Tag Archives: mathematics

White Paper: The Relevance of the No Free Lunch Theorems to Unguided Stepwise Searches for Solutions

Posted on August 11, 2025 by nathanalbright

Abstract The No Free Lunch (NFL) theorems, originally formulated in the context of optimization and machine learning, establish that averaged over all possible objective functions, all search and optimization algorithms perform equally well. Any algorithm’s advantage in one class of … Continue reading →

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White Paper: How Fermat Might Have Thought He Could Prove His Last Theorem

Posted on August 11, 2025 by nathanalbright

Abstract Fermat’s Last Theorem — the assertion that there are no nonzero integer solutions to the equation x^n + y^n = z^n for n > 2 — remained unproven for 358 years. Pierre de Fermat’s marginal note in his copy … Continue reading →

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White Paper: Verifying Theoretical Closure—The Role of Proof Assistants in Discovering and Exhausting Mathematical Corollaries

Posted on August 7, 2025 by nathanalbright

Executive Summary This white paper explores the epistemological and practical question of how we can know whether all corollaries and “obvious” proofs have been derived from a given set of mathematical theorems. In doing so, it evaluates the limitations of … Continue reading →

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Book Review: The Theory That Would Not Die

Posted on September 9, 2024 by nathanalbright

The Theory That Would Not Die: How Bayes’ Rule Cracked The Enigma Code, Hunted Down Russian Submarines & Emerged Triumphant From Two Centuries Of Controversy, by Sharon Bertsch McGrayne The intersection of probability, politics, and history is a strange place … Continue reading →

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Book Review: Escape From Model Land

Posted on May 23, 2024 by nathanalbright

Escape From Model Land: How Mathematical Models Can Lead Us Astray And What We Can Do About It, by Erica Thompson In many ways, this book is a product of its time, and unhappily so. The book was written by … Continue reading →

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Book Review: The Call Of The Primes

Posted on April 22, 2024 by nathanalbright

The Call Of The Primes: Surprising Patterns, Peculiar Puzzles, And Other Marvels Of Mathematics, by Owen O’Shea This book happens to sit in an unhappy place as far as books about mathematics go. On the one hand, this book is … Continue reading →

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Book Review: Mathematics Minus Fear

Posted on April 20, 2024 by nathanalbright

Mathematics Minus Fear: How to Make Math Fun And Beneficial To Your Everyday Life, by Lawrence Potter It is well known and well-understood that people tend to struggle mightily with mathematics and that a great many people fear and hate … Continue reading →

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Book Review: Ages Of Discord

Posted on April 15, 2024 by nathanalbright

Ages Of Discord: A Structural-Demographic Analysis Of American History, by Peter Turchin In reading this book, I was struck by the fact that there are really two types of books by this author, and both of them are great kinds … Continue reading →

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Book Review: The Theoretical Minimum

Posted on January 26, 2024 by nathanalbright

The Theoretical Minimum: What You Need To Know To Start Doing Physics, by Leonard Susskind and Geoge Hrabovsky When I first looked at this book, I thought that this book was about the theoretical minimum relating to physics that people needed … Continue reading →

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Book Review: The Nothing That Is

Posted on June 8, 2021 by nathanalbright

The Nothing That Is: A Natural History Of Zero, by Robert Kaplan This book is a reminder that natural histories of anything tend to be dodgy and unsatisfactory affairs. Of all of the genres of books that I read and … Continue reading →

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