The Mathematician: 17th June 2025

Dijkstra on Language (realphysics.blogspot.com, 2025-06-14). Dijkstra critiques natural language programming, arguing for formal symbolisms over ambiguous native languages, emphasizing their role in simplifying machine-human interaction and exploring historical perspectives on mathematics

16 (thonyc.wordpress.com, 2025-06-11). Celebrating sixteen years of blogging, the Renaissance Mathematicus explores the mathematical significance of the number 16, including its properties in integer mathematics and applications in hexadecimal number systems

(-e^{i\pi}) to Watch: Boppana Math (aperiodical.com, 2025-06-16). Ravi Boppana discusses his YouTube channel, Boppana Math, which focuses on pure mathematics, particularly discrete mathematics, with accessible videos averaging 15-25 minutes, including highlights like his Honorable Mention on hypergraphs

Robert Woodrow (cameroncounts.wordpress.com, 2025-06-15). Peter Cameron reflects on the life of Robert Woodrow, a generous friend and academic, highlighting his contributions to Fraïssé theory and fond memories shared at various conferences and trips

Nigel Boston (1961-2024) (quomodocumque.wordpress.com, 2025-06-15). Nigel Boston, a pivotal figure in arithmetic statistics and number theory, championed non-abelian Cohen-Lenstra theory and emphasized computational understanding, influencing many at recent conferences and among colleagues

Parker Glynn-Adey (pgadey.ca, 2025-06-12). Parker Glynn-Adey teaches math at the University of Toronto Scarborough, offers reading recommendations, provides reference letter guidelines, and shares various content through his personal website

Ohmaps: crossing the Wheatstone bridge (hunsley.io, 2025-06-12). Exploring ohmaps for analyzing resistor networks, including a unique 'W5' circuit, using Kirchhoff’s laws and sympy for linear equation solutions involving voltages and conductances

Solving LinkedIn Queens with SMT (buttondown.com/hillelwayne, 2025-06-12). Using SMT solvers like Z3, a variant of the N-Queens puzzle called LinkedIn Queens is solved more easily than with SAT. The code is demonstrated with explanations of key constraints and concepts involved

Does Form Really Shape Function? (quantamagazine.org, 2025-06-12). L. Mahadevan discusses the relationship between biological form and function, exploring concepts like morphogenesis and the geometry of structures, including Möbius strips, using tools like gels and physics principles

Epic Effort to Ground Physics in Math Opens Up the Secrets of Time (quantamagazine.org, 2025-06-11). Three mathematicians have proven the connection between microscopic particle motion and macroscopic fluid behavior through Boltzmann and Navier-Stokes equations, shedding light on time's irreversible nature in fluid dynamics

From Abstract Puzzles to Practical Innovations: The Infinite Resistor Grid's Hidden Impact on Engineering and Quantum Technology (eliza-ng.me, 2025-06-15). Explores the infinite resistor grid's relevance to electrical engineering and quantum technology, emphasizing its implications for noise management in integrated circuits and the essential bridge between theoretical concepts and practical applications

Proving Superdiffusion (fyfluiddynamics.com, 2025-06-12). A group of mathematicians has mathematically proven superdiffusion—the phenomenon where particles in turbulent flows disperse quicker than expected—using a technique called homogenization

The Hat, the Spectre and SAT Solvers (2024) (nhatcher.com, 2025-06-13). Explore the Hat and Turtle concepts alongside powerful SAT solvers, SATisfiability, and innovative applications including Sudoku resolution and finite plane tiling techniques, all utilizing web assembly technologies

-1/12 and the area under the sum function (zmatt.net, 2025-06-15). Explores -1/12 value via Ramanujan summation and Riemann zeta function, integrating sum functions over intervals to reveal surprising constants which relate to curvature and have implications in physics

Ratio of square side to chord (mindyourdecisions.com, 2025-06-13). Explore the geometric relationship between the square side and the chord, leading to the ratio a/b = √2 through trigonometric concepts and right triangle properties in Presh Talwalkar's analysis

The Mean and Variance as Dual Concepts (ellerman.org, 2025-06-16). David Ellerman explores the duality between mean and variance, linking probability theory and information theory through the concepts of subsets and partitions, introducing a new derivation for variance based on a two-sample approach

Golden powers revisited (johndcook.com, 2025-06-10). The powers of the golden ratio, φ, are nearly integers and can be expressed as sums of Fibonacci numbers, with errors decreasing exponentially according to ψ, the smaller root of the characteristic equation

Lectures on Set Theory, Beijing, June 2025 (jdh.hamkins.org, 2025-06-11). A series of advanced lectures on set theory, addressing topics like forcing, large cardinals, the continuum hypothesis, and definability, set to take place at Peking University in June 2025

The Mathematical Foundations of Self-Referential Systems: From Computability to Transfinite Dynamics (novaspivack.com, 2025-06-16). This treatise presents Recursive Representation Theory and Self-Referential Renormalization Group, addressing self-referential systems, their dynamics, and implications for computability, self-knowledge, and applications across physics, biology, and artificial intelligence

E, The Transiad: Mathematical Structure and Trans-Computational Dynamics of Expressed Reality (novaspivack.com, 2025-06-15). This paper explores E (The Transiad) as a mathematical structure embodying Alpha's potential, employing higher category theory, topos theory, hypergraph models, and non-well-founded sets to analyze trans-computational dynamics and emergent physical laws

The Future of AI Maths May Be Deeply Weird (stephendiehl.com, 2025-06-11). The rise of AI in mathematics involves tools like Lean4, automated theorem proving, and collaborative libraries, enabling a future where proof construction may be collaborative and machine-checkable, reshaping mathematical practice

The Beautiful Embarrassment: What AI Cannot See in Human Discovery (medium.com/intuitionmachine, 2025-06-15). Terence Tao underscores AI's limitations in mathematical discovery, highlighting the value of human trial and error—often seen as embarrassing—that fuels true breakthroughs through aesthetic intuition and creative courage

Reviving DSP for Advanced Theorem Proving in the Era of Reasoning Models (arxiv:cs, 2025-06-13). DSP+ enhances the Draft, Sketch, and Prove framework with neuro-symbolic methods, achieving significant theorem proving success, including unresolved problems, while generating human-comprehensible proof patterns and requiring fewer resources than existing approaches

StepProof: Step-by-step verification of natural language mathematical proofs (arxiv:cs, 2025-06-12). StepProof introduces a step-by-step verification method for natural language mathematical proofs, improving autoformalization by breaking proofs into subproofs, enhancing success rates and efficiency over traditional theorem proving approaches

Beyond Gold Standards: Epistemic Ensemble of LLM Judges for Formal Mathematical Reasoning (arxiv:cs, 2025-06-12). A systematic method using an ensemble of LLM judges evaluates autoformalization in formal mathematics, focusing on logical preservation, mathematical consistency, formal validity, and formal quality, correlating better with human assessments

Joint Complete Monotonicity of reciprocal of a polynomial in two variables (arxiv:math, 2025-06-10). Studying joint complete monotonicity of reciprocal polynomials in two variables leads to sufficient and necessary conditions, kernel Hilbert space, and properties of a weighted shift, particularly for degrees of polynomials involved

On Singer's conjecture for the fourth algebraic transfer in certain generic degrees (arxiv:math, 2025-06-11). This paper proves Singer's conjecture for the fourth algebraic transfer, establishing injectivity in generic degrees linked to the cohomology groups of the Steenrod algebra via the general linear group G(q)

A survey of The Prouhet-Tarry-Escott Problem and its Generalizations (arxiv:math, 2025-06-13). Explores Prouhet-Tarry-Escott problems, generalizations, and novel computational methods, including multigrade chains, Girard-Newton Identities, and a normalized GPTE approach with conjectures for integer solution bounds and parametric methods

Matrix best approximation in the spectral norm (arxiv:cs, 2025-06-11). A matrix formulation for best approximation in the spectral norm is derived, linking spectral approximations to semidefinite programming, with conditions for max-min and min-max equality and MATLAB code for numerical solutions

Last fifty years of integer linear programming: Recent practical advances (inria.hal.science, 2025-06-14). Mixed-integer linear programming (MILP) showcases significant advancements in solution methodologies, focusing on branch-and-cut, Dantzig-Wolfe decomposition, and Benders decomposition, addressing challenges in varied applications across industries

100 years of Zermelo's axiom of choice: What was the problem with it? (2006) (research.mietek.io, 2025-06-13). P. Martin-Löf examines Zermelo's axiom of choice, its introduction, the resulting debates among mathematicians, and the intuitionist rejection of the axiom, highlighting the development of constructive mathematics and related logical principles