Magic Internet Math

We celebrated June 28 as “Perfect Number Day” and finally told one of my favorite origin stories behind this whole project: a late-night drive home from a Phish show with Kayla, where a quick conversation about why 6 and 28 are perfect numbers turned into a full-blown family math obsession. We revisited how that curiosity led us to trial-and-error the next perfect number, fire up a Raspberry Pi, w...

In this Father’s Day episode of Magic Internet Math, I welcomed my daughter Kayla to the mic for her first appearance on the show. We started with her recent work explaining group theory in just three minutes, then used that as a jumping-off point to talk about why ideas like groups, inverses, isomorphisms, elliptic curves, and point addition matter so much in Bitcoin and cryptography. We also got...

Rob and Brian shake off the dust after a busy stretch of conferences and a milestone YouTube debut with guest Alan, then map the road from elliptic curves to an upcoming mini‑series on hash functions. We talk Prague plans (a keynote on “the mathematical layer of sovereignty” and a quantum‑security panel with Trezor), growing Miniscript adoption (Liana, Trezor), and why the Magic Internet Math plat...

In this first-ever guest episode of Magic Internet Math, Rob Hamilton and I (Brian Hirschfield) welcome author and thinker Allen Farrington for an unfiltered tour through math as a liberal art, why rigor matters more than vibes, and how curiosity—not applications—often drives real progress. We trade stories about learning (and unlearning) math, from the lore of the irrationality of √2 and CP Snow’...

The Study guide: https://ecc-study-guide.magicinternetmath.com/guide.pdf In this episode, I (Brian) finally introduce myself properly and Rob and I kick off with a Vegas + Bitcoin++ recap before diving back into Chapter 6 of our elliptic curve study guide. We talk small, dev‑focused conferences versus mega‑cons, the Hoover Dam power-plant tour, and the standout conversations around quantum risk, B...

In this podcast episode, Brian and Rob from Magic Internet Math discuss verifying Bitcoin, focusing on the underlying math and cryptography to understand the validity of private keys and transactions. Key Topics: Verification of Bitcoin Elliptic Curve Cryptography Modular Arithmetic Inverse Relationships Quantum Computing and Bitcoin Security Importance of Entropy Summary: Brian and Rob introduce...

The Study guide: https://ecc-study-guide.magicinternetmath.com/guide.pdf In this episode of Magic Internet Math, Rob and Brady discuss the discrete log problem and its importance to Bitcoin's security. Key Topics: Discrete Log Problem Modular Arithmetic Elliptic Curve Cryptography Quantum Computing Bitcoin Transactions Summary: Rob and Brady revisit the math study guide, now nearing its end. They...

In this solo episode of the Magic Internet Math podcast, the host discusses the current status of the Magic Internet Math website, his personal journey into math education, and his vision for teaching math as a liberal art. Key Topics: Magic Internet Math website status Personal journey into mathematics Teaching math as a liberal art Subscriber benefits and future plans for the website Rudolf Stei...

The Study guide: https://ecc-study-guide.magicinternetmath.com/guide.pdf In this episode of the Magic Internet Math Podcast, the hosts continue their exploration of elliptic curve cryptography, focusing on the inverse problem and the mathematical structures that ensure its existence, as part of their series on Bitcoin security. Key Topics: Inverse Problem Modular Arithmetic Groups and Fields Eucli...

The Study guide: https://ecc-study-guide.magicinternetmath.com/guide.pdf In this episode of Magic Internet Math, Rob and Fundamentals discuss the math behind Bitcoin's security, exploring elliptic curve cryptography, modulo arithmetic, and digital signatures. Key Topics: Seed-Phrase Generation Elliptic Curve Cryptography Modulo Arithmetic Securing Bitcoin with Math The Importance of Primes Underst...

This podcast episode of Men of Mathematics discusses the life and work of Joseph Fourier, focusing on his contributions to mathematics, physics, and engineering, particularly his discovery of Fourier series and its wide-ranging applications. Key Topics: Fourier Series Heat Equation Applications of Fourier Analysis Fourier's Life and Career Greenhouse Effect Summary: Fourier's groundbreaking work d...

This podcast episode of Men of Mathematics discusses Gaspard Monge, the inventor of descriptive geometry and founder of the École Polytechnique, whose work significantly shaped technical education. Key Topics: Descriptive Geometry École Polytechnique Optimal Transport Problem French Revolution's Impact on Education Monge's relationship with Napoleon Summary: Gaspard Monge, born in 1746 in Burgundy...

This podcast episode of Men of Mathematics discusses the life and work of Pierre-Simon Laplace, a French mathematician and physicist who made significant contributions to celestial mechanics, probability theory, and mathematical physics. Key Topics: Celestial Mechanics Probability Theory Laplace Transform Determinism Laplace's Equation Summary: Laplace, born in Normandy in 1749, quickly rose to pr...

This podcast episode explores the life and mathematical contributions of Joseph Louis Lagrange, highlighting his transformation of physics into pure algebra and his significant impact on various fields. Key Topics: Lagrange's early life and career Lagrange's contributions to mechanics Lagrange multipliers Lagrange's work in number theory and algebra Lagrange's role in the French Revolution and the...

This podcast episode of Men of Mathematics discusses the life and accomplishments of Leonhard Euler, a prolific mathematician who made significant contributions to various branches of mathematics and other fields. Key Topics: Leonhard Euler's early life and education Euler's contributions to mathematics Euler's blindness and its impact on his work Euler's influence and legacy Summary: Euler was bo...

This podcast episode of "Men of Mathematics" delves into the history of the Bernoulli family of Basel, a dynasty of mathematicians spanning three generations who made significant contributions to various fields despite their intense rivalries. Key Topics: Bernoulli Family Jacob Bernoulli Johann Bernoulli Daniel Bernoulli Calculus Probability Theory Fluid Dynamics Summary: The episode concludes by...

This episode of Men of Mathematics discusses the life and work of Gottfried Wilhelm Leibniz, a philosopher, mathematician, diplomat, and inventor who was a contemporary and rival of Isaac Newton. Key Topics: Leibniz's early life and education Leibniz's work on binary code Leibniz's invention of calculus and the controversy with Newton Leibniz's philosophical contributions Leibniz's work as a diplo...

This podcast episode of Men of Mathematics introduces Isaac Newton, a highly influential scientist and mathematician known for his contributions to calculus and his complex personality. Key Topics: Isaac Newton Summary: Isaac Newton is portrayed as one of the most influential scientists in history, despite his secretive nature and contentious relationships with rivals. The episode sets the stage f...

This podcast episode explores the life and accomplishments of Blaise Pascal, a mathematician, physicist, inventor, philosopher, and theologian. Key Topics: Pascal's early life and education Pascal's contributions to mathematics Pascal's invention of the mechanical calculator Pascal's religious experience and shift to theology Pascal's later life and legacy Summary: Pascal's father, Étienne, forbad...

This podcast episode of Men of Mathematics introduces Pierre de Fermat, a contemporary and rival of Rene Descartes, who is considered one of the greatest amateur mathematicians. Key Topics: Fermat's background Fermat's contributions to mathematics Summary: Pierre de Fermat was a lawyer by profession but is renowned as perhaps the greatest amateur mathematician in history. Although not a profession...

This podcast episode discusses the Genesis Block in Bitcoin, created by Satoshi Nakamoto on January 3, 2009, and its significance as the foundation of the Bitcoin network. Key Topics: Genesis Block Satoshi Nakamoto Financial Crisis of 2008 Immutability Bitcoin Transactions Summary: The Genesis Block, also known as Block Zero, is the first block in the Bitcoin blockchain, created by Satoshi Nakamot...

This podcast episode of Satoshi's Complete Writings discusses the concept of Proof of Work in Bitcoin, its significance in preventing Sybil attacks and double-spending, and its role in establishing decentralized consensus. Key Topics: Sybil Attack Problem Proof of Work Decentralized Consensus Honest Majority Assumption Bitcoin Security Model Summary: The episode addresses the challenge of determin...

This podcast episode of Satoshi's Complete Writings, titled "Double Spending Solved," discusses how Bitcoin solved the double spending problem, which had plagued previous digital cash attempts. Key Topics: Double Spending Problem Centralized vs. Decentralized Systems Blockchain as a Solution Transaction Validation Summary: The episode begins by highlighting that the fundamental requirement for an...

This podcast episode discusses Satoshi Nakamoto's vision of replacing institutional trust with cryptographic proof in a peer-to-peer electronic cash system. Key Topics: Trust in Financial Systems Cryptographic Proof vs. Trust Trustlessness in Bitcoin The Genesis Block Summary: Satoshi Nakamoto's core vision was to create a purely peer-to-peer electronic cash system that could operate without trust...

This is the second episode of the Internet Math podcast, where the hosts discuss their views on math, its connection to spirituality, and the importance of individual knowledge creation. Key Topics: Ice storm in Nashville The role of mathematics in spirituality and understanding the universe. Pascal's Wager and its relevance to decision-making, particularly in the context of Bitcoin. The importanc...