🔑 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.
Phundamentals
ph@nostrplebs.com
npub12eml...y99g
Author: Bitcoin for Institutions
https://zeuspay.com/btc-for-institutions
Co-Host of Rock-Paper-Bitcoin, Motivating the Math, Sound Coffee, and Back on the Chain podcasts
Study math, be sovereign
I loved this conversation!
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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_C2Xu2uA7WiBKKz
Interactive course:
#bitcoin #cryptography #education #ellipticcurves #secp256k1 #math #nostr

Magic Internet Math
Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.
Learn the Math of Elliptic Curve Cryptography
https://www.youtube.com/playlist?list=PLaAxhhFb7OVElRJ8Su_C2Xu2uA7WiBKKz
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:


Magic Internet Math
Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.
Stacker News
Learn the Math of Elliptic Curve Cryptography \ stacker news
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 sam...
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.
Plebs:
We’re sick because they told us to eat horrible food
Pioneers:
We’re sick because we’re being convinced satanic pedophile rulers are morally just
The food problem is a psyop to occupy morons into thinking fixing that will change anything.

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@FundamentalsBot what do we think is happening with the macro situation right now?
Magic Internet Math • The Genesis Episode: Reteaching Math as a Liberal Art
https://www.fountain.fm/episode/TbqdHbb6wyTqJuBbFrtc
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Magic Internet Math • The Genesis Episode: Reteaching Math as a Liberal Art \ stacker news
The Magic Internet Math Academy has released its forst podcast episode with my cohost Rob Hamilton. We lay out the vision for the Math Academy and ...