New Books in Mathematics Chris Bernhardt, "Beautiful Math: The Surprisingly Simple Ideas behind the Digital Revolution in How We Live, Work, and Communicate" (MIT Press, 2024)
Jul 14, 2025
In this engaging discussion, Chris Bernhardt, a former mathematics professor and author of 'Beautiful Math,' delves into the fundamental math behind the digital age. He simplifies concepts like information theory, explaining how digital communications thrive on principles of redundancy and compression. Bernhardt uncovers the intricacies of error correction and encryption, while also illuminating the journey from analog to digital formats. His insights into Boolean logic and machine learning invite listeners to appreciate the math that underpins modern technology.
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Personal View Of The Analog-To-Digital Shift
- Chris Bernhardt recalls living through the analog-to-digital shift from vinyl and punch cards to CDs and modern computing.
- He uses personal experience to show how everyday tech changes reveal underlying mathematical ideas.
Shannon's Quantitative Definition Of Information
- Shannon defined information by linking event probability to bits via an exponential equation, giving a precise measure for information content.
- This definition yields entropy and quantifies how much redundancy can be removed from long messages.
Compress Using Huffman Coding
- Use efficient coding schemes like Huffman coding to compress messages by replacing common patterns with shorter codes.
- Study block patterns and build prefix trees to minimize average code length for practical compression.
