The Mathematician

Memorial Volume for Sayan Mukherjee (appliedtopology.org, 2025-05-05). A special issue of the Vietnam Journal of Mathematics is being edited to honor Sayan Mukherjee, inviting contributions on qualitative data analysis and related topics, with a submission deadline of March 31, 2026

Dimension 126 Contains Twisted Shapes, Mathematicians Prove (quantamagazine.org, 2025-05-05). Mathematicians have proven that dimension 126 can host anomalous twisted shapes, utilizing techniques like surgery and Kervaire invariants, concluding a 65-year quest to classify strange manifolds in various dimensions

Numerical Linear Algebra Class in Julia TUM (venkovic.github.io, 2025-05-03). This course covers Numerical Linear Algebra in Julia for Computational Science and Information Engineering, featuring 18 lectures on topics such as direct methods, iterative methods, preconditioners, and matrix function evaluation

Critique of Article: Why Tacit Knowledge is More Important Than Deliberate Practice (justinmath.com, 2025-05-03). Justin Skycak critiques the argument that tacit knowledge is more important than deliberate practice, emphasizing its relevance for advanced learners while advocating foundational skills for beginners in fields like mathematics

P v NP Papers Galore (blog.computationalcomplexity.org, 2025-04-30). Lance Fortnow discusses the recent influx of P vs NP proofs, distinguishing meaningful contributions using techniques like non-relativizing diagonalization and Coq verification, while acknowledging the skeptics' responses and the importance of rigorous analysis

Studying specifics (notebook.drmaciver.com, 2025-05-01). Explores the benefits of studying beyond necessity, emphasizing existence proofs, heavy learning, and the need to pick topics arbitrarily, to leverage joy and curiosity while addressing resource constraints

From τὰ φυσικά (ta physika) to physics – XLIII (thonyc.wordpress.com, 2025-04-30). Galileo's correspondence with Benedetto Castelli in 1613 touches on heliocentrism, biblical interpretation, sunspot observations, and early hydraulics, showcasing Castelli's contributions and controversies with the Church

Percy Ludgate: Early Computer Pioneer and his Irish Logarithms (liveatthewitchtrials.blogspot.com, 2025-05-01). Percy Ludgate, an early computer pioneer, developed Irish Logarithms for multiplication in 1909. This method uses precomputed log values to simplify arithmetic. His contributions include the design of a Turing complete computer

Julia Parsons, "Code Girl", 1921-2025 (rdvlivefromtokyo.blogspot.com, 2025-05-06). Julia Parsons, a key figure in WWII codebreaking, passed away at 104. She deciphered Enigma messages using the Navy Bombe, contributing significantly to Allied efforts against German U-boats

Free Creations of the Human Mind: A New Biography of Einstein (caltech.edu, 2025-05-01). Diana Kormos-Buchwald and Michael Gordin's biography of Albert Einstein explores his life and work, debunking myths and emphasizing primary sources, including his scientific contributions to relativity and quantum mechanics

A puzzle about balancing test tubes in a centrifuge (blog.plover.com, 2025-05-01). Explore the challenge of balancing test tubes in a circular centrifuge with varying slots and configurations, utilizing concepts from number theory like gcd and combinatorial arrangements to ensure safe operation

Proof by insufficient information (blog.plover.com, 2025-04-30). Proof by insufficient information discusses the impossibility of determining the area of a quadrilateral solely from its vertex coordinates, highlighting the importance of order through examples like Heron's formula and logical independence proofs

A Script for Wadler’s Parable of LEM (queuea9.wordpress.com, 2025-04-30). A script inspired by Phil Wadler and Frank Pfenning's performance illustrates the Law of Excluded Middle through Curry-Howard, incorporating a twist that relates to wishes and proofs within a mathematical context

Juggling-ball pyramids and a Christmas song (redfrontdoor.org, 2025-05-02). The Hockey-Stick Identity connects juggling-ball pyramids and The Twelve Days of Christmas, highlighted in Ben North's blog post featuring an interactive element made with markdown and JavaScript

Recamán’s sequence (johndcook.com, 2025-05-06). Recamán's sequence is explored through Python code, visualizations using matplotlib, and musical interpretations, showcasing its unique backward and forward movement rules in generating integer sequences

Bang’s Theorem on Tetrahedra (futilitycloset.com, 2025-05-02). Bang's Theorem states that in a tetrahedron with an inscribed sphere, connecting vertices to the tangency point yields equal angles on each face and congruent triangle pairs across edges

Debugging a Logic Circuit in IDP-Z3 (simonvandevelde.be, 2025-05-03). Using IDP-Z3, the blog explores diagnosing faulty logic circuits based on input-output observations, through modeling gates, wires, and testing values, ultimately finding broken components with minimal assumptions

A proof of concept tool to verify estimates (terrytao.wordpress.com, 2025-05-02). Terence Tao presents a proof-of-concept tool for verifying asymptotic estimates using Python, addressing the automation of inequalities verification, with integration of large language models and suggestions for future collaborative development

Learn you Galois Fields for Great Good (09): Linear Algebra (xorvoid.com, 2025-05-01). Explore linear algebra concepts implemented over finite fields, specifically GF(256), using matrix operations and element indexing. Tools and techniques including matrix multiplication and LU factorization are discussed

Rotation with Modulo (juliabloggers.com, 2025-05-03). Explore rotating a j-digit number n by k digits using modulo operations, implemented in R, Julia, and APL, showcasing tools like the ndigits function and the rotate glyph

Translating the Formula for Primes to Rust With AI (akos.ma, 2025-05-02). The C++ implementation of C. P. Willans' formula for primes is translated to Rust using AI, showcasing concurrency with rayon and advanced numerical computations with libraries like rug and num-bigint

Matrix Inverse Using Cayley-Hamilton With JavaScript (jamesmccaffrey.wordpress.com, 2025-05-05). Explores using Cayley-Hamilton theorem to compute matrix inverses in JavaScript, illustrating coefficients of characteristic polynomial, Faddeev-LeVerrier algorithm, and limitations for practical use on larger matrices

Working Through A Trivial Algorithm Whose Analysis Isn’t (win-vector.com, 2025-04-29). John Mount explores Jonassen and Knuth's 1978 analysis of 2 to 3 node search trees, translating complex arguments into executable Python code, revealing unexpected intricacies in what seems to be a trivial algorithm

Optimizing Barrett Reduction: Tighter Bounds Eliminate Redundant Subtractions (blog.zksecurity.xyz, 2025-05-01). Barrett reduction optimization reveals tighter error bounds for modular arithmetic, enabling 14% performance improvement in cryptographic scalar multiplication by reducing unnecessary subtractions

25.8 The sphere: tangent plane, surface area and volume (thinking-about-science.com, 2025-05-03). The post examines the sphere's properties, including perpendicular radii to tangent planes, surface area (4πR²), and volume ((4/3)πR³), utilizing spherical and cylindrical polar coordinate systems for derivations

Sign Issues in Integration (themathdoctors.org, 2025-05-03). Exploring integration sign issues, including multiplying by sgn(x) for clarity, dealing with absolute values, and the importance of continuity in piecewise functions to avoid multi-valued outputs

Practical Eigenvectors (towardsdatascience.com, 2025-05-02). Eigenvectors are vital in linear algebra, affecting transformations. This practical overview covers vector spaces, basis changes, operators like scale and shear, eigenvalues, and eigenvectors using matrix representations and examples

Geometrically understanding calculus of inverse functions (2023) (tobylam.xyz, 2025-05-05). Explores geometric understanding of inverse function theorem and Legendre transformation, demonstrating how to derive derivatives and integrals of inverse functions using graph reflections

Matroids of large girth (matroidunion.org, 2025-05-04). Explores characteristics of cosimple matroids of large girth, discussing unavoidable minors, graphic and cographic matroids, and recent findings on $GF(q)$-representability, with conjectures on unavoidable cosimple matroids

Orders of infinity (terrytao.wordpress.com, 2025-05-04). Terence Tao explores orders of infinity, their algebraic structure in nonstandard analysis, and completeness properties, discussing implications for symbolic computations and optimization problems in analysis and related fields

Cycle order in period doubling region (johndcook.com, 2025-05-05). The cycle order in the period doubling region of the logistic map is explored, revealing a pattern in the visitation order of cycles, specifically listing patterns for multiple regions

DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition (arxiv:cs, 2025-04-30). DeepSeek-Prover-V2 is an open-source large language model for formal theorem proving in Lean 4, achieving 88.9% pass ratio on the MiniF2F-test and narrowing the gap between formal and informal mathematical reasoning

FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models (arxiv:cs, 2025-05-05). FormalMATH, a Lean4 benchmark with 5,560 verified problems, employs a human-in-the-loop autoformalization pipeline using specialized LLMs, revealing significant limitations of existing LLM-based theorem provers in formal mathematical reasoning

A decomposition lemma in convex integration via classical algebraic geometry (arxiv:math, 2025-04-30). A decomposition lemma reduces primitive matrices in convex integration of flexible C^(1,α) solutions for nonlinear PDEs, leveraging algebraic geometry tools, including Radon-Hurwitz numbers and elliptic methods to enhance regularity and bounds

A family of polynomials and related congruences and series (arxiv:math, 2025-05-05). Explores a polynomial family S_n^(m)(x), demonstrating congruence properties and conjecturing novel infinite series connections involving prime-related transformations of polynomial sums

Generalized Double Operator Integrals for Continuous Spectrum Operators (arxiv:math, 2025-05-04). Generalized Double Operator Integrals extend traditional DOI theory to non-self-adjoint continuous spectrum operators, enhancing functional calculus with applications in quantum mechanics, control theory, and stochastic analysis

Abstract computation over first-order structures. Part IIa: Moschovakis' operator and other non-determinisms (arxiv:math, 2025-04-29). BSS RAMs over first-order structures characterize algorithm processing, integrating Moschovakis' search operator and enhancing non-deterministic capabilities for computable functions, focusing on properties like semi-decidability and identity relation recognizability

On homomorphisms from finite subgroups of $SU(2)$ to Langlands dual pairs of groups (arxiv:math, 2025-05-02). The study explores homomorphisms from finite subgroups of $SU(2)$ to Langlands dual pairs $G$ and $ ilde G$, confirming a conjecture in specific cases and seeking a uniform proof for all configurations

Topology of univoque sets in double-base expansions (arxiv:math, 2025-04-30). This study examines the topology of univoque sets in double-base expansions, extending previous research on equal bases to cases with distinct bases q_0 and q_1, revealing new complexities in unique expansions

[$Λ_p$ Style Bounds in Orlicz Spaces Close to $L^2$]{$Λ_p$ Style Bounds in Orlicz Spaces Close to $L^2$} (arxiv:math, 2025-04-30). Resolves bounds in Orlicz spaces for orthogonal functions near L^2, improving previous results with sharper constants and simpler proof techniques

DeepSeek-Prover-V2 (github.com, 2025-04-30). DeepSeek-Prover-V2 combines reinforcement learning with formal theorem proving in Lean 4, utilizing subgoal decomposition to enhance reasoning capabilities, achieving state-of-the-art performance in neural theorem proving