Motivate the Math

Fundamentals and average_gary

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What is the math that enables cryptography?

12/25/2025

MTM23: QED

Fundamentals. @Fundamentals21m Book: https://zeuspay.com/btc-for-institutions npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g AverageGary npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9 In this closing episode, I reflect with Gary on a year of building Motivate the Math—what we learned, where we fell short, and why the mission continues. We talk candidly about accountability, shifting priorities toward local, in‑person impact, and why Gary is stepping back to double down on family and community. I share how this project validated the need for stronger technical literacy in Bitcoin, the allies we found along the way, and how this work evolves next through Magic Internet Math and a broader Math Academy vision. We revisit the soft‑fork kerfuffle as a case study in how technical gaps fuel FUD, and why raising the baseline in math and cryptography matters for Bitcoiners, institutions, and anyone navigating an info‑war frontier. Looking ahead, I outline plans to keep the conversation going with a new podcast and more instructional content, plus a push toward local teaching hubs and in‑person collaboration. The goal remains the same: turn intimidating math into familiar terrain so fewer people get shaken out by technical fear. This show was a first brick—thank you to everyone who supported the mission and helped prove its importance. The work goes on.

36 min
10/13/2025

MTM22: The Cryptography Workbook (part 1)

Fundamentals. @Fundamentals21m Book: https://zeuspay.com/btc-for-institutions npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g AverageGary npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9 Cryptography Wookbook: https://github.com/cryptography-camp/workbook ---- navigate to the current release on the right tab to download the workbook ---- DO NOT LISTEN TO THE EPISODE UNLESS YOU HAVE THE WORKBOOK HANDY We’re back and recommitting to our North Star: getting comfortable with the math behind Bitcoin-grade cryptography. In this kickoff, we set the stage for a multi‑episode journey through a cryptography “workbook” on discrete‑log‑based multiparty signatures—using it as a scaffold to build real intuition for groups, fields, rigor, and proofs without being intimidated by jargon. We talk prerequisites (Z_p operations, cyclic groups, conditional probability, union bound, proof by contraposition), why rigor matters more than vibes, and how abstraction lets us reason cleanly about things like elliptic‑curve “addition” and key‑tweaking. We also peek at the table of contents we’ll tackle: negligible functions, games and asymptotic security, hash functions and collision resistance, commitments and accumulators (hello, Utreexo), one‑time and Lamport signatures, the discrete log problem, Pedersen commitments, DDH, ElGamal, the random‑oracle model and forking lemma, all the way to Schnorr signatures, key‑tweaks, and interactive aggregate signatures (e.g., DahLIAS). Expect a mix of precise definitions, worked examples, and occasional reinforcements from friends smarter than us—plus some probability detours like Monty Hall and Poisson to keep our statistical muscles warm.'DahLIAS: Discrete Logarithm-Based Interactive Aggregate Signatures': https://eprint.iacr.org/2025/692'BIP-340: Schnorr Signatures for secp256k1': https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki'Bitcoin Optech Topic: Schnorr Signatures': https://bitcoinops.org/en/topics/schnorr-signatures/'Taproot (overview)': https://bitcoinops.org/en/topics/taproot/'Utreexo: A dynamic hash-based accumulator optimized for the Bitcoin UTXO set (MIT DCI)': https://www.dci.mit.edu/utreexo'Random Oracle Model (overview)': https://en.wikipedia.org/wiki/Random_oracle'Forking Lemma (cryptography)': https://en.wikipedia.org/wiki/Forking_lemma'Decisional Diffie–Hellman (DDH) assumption': https://en.wikipedia.org/wiki/Decisional_Diffie%E2%80%93Hellman_assumption'Diffie–Hellman key exchange': https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange'ElGamal cryptosystem': https://en.wikipedia.org/wiki/ElGamal_encryption'Pedersen commitment': https://en.wikipedia.org/wiki/Pedersen_commitment'Lamport signature': https://en.wikipedia.org/wiki/Lamport_signature'Discrete logarithm (background)': https://en.wikipedia.org/wiki/Discrete_logarithm'Finite field (Z_p basics)': https://en.wikipedia.org/wiki/Finite_field'Cyclic group': https://en.wikipedia.org/wiki/Cyclic_group'Conditional probability': https://en.wikipedia.org/wiki/Conditional_probability'Union bound': https://en.wikipedia.org/wiki/Union_bound'Monty Hall problem': https://en.wikipedia.org/wiki/Monty_Hall_problem'Poisson distribution': https://en.wikipedia.org/wiki/Poisson_distribution'Contraposition (proof technique)': https://en.wikipedia.org/wiki/Contraposition'Riverside (recording platform)': https://riverside.fm'Nostr protocol (reference repo)': https://github.com/nostr-protocol/nostr

51 min
08/29/2025

MTM21: Probability, Poisson, and Adversarial Noderunning

Fundamentals. @Fundamentals21m Book: https://zeuspay.com/btc-for-institutions npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g AverageGary npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9 Pascal's Triangle https://en.wikipedia.org/wiki/Pascal's_triangle In this episode, we delve into the fascinating world of probability distributions and their relevance to Bitcoin's security and mining processes. We start by discussing the concept of probability distributions, such as binomial and Poisson distributions, and how they help us understand the likelihood of different outcomes in various scenarios. This understanding is crucial for modeling events like coin flips or mining block rewards, where knowing the average payout and the necessary capital to sustain operations over time is essential. We also touch on the importance of randomness and entropy in cryptographic applications, emphasizing the need for truly random variables to ensure security. The conversation then shifts to the adversarial nature of Bitcoin's network, highlighting the importance of understanding potential attack vectors, such as a 51% attack. We explore how the Poisson distribution is used to model the probability of mining success over a given period, and why it's vital for the network to be tested through both simulated and real-world attacks. The episode underscores the necessity of open-source software in creating robust systems that can withstand various threats, and the role of probability in ensuring the resilience and security of Bitcoin's decentralized network.

1h 8m
07/30/2025

MTM20: Quantum FUD Risks & Myths

Fundamentals. @Fundamentals21m Book: https://zeuspay.com/btc-for-institutions npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g AverageGary npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9 In this episode, we dive into the intriguing world of quantum computing and its potential impact on Bitcoin, specifically focusing on the vulnerabilities associated with Taproot and Schnorr signatures. We explore the concept of quantum FUD (Fear, Uncertainty, and Doubt) and discuss whether the threat of quantum computing is overblown or a legitimate concern. Our conversation touches on the mathematical underpinnings of cryptography, the discrete log problem, and the potential for quantum computers to break current cryptographic schemes. We also discuss the implications of exposed public keys in Taproot and the potential risks they pose in a future where quantum computing becomes a reality. Additionally, we delve into the broader implications of energy consumption and AI's role in the future of computing. We explore the Kardashev scale and the potential for Bitcoin mining and AI to drive humanity towards harnessing greater energy resources. The discussion also touches on the philosophical aspects of technological advancement, the potential for cooperation over conflict, and the role of cryptography in securing digital assets. Throughout the episode, we emphasize the importance of understanding and preparing for future technological shifts while maintaining a healthy skepticism towards sensationalized threats.

59 min
07/04/2025

MTM19: Linear Algebra, Bitcoin as a Standard Basis for Money

Fundamentals. @Fundamentals21m Book: https://zeuspay.com/btc-for-institutions npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g AverageGary npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9 In this episode, we dive into the challenges of keeping up with podcast production and the importance of discourse in understanding different perspectives. We reflect on the emotional roller coaster of attending the BPI summit, where the irrefutable truth of cryptographic math and its role in a peaceful revolution were discussed. The conversation also touches on the significance of meeting highly motivated individuals in the Bitcoin space and the impact of laws on the development of this technology. We explore the complexities of linear algebra and its applications in machine learning, discussing the concept of vector spaces and the challenges of mastering this mathematical field. The episode delves into the idea of a standard basis in nature and how Bitcoin represents a return to such a basis. We also consider the role of open-source software in creating systems that resist corruption and the importance of perseverance in overcoming difficult subjects like math. The discussion concludes with reflections on the nature of learning and the motivation to push through challenging topics.

55 min
07/03/2025

MTM18: DahLIAS: We Tried (part 2)

The paper: https://eprint.iacr.org/2025/692.pdf Fundamentals. @Fundamentals21m npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g XMR: xmrchat.com/fundamentals AverageGary npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9

53 min
05/25/2025

MTM17: DahLIAS: We Tried

The paper: https://eprint.iacr.org/2025/692.pdf Fundamentals. @Fundamentals21m npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g XMR: xmrchat.com/fundamentals AverageGary npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9 In this episode, we dive into the intricacies of Bitcoin, cryptography, and the fascinating world of aggregate signatures. We discuss the upcoming Shenandoah Bitcoin Club meeting, which will feature a Spanish-speaking sidebar, highlighting the growing need for multilingual resources in the Bitcoin community. The conversation shifts to the exciting events surrounding Baseload's birthday bash, featuring live music performances and the potential for future shows in the Shenandoah Valley. We explore the connection between music and math, and the importance of not being overly impressed by perceived intelligence, especially in fields like mathematics and cryptography. We also delve into a recent paper on DahLIAS, an aggregate signature scheme that offers constant size signatures, which could have implications for Bitcoin's future. The discussion covers the technical aspects of the paper, including the local forking lemma and the challenges of understanding complex cryptographic proofs. We reflect on the importance of continuous learning in the Bitcoin space, especially in cryptography, and the value of tools like Sparrow Wallet in navigating the complexities of Bitcoin transactions. The episode wraps up with a reflection on the journey of understanding and the motivation to delve deeper into cryptographic studies.

56 min
05/19/2025

MTM16: Showing Up, Making Blocks

Fundamentals. @Fundamentals21m npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g AverageGary npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9 In this episode, we delve into the complexities of showing up and the energy it requires, especially in the context of Bitcoin mining and decentralization. The conversation touches on the challenges of mining centralization, the concept of Fedi pools, and the lack of healthy dialogue in the Bitcoin community. We explore the social dynamics at play and the potential attacks on Bitcoin's integrity, emphasizing the importance of understanding the financial engineering behind mining and the role of social layers in Bitcoin's ecosystem. We also discuss the intriguing concept of fungibility over time and how Bitcoin might be the solution to maintaining balance in the financial world. The episode highlights the significance of understanding the math and financial engineering involved in Bitcoin mining, the role of decentralized hash rates, and the potential of projects like Bitaxe. Ultimately, the conversation underscores the need for a long-term perspective and the importance of embracing volatility and doing hard things to ensure Bitcoin's future.

1h 3m

What is the math that enables cryptography?

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Fundamentals and average_gary
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Motivate the Math