (blog.computationalcomplexity.org, 2025-06-04). Lance Fortnow discusses the differences between rules and standards within computational complexity, touching on various mathematical concepts and tools relevant to the field

What’s Next for AI and Math: Unlocking a New Era of Discovery (cosmicmeta.io, 2025-06-07). AI and mathematics are converging, transforming automated theorem proving, collaborative research, and math education through tools like OpenAI's models and AI-powered platforms to redefine discovery and learning

Inside the Secret Meeting Where Mathematicians Struggled to Outsmart AI (cosmicmeta.io, 2025-06-07). Thirty mathematicians gathered to challenge OpenAI’s o4-mini model, probing if human creativity can outpace AI, revealing concerns about rigor in mathematics as AI demonstrates advanced reasoning skills

Simpson's Rule on the Logarithmic Scale (austinrochford.com, 2025-06-06). This post discusses adapting Simpson's Rule for numerical integration on a logarithmic scale, using Python's SciPy for LogSumExp calculations, addressing floating point issues with small probabilities

Graph connectivity as constraints (yetanothermathprogrammingconsultant.blogspot.com, 2025-06-03). Exploration of graph connectivity constraints utilizing nodes and their interrelationships for optimization in mathematical programming applications

A Neat Not-Randomized Algorithm: Polar Express (ethanepperly.com, 2025-06-07). The Polar Express algorithm optimizes matrix sign methods using compositions of polynomials for efficient singular value transformations, crucial for GPU-based neural network applications, especially in scenarios avoiding expensive SVD computations

Math symbol frequencies (leancrew.com, 2025-06-04). Exploration of math symbol frequencies reveals insights from Raúl Rojas's 'The Language of Mathematics,' including issues in symbol representation and implications for mathematical handwriting recognition software

Approximation of Inverse, Inverse of Approximation (johndcook.com, 2025-06-03). The inverse of an approximation serves as an approximation of the inverse, highlighting concepts such as the inverse function theorem, linear approximations, derivatives, and the distinction in approximation quality in one and multiple variables

Epistemic failure of epistemic failure (liorpachter.wordpress.com, 2025-06-03). Lior Pachter discusses Daniel Litt's question on true mathematical results with erroneous proofs, exemplified by Atteson’s conjecture, highlighting the complexity of knowledge and the importance of correction in scientific literature

Inductive definitions (lawrencecpaulson.github.io, 2025-06-09). Inductive definitions outline recursive data types like lists and trees, utilizing concepts such as mathematical induction, Prolog programming, and Isabelle proofs to establish properties like function behavior and list appending

The concept of definition: in mathematics, and in computational logic (lawrencecpaulson.github.io, 2025-06-04). Definitions in mathematics and computational logic are pivotal for consistency, impacting proofs in systems like Isabelle and HOL. Concepts like groups, topological spaces, and practices around circular definitions are explored

The Hypothesis-Testing Philosophy of Harold Jeffreys Expressed As a 13-Word Slogan (bayesianspectacles.org, 2025-06-04). Harold Jeffreys' Bayesian philosophy on hypothesis testing emphasizes caution, supporting point-null hypotheses until alternatives offer improved predictive power, encapsulating his approach in a succinct 13-word slogan related to scientific reasoning

Don't LLM what you can code (june.kim, 2025-06-06). Explore the importance of not relying on language models for mathematical calculations and the need for structured, deterministic code in complex operations like category theory transformations

Infinite binary strings (veitner.bearblog.dev, 2025-06-09). Infinite binary strings are analyzed through binary expansion mappings to real numbers, exploring injectivity, surjectivity, and the prefix concept related to finite binary strings and corresponding intervals

A brain dump from Matrix Dreams: A better-defined series of sets (lordmatt.co.uk, 2025-06-07). Matthew Brown explores a series of sets called MattSets, defining even and odd sets based on powers of two and integers, questioning the completeness of MattSet Prime regarding positive integers

Decomposing a factorial into large factors (second version) (terrytao.wordpress.com, 2025-06-04). Terence Tao and collaborators present a second version of 'Decomposing a factorial into large factors', offering precise bounds and settling previous conjectures using linear programming and insights into the bin covering problem

Euler’s Equation Interpreted in Quaternion Process Theory (medium.com/intuitionmachine, 2025-06-06). Euler's equation e^(iπ) + 1 = 0 embodies the dynamic process of mathematics, connecting concepts like growth (e), transformation (i), cyclical patterns (π), unity (-1), and wholeness (0) as a living language

Binomial number system (johndcook.com, 2025-06-05). The binomial number system uses the representation (a, b, c) to uniquely express non-negative integers, utilizing binomial coefficients and Python functions for efficient computation

MATP-BENCH: Can MLLM Be a Good Automated Theorem Prover for Multimodal Problems? (arxiv:cs, 2025-06-06). MATP-BENCH introduces a benchmark for evaluating Multimodal Large Language Models in automated theorem proving, featuring 1056 multimodal theorems and formalizations in Lean 4, Coq, and Isabelle to challenge models in visual and symbolic reasoning

The affirmative answer to Singer's conjecture on the algebraic transfer of rank four (arxiv:math, 2025-06-03). This research confirms that Singer's conjecture on the algebraic transfer, which maps coinvariants of general linear group representations to the mod-2 cohomology of the Steenrod ring, holds true for homological degree four

Generalized Hardy's identity for the astroid-type p-circle lattice point problem (arxiv:math, 2025-06-03). This study derives a generalized Hardy's identity for astroid-type p-circle lattices, utilizing generalized Bessel functions and a differential formula linked to the Erdélyi-Kober operator, aiding in the error evaluation of area approximations

Safe: Enhancing Mathematical Reasoning in Large Language Models via Retrospective Step-aware Formal Verification (arxiv:cs, 2025-06-05). The Safe framework enhances mathematical reasoning in LLMs by utilizing formal verification through Lean 4, improving performance, and offering interpretable proofs, while defining the FormalStep benchmark for mathematical statement correctness

Higher Order Rigidity and Energy (arxiv:math, 2025-06-03). The paper links higher-order rigidity of bar-and-joint frameworks to energy function growth, proposing a rigidity order definition and introducing fourth derivative tests to determine rigidity without second-order flexes

Beyond Worst-Case Analysis for Symbolic Computation: Root Isolation Algorithms (arxiv:math, 2025-06-04). Beyond worst-case analysis in symbolic computation introduces a smoothed analysis framework for root isolation, demonstrating (quasi-)linear complexity bounds for Descartes' algorithm and analyzing Sturm's solver and ANewDsc