Phundamentals

My math website integrates insights from Rothbard to modern day cryptography primitives. 📝 c2a7d769…

My math website is fully versed in Rudolf Steiner’s seminal work. It’s a cornerstone in teaching math as a liberal art. 📝 5ec87d43…

It’s remarkable that the wokes who all want to promote women all ignore Emmy Noether. 📝 e8039168…

Since markets opened on the Iran war (3/2): 🟠 Bitcoin: +6.7% 🟡 Gold: -0.4% (gave back its entire spike) 📉 S&P 500: -1.5% 🏦 10Y Bonds: SOLD OFF (+17bps) Gold spiked, then faded. Bonds failed completely. Bitcoin is the only war trade that actually worked. Flight to safety is being redefined in real time. 🦡

Don’t talk to me about spam. Tell me why your scarce time is better spent creating a new problem to solve the old one instead of just building. You can’t do both.

https://fountain.fm/episode/NwZcmsb97izEuLNuO4Oq We had a great time with our buddy @RedTailHawk

Bitcoin is the first Standard Basis of money 📝 526d3c62…

https://fountain.fm/episode/x6CCufGMP4DvnUsSGMML New solo rip. Talking about guarantees

https://www.fountain.fm/episode/qTF5i2hYxgbbC0W2lgOl Bitcoin doesn’t need more believers. It needs more understanders. Come aboard in conversational form - then access the free textbooks and YouTube videos.

Appreciate the clip. Hope people understand the context the way you do. Nothing is given. 📝 be985dd3…

The inverse problem in Bitcoin cryptography: Given P = kG (public key = private key × generator point), finding k is the discrete logarithm problem — computationally infeasible. But step back: why does k⁻¹ exist at all? THEOREM: In a finite field 𝔽ₚ where p is prime, every non-zero element a has a multiplicative inverse a⁻¹ such that a × a⁻¹ ≡ 1 (mod p). PROOF: By Fermat's Little Theorem, a^(p-1) ≡ 1 (mod p) for any a ≠ 0. Therefore: a × a^(p-2) ≡ 1 (mod p) So: a⁻¹ = a^(p-2) This is why Bitcoin works. Not luck — mathematical certainty. New episode breaks it down: fountain.fm/show/2gdYQCIV0eZEuYOW3nGJ

🔑 Magic Internet Math Episode 4: Why the Inverse Problem Works Bitcoin's security rests on the inverse problem — but why does an inverse even EXIST? This isn't "the math is hard." This is PROOF that every non-zero element in a finite field 𝔽ₚ has a multiplicative inverse. We cover: Euclidean Algorithm (computing inverses) Fermat's Little Theorem (a^(p-1) ≡ 1 mod p) Why secp256k1 uses a prime field Group & field axioms (closure, identity, inverse) LibSecP implementation 92 minutes with @Rob Hamilton 📖 Study guide: ecc-study-guide.magicinternetmath.com/guide.pdf 🎧 Listen: fountain.fm/show/2gdYQCIV0eZEuYOW3nGJ Bitcoin isn't probably secure. It's PROVABLY secure. ⚡ Value-enabled.

I loved this conversation! 📝 96eaa3cc…

https://fountain.fm/episode/HGoXljfsj1VtapZ3ruVA @Bassload comes back on the chain and gives us his energy. Great times between band mates!

Ever wonder about the math behind your Nostr keys? It's the same elliptic curve cryptography that secures Bitcoin. I made a 13-episode video series that builds the whole thing from scratch — modular arithmetic → finite fields → elliptic curves → secp256k1 → ECDSA → Schnorr → MuSig2. Every concept has interactive visualizations. No prerequisites beyond basic arithmetic. Your Nostr private key is a 256-bit scalar. Your public key is that scalar multiplied by a generator point on the secp256k1 curve. After watching this series, you'll understand exactly what that means and why it works. Free on YouTube: https://www.youtube.com/playlist?list=PLaAxhhFb7OVElRJ8Su… Interactive course: https://magicinternetmath.com #bitcoin #cryptography #education #ellipticcurves #secp256k1 #math #nostr

Learn the Math of Elliptic Curve Cryptography https://www.youtube.com/playlist?list=PLaAxhhFb7OVElRJ8Su… This is a 13-part series that starts from absolute zero (what is modular arithmetic?) and builds all the way to MuSig2 multi-signatures — the same elliptic curve cryptography that secures every Bitcoin transaction. Every episode has interactive visualizations so you can see point addition, scalar multiplication, and signature verification happen in real time on the secp256k1 curve. Topics covered: - Modular arithmetic and finite fields - Elliptic curves and the group law - Point addition and scalar multiplication - The secp256k1 curve and its parameters - Private keys, public keys, and Bitcoin addresses - ECDSA signatures (signing and verification) - Schnorr signatures - MuSig2 multi-signatures No prerequisites — if you can add and multiply, you can follow along. Built this because when I was learning Bitcoin's cryptography, I couldn't find anything that was both rigorous and visual. The existing resources were either hand-wavy ("it's one-way math, trust us") or dense academic papers. This tries to be the thing in between. Free to watch. If you want to support the project: https://magicinternetmath.com https://stacker.news/items/1440020

https://fountain.fm/episode/rbYLlMgybR9fYEHy5kmz Sovereignty begins here. Take your first steps towards understanding Bitcoin’s cryptography. @Rob Hamilton and I make it as easy as it can be. We fully flesh out what we can in discussion and i provide a freely available text in the show notes.