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, write Python code, hit the limits of the machine, and eventually discover just how deep number theory goes—from the Pythagoreans to Euclid, Mersenne primes, and the still-open questions around perfect numbers.From there, we closed out our elliptic curve study guide by turning to Schnorr signatures, Taproot, MuSig, FROST, libsecp256k1, and the practical realities of Bitcoin development. We talked through why Schnorr is cleaner than ECDSA, how signature aggregation improves privacy and scalability, why wrench-attack resistance matters, and why the ecosystem around libsecp256k1 deserves far more attention. We also reflected on the tiny, careful pace of high-stakes Bitcoin cryptography work, the importance of maintainers like Jonas Nick, Pieter Wuille, Tim Ruffing, and Andrew Poelstra, and why understanding these mathematical foundations is the whole point of Magic Internet Math.Magic Internet Math: https://magicinternetmath.com/Magic Internet Math Podcast: https://podcasts.apple.com/us/podcast/magic-internet-math/id1868224151Phish Tour Archives: https://phish.com/tour-archives/BIP 340 — Schnorr Signatures for secp256k1: https://bips.dev/340/BIP 341 — Taproot: SegWit version 1 spending rules: https://bips.dev/341/BIP 342 — Validation of Taproot Scripts: https://bips.dev/342/BIP 327 — MuSig2 for BIP340-compatible Multi-Signatures: https://bips.dev/327/RFC 6979 — Deterministic Usage of DSA and ECDSA: https://www.rfc-editor.org/info/rfc6979/RFC 9591 — FROST Threshold Schnorr Signatures: https://www.rfc-editor.org/info/rfc9591/libsecp256k1: https://github.com/bitcoin-core/secp256k1rust-bitcoin: https://rust-bitcoin.org/AnchorWatch: https://www.anchorwatch.com/Blockstream: https://blockstream.com/Blockstream Research: https://research.blockstream.com/Jonas Nick: https://blog.blockstream.com/author/jonas/Andrew Poelstra and the Blockstream Research team: https://blog.blockstream.com/blockstream-research-the-focus/Pieter Wuille (sipa): https://github.com/sipaDaniel Shanks — Solved and Unsolved Problems in Number Theory: https://bookstore.ams.org/chel-297/SHAttered (the SHA-1 collision project): https://shattered.io/sha1-collision/

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 platform now extends into local community with a new math‑forward BitDevs in Philadelphia. Along the way we reflect on conferences as cultural glue and classrooms for Bitcoiners. The back half is a detour into poker as a living analogy for Bitcoin: bankroll management, game selection, Kelly criterion, and conviction under volatility. We kick around time‑preference versus risk‑preference, the perils of leverage, and treasury/custody tradeoffs—from digital credit notes and proof‑of‑reserves to insurance‑backed multisig. Expect practical takes on River’s yield accounts, ETF custody signals (Bitwise/Coinbase), and why resilient operations matter more than narratives—plus a few fun asides from WSOP lore to Rounders and the Potoshi pattern.'AnchorWatch': https://www.anchorwatch.com'Miniscript (reference implementation by sipa)': https://github.com/sipa/miniscript'Liana wallet (WizardSardine)': https://wizardsardine.com/liana/'WizardSardine': https://wizardsardine.com'Pay to Script Hash (P2SH) – Bitcoin Wiki': https://en.bitcoin.it/wiki/Pay_to_script_hash'Pay to Witness PubKey Hash (P2WPKH) – Bitcoin Wiki': https://en.bitcoin.it/wiki/Pay_to_witness_public_key_hash'NYC BitDevs': https://bitdevs.org/nyc'BTC Prague': https://www.btcprague.com'Zeus Wallet': https://zeusln.com'River': https://river.com'River Transparency / Proof‑of‑Reserves': https://river.com/transparency/'Kelly Criterion – Wikipedia': https://en.wikipedia.org/wiki/Kelly_criterion'Factorial (52! for deck permutations) – Wikipedia': https://en.wikipedia.org/wiki/Factorial'World Series of Poker (WSOP)': https://www.wsop.com'Binion’s Gambling Hall (WSOP origins)': https://www.binions.com'Rounders (1998) – IMDb': https://www.imdb.com/title/tt0128442/'Arkham Intelligence': https://arkhamintelligence.com'Holt’s Cigar Company (Philadelphia)': https://www.holts.com

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’s Two Cultures, to Paul Lockhart’s Mathematician’s Lament, Joel David Hamkins’ philosophy of mathematics, and the perennial tug-of-war between pure and applied work. We also dig into education: what good teaching feels like, why boredom or excessive difficulty turn students off, and how letting people “cook” can build conviction and genuine understanding.From elliptic curves to hash functions, we connect math to Bitcoin without turning into “I f’ing love science” cosplay. Allen throws down a challenge on explaining why hash functions have the properties we rely on (beyond just how they’re built or what they do), teeing up our next series. Along the way we touch cryptography culture, modular arithmetic, the modularity theorem vs. Fermat’s Last Theorem credit, and how AI tools help—and fail—when you push past the training data. Come for the banter; stay for the foundations, the philosophy, and the mission to create shareholder value by going pointlessly deep in order to build practical tools later.'Allen Farrington – Bitcoin is Venice': https://bitcoinisvenice.com/'AnchorWatch (company)': https://anchorwatch.com/'Joel David Hamkins – personal site': https://jdh.hamkins.org/'Lectures on the Philosophy of Mathematics (Joel David Hamkins)': https://jdh.hamkins.org/lectures-on-the-philosophy-of-mathematics/'Lex Fridman Podcast – Joel David Hamkins episode (show hub)': https://lexfridman.com/podcast/'C. P. Snow – The Two Cultures (overview)': https://en.wikipedia.org/wiki/The_Two_Cultures'Paul Lockhart – A Mathematician’s Lament (book page)': https://blpress.org/books/a-mathematicians-lament/'The Cult of Statistical Significance (Ziliak & McCloskey) – publisher page': https://press.umich.edu/Books/T/The-Cult-of-Statistical-Significance2'Learn Me A Bitcoin (educational site)': https://learnmeabitcoin.com/'NIST FIPS 180-4 – Secure Hash Standard (SHA-256 etc.)': https://csrc.nist.gov/publications/detail/fips/180/4/final'RFC 1321 – The MD5 Message-Digest Algorithm': https://www.rfc-editor.org/rfc/rfc1321'NIST guidance on SHA-1 (project page)': https://csrc.nist.gov/projects/hash-functions/sha-1'Andrew Poelstra – Blockstream profile': https://blockstream.com/team/andrew-poelstra/'Jonas Nick – Blockstream profile': https://blockstream.com/team/jonas-nick/'Peter Wuille (sipa) – GitHub': https://github.com/sipa'MathOverflow (research Q&A)': https://mathoverflow.net/'Math Girls (Hiroshi Yuki) – publisher page': https://bentobooks.com/math-girls/'Range (David Epstein) – publisher page': https://www.penguinrandomhouse.com/books/557690/range-by-david-epstein/