New Books in Mathematics14 Juli 2025

Chris Bernhardt, "Beautiful Math: The Surprisingly Simple Ideas behind the Digital Revolution in How We Live, Work, and Communicate" (MIT Press, 2024)

Most of us know something about the grand theories of physics that transformed our views of the universe at the start of the twentieth century: quantum mechanics and general relativity. But we are much less familiar with the brilliant theories that make up the backbone of the digital revolution. In Beautiful Math: The Surprisingly Simple Ideas behind the Digital Revolution in How We Live, Work, and Communicate (MIT Press, 2024) Chris Bernhardt explores the mathematics at the very heart of the information age. He asks questions such as: What is information? What advantages does digital information have over analog? How do we convert analog signals into digital ones? What is an algorithm? What is a universal computer? And how can a machine learn?
The four major themes of Beautiful Math are information, communication, computation, and learning. Bernhardt typically starts with a simple mathematical model of an important concept, then reveals a deep underlying structure connecting concepts from what, at first, appear to be unrelated areas. His goal is to present the concepts using the least amount of mathematics, but nothing is oversimplified. Along the way, Bernhardt also discusses alphabets, the telegraph, and the analog revolution; information theory; redundancy and compression; errors and noise; encryption; how analog information is converted into digital information; algorithms; and, finally, neural networks. Historical anecdotes are included to give a sense of the technology at that time, its impact, and the problems that needed to be solved.

Taking its readers by the hand, regardless of their math background, Beautiful Math is a fascinating journey through the mathematical ideas that undergird our everyday digital interactions.

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Pablo F. Gomez, "Bloody Numbers: The Early Atlantic Slave Trade and the Invention of Modern Corporeality" (U Chicago Press, 2026)

In my conversation with Professor Pablo F. Gómez about his new book, Bloody Numbers: The Early Atlantic Slave Trade and the Invention of Modern Corporeality, published by the University of Chicago Pre...

20 Sep 52min

Xiaochang Li, "Divination Engines: Natural Language Processing, Artificial Intelligence, and the Making of Algorithmic Culture" (U Chicago Press, 2026)

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Richard Elwes, "Huge Numbers: A Story of Counting Ambitiously, from 4 1/2 to Fish 7" (Basic Books, 2026)

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22 Maj 1h 3min

Drew M. Dalton, "The Matter of Evil: From Speculative Realism to Ethical Pessimism" (Northwestern UP, 2024)

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Antony Valentini, "Beyond the Quantum: A Quest for the Origin and Hidden Meaning of Quantum Mechanics" (Oxford UP, 2026)

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5 Maj 1h 30min

Raffaele Danna, "The Craft of Indo-Arabic Numerals: How Practical Arithmetic Shaped Commerce and Mathematics in Western Europe, 1200–1600" (Harvard UP, 2026)

In the thirteenth-century Mediterranean, commerce transformed as merchants shifted from Roman to Indo-Arabic numerals—an alternative that better facilitated complex calculations. It has long been know...

28 Apr 1h 6min

Antonio Padilla, "Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity" (FSG,2022)

A fun, dazzling exploration of the strange numbers that illuminate the ultimate nature of reality. For particularly brilliant theoretical physicists like James Clerk Maxwell, Paul Dirac, or Albert Ei...

15 Feb 1h 2min