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Beautiful Math: The Surprisingly Simple Ideas behind the Digital Revolution in How We Live, Work, and Communicate
From the bestselling author of Quantum Computing for Everyone, a concise, accessible, and elegant approach to mathematics that not only illustrates concepts but also conveys the surprising nature of the digital information age.Most of us know something about the grand theories of physics that transformed our views of the universe at the start of the twentieth 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, Chris Bernhardt explores the mathematics at the very heart of the information age. He asks questions such 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.
240 pages, Hardcover
Published September 17, 2024
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Displaying 1 - 4 of 4 reviews
May 27, 2025
Got this as a gift. A very technical book, the author discusses the mathematics behind the digital revolution. "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? 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."
Read it if you're a techie and want a trip through memory lane.
Read it if you're a techie and want a trip through memory lane.
November 27, 2024
Really sweet. The author experiences math in much the same visual, applied way that I do. Also happened to succinctly connect blockchain’s proof-of-work with my abstract algebra class with its subchapter on AES and information theory while I was reading both for unrelated classes. Very cool all around
August 12, 2025
Really good book, very well rounded, covered many aspect that a university may not teach for computer science student. Not super deep on all the topics but good enough to get the idea and appreciate math.
Do have a few typos mistakes appear in the book, so if anything does not make sense, its probably you are mislead by the error in the book.
Do have a few typos mistakes appear in the book, so if anything does not make sense, its probably you are mislead by the error in the book.
June 30, 2026
I read Beautiful Math from the perspective of a digital archives, which is where I currently work as a product manager. I was interested in its relevance to digital storage and preservation, metadata, access, authenticity, compression, AI, and system design.
From that perspective, I found the book very helpful. By chapter it covers information theory, compression, error correction, encryption, analog-to-digital conversion, computation, machine learning, and neural networks.
Its main value is that it shows how much the digital world depends on mathematical abstraction. Sounds become samples. Images become pixels. Messages become strings of symbols. Logic becomes circuits. Learning (by machine) becomes pattern-fitting.
For a digital archives this actually matters. Preserving bits and bytes is definitely not the same as preserving human meaning. Records also need added context, metadata, provenance, format information, and documented evidence of how they have been transformed to enable them to be preserved for future generations.
Overall, this is a useful and concise book. Some readers may find parts of it demanding because of the maths. But for anyone interested in how digital technology works it deepens your understanding.
4+ stars.
Full disclosure: I was never especially strong at maths in school. But many of the mathematical concepts in this book are familiar to me, at least at a high level, as I've been exposed to them in various settings over the course of my career. If you work in a computational field it is likely the same for you.
From that perspective, I found the book very helpful. By chapter it covers information theory, compression, error correction, encryption, analog-to-digital conversion, computation, machine learning, and neural networks.
Its main value is that it shows how much the digital world depends on mathematical abstraction. Sounds become samples. Images become pixels. Messages become strings of symbols. Logic becomes circuits. Learning (by machine) becomes pattern-fitting.
For a digital archives this actually matters. Preserving bits and bytes is definitely not the same as preserving human meaning. Records also need added context, metadata, provenance, format information, and documented evidence of how they have been transformed to enable them to be preserved for future generations.
Overall, this is a useful and concise book. Some readers may find parts of it demanding because of the maths. But for anyone interested in how digital technology works it deepens your understanding.
4+ stars.
Full disclosure: I was never especially strong at maths in school. But many of the mathematical concepts in this book are familiar to me, at least at a high level, as I've been exposed to them in various settings over the course of my career. If you work in a computational field it is likely the same for you.
Displaying 1 - 4 of 4 reviews