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 knock on? Then he and Brian walk through every one of them, live.The result is a red-team tour of secp256k1. There are six offensive open problems and three defenses nobody has been able to prove, and each comes with the specific math that would have to break. Along the way: what Lean proofs actually are, why the discrete log problem is where the hardness lives, why "elliptic curve cryptography has been broken" will probably be a headline about some curve Bitcoin doesn't use, and why Big Bitcoin and Big Math are on a collision course.In this episode:• OpenAI's ~300-paper drop, the "11 squares" packing result everyone memed, and the human who immediately found the beautiful version nobody paid for• Lean explained: an audit trail for what the AI did, built up from the foundations of math• Why mathematicians are upset (the funding model behind long-standing problems), and Terence Tao's case that humans still matter• Division of labor between people and machines, and Brian's advice to his daughter Kayla, a senior math major: apprentice on Lean now, then go do your research• Big-O notation in two minutes, and why it's the first page of Neal Koblitz's number theory and cryptography book• The matrix-multiplication race (Strassen's ~2.8 down to ~2.37 and below) and why faster linear algebra is the real prize for AI• secp256k1 from first principles: y² = x³ + 7 over a finite field, point addition, and why public → private is a one-way street• Pollard's rho and the real defense line of 2¹²⁸, plus the Coldcard reminder: 2³² falls to one computer and ~2⁷⁰ still costs real money• Door 1: point factoring• Door 2: the "minors" attack. Build a big matrix and hunt for a vanishing determinant. Solved toy curves at 2⁵⁰, but an Aug 2026 follow-up showed it costs more than brute force at scale• Door 3: beating the generic √n bound (Shoup)• Door 4: the Koblitz-curve symmetry Satoshi chose for speed, and a 2026 Lean result that found only the trivial symmetry survives• Door 5: lifting the problem to a smooth curve, and why the height penalty blows up• Door 6: isogenies and the "weak cousin" curve, why GRH says every door in the family is equally strong, and why this is a combo pool shot rather than a break• The defenses no one can climb: one-way functions, proving the discrete log is hard, and P vs NP• Yehuda Lindell's (Coinbase) thread: AI proving hard theorems is no evidence that elliptic curve hardness is in danger• Shor's algorithm as an engineering and physics problem, not a math one, and the post-quantum camps (hash-based, lattices, isogenies)• A preview of the math panel at BTC Amsterdam: "do a podcast to get inspiration for the conference talk"️ Brian Hirschfield × Rob Hamilton Magic Internet Math: a first-principles podcast about mathematics, Bitcoin, and meaning⚡ Follow:Brian on X: https://x.com/Fundamentals21mRob Hamilton on X: https://x.com/Rob1HamAnchorWatch: https://anchorwatch.comMagic Internet Math: https://magicinternetmath.com Further reading:secp256k1: Security Status & Open Problems (episode companion): https://bitdevs.magicinternetmath.com/content/secp256k1-open-problemsOpenAI math results (Lean): https://github.com/openai/math#Bitcoin #EllipticCurves #secp256k1 #Cryptography #DiscreteLog #Lean #FormalProofs #OpenAI #PvsNP #PostQuantum #MagicInternetMath #Mathematics #RobHamilton