Magic Internet Math

OpenAI just dropped roughly 300 math papers with Lean proofs, mathematicians are crashing out, and the vague-posting has started: "math is breaking, so cryptography is next." Brian and Rob Hamilton refuse to hand-wave. Rob fed the Magic Internet Math elliptic-curve study guide and the open theorems into a model and asked it straight: if you wanted to break Bitcoin's curve, which doors would you kn...

Magic Internet Math: https://www.magicinternetmath.com/ Shout out to https://x.com/uncleJim21 for the Alice in Wonderland story and the following rebuke of Lewis Carroll: https://www.youtube.com/shorts/33FYXpEWgyA This week we kept it loose but still got our reps in. We talked about why the math side of Bitcoin is starting to matter more in public, from conference panels and keynotes to the kinds...

We’re back because math keeps refusing to stay in the classroom. In this episode, I unpack two very different kinds of “math pop culture.” First, we revisit entropy, seed generation, and wallet security through a Bitcoin lens: dice rolls versus machine randomness, Bitkey’s firmware checks, Bitcoin Core as the most-reviewed software stack in the room, and why truly understanding how keys are made m...

Magic Internet Math is back. After the summer that set the Bitcoin world on fire — the Cold Card entropy disaster — Brian and Rob Hamilton (AnchorWatch) reunite for a two-hour deep dive on the event Rob spent three sleepless weeks at the center of, and what it taught them about AI, entropy, censorship, and self-custody. The spine of it: when funds started moving off Cold Cards, Rob loaded the firm...

In this episode, Rob and I sit down with Brandon Black (aka Rearden Code) for a deep dive into the quantum-computing debate around Bitcoin. We unpack why Brandon thinks the more useful framing is not “post-quantum” but “post-secp256k1,” and why Bitcoiners should care less about sci-fi narratives and more about understanding the actual cryptographic assumptions that protect coins today. Along the w...

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...