Fundamentals.  @Fundamentals21m
npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g

AverageGary
npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9

Jiimmy Breedlove's nostr post:
https://cdn.satellite.earth/83a0e194c453c9cab247e63d9fb15ef81d8a55af10d0f76df111a205b065bcf5.jpg

In this episode, we dive into the intricacies of balancing personal and professional life, as the hosts discuss taking a break from podcasting to recharge and manage multiple responsibilities. The conversation transitions into the unique dynamics of working within corporate structures while pursuing personal passions, highlighting the freedom and constraints that come with such arrangements.

The discussion then shifts to the technical realm of Bitcoin and cryptography, exploring the mathematical foundations that underpin these technologies. The hosts delve into the complexities of understanding cryptographic signatures, the importance of modular arithmetic, and the challenges of verifying Bitcoin's cryptography. They also touch on the philosophical aspects of mathematics and its parallels with Austrian economics, emphasizing the need for a deeper understanding and verification of the math behind Bitcoin.

Fundamentals.  @Fundamentals21m
npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g

AverageGary
npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9

Dr. Peyam Youtube
https://www.youtube.com/c/drpeyam

BIP340
https://github.com/bitcoin/bips/tree/master/bip-0340

In this episode, we dive into the world of mathematics and cryptography, exploring the nuances of teaching and learning math as an art form. We discuss the importance of passionate educators and the impact they have on students, drawing parallels between teaching and creative expression. The conversation touches on the struggles of learning complex subjects, like math, and the joy that can be found in understanding and mastering them. We also highlight the role of coding in appreciating math as an art and the satisfaction that comes from solving complex problems through code.

We further explore the intricacies of cryptographic protocols, focusing on Schnorr signatures and their advantages over ECDSA, particularly in the context of multisignature schemes. The discussion delves into the technical aspects of Schnorr's linearity and closure properties, and how protocols like Frost and Musig enhance its functionality. We also touch on the broader implications of cryptography in ensuring privacy and sovereignty, emphasizing the need for a deeper understanding of math to fully grasp these concepts. The episode concludes with reflections on the importance of local collaboration and the potential for Bitcoin to drive hyper-localization in cryptographic practices.

Fundamentals.  @Fundamentals21m
npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g

AverageGary
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In this episode, I'm joined by Average Gary as we delve into the fascinating intersection of mathematics and music, exploring how mathematical concepts can be applied to understand musical patterns and time signatures. We discuss the intriguing idea of pattern recognition and its role in both mathematics and music, highlighting how humans are naturally wired to recognize patterns, which can be mistaken for mathematical talent. We also touch on the concept of mastery, emphasizing the importance of putting in the hours and the will to learn, even when it seems like a waste of time.

We further explore the idea of being a generalist versus a specialist, and how this relates to understanding complex systems like Bitcoin. The conversation shifts to the importance of struggling and pushing oneself to the edge of one's abilities to truly master a subject. We discuss the concept of escape velocity in learning and how reducing friction can help achieve mastery. The episode concludes with reflections on how Bitcoin can serve as a tool for learning and understanding complex systems, and the importance of finding one's unique path in the world of mathematics and beyond.

A Mathemetician's Lament
https://cdn.satellite.earth/473cc46a079cb18196fb3b9b11933b373b607d5e3f8b5e581f3147387b0f17dd.pdf

Learn Me a Bitcoin: Schnorr
https://learnmeabitcoin.com/technical/cryptography/elliptic-curve/schnorr/

Fundamentals
npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g

AverageGary
npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9

Motivate the Math Nostr Community
https://satellite.earth/n/MotivateTheMath/npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g

A First Course in Abstract Algebra Textbook
https://a.co/d/ekzPCaQ

Isomorphism Between Elliptic Curve Addition and "Regular" Addition
https://math.stackexchange.com/questions/3831478/isomorphism-between-elliptic-curve-group-over-mathbb-r-and-0-1-under-addi

Hasse's Bound
https://planetmath.org/hassesboundforellipticcurvesoverfinitefields

Bitcoin's Prime Number
https://math.stackexchange.com/questions/3931161/is-secp256k1s-prime-prime

Fundamentals.  @Fundamentals21m
npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g

AverageGary
npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9

Square and Multipply Algorithm
https://www.youtube.com/watch?v=cbGB__V8MNk

Fundamentals
npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g

AverageGary
npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9

Proofs
https://www.youtube.com/watch?v=HIkIqt_ytdc

Fermat's Little Theorem
 https://mathworld.wolfram.com/FermatsLittleTheorem.html
Euler's Function
 https://en.wikipedia.org/wiki/Euler's_totient_function
Elliptic Curves: Point Addition
 https://www.rareskills.io/post/elliptic-curves-finite-fields
 
Fundamentals
npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g
AverageGary
npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9

Proof by Mathematical Induction
https://youtu.be/Tm2PJPvAULs?si=H_RJ5rmVeyPDYM9W
https://youtu.be/KW5k7ZsQmwo?si=8rEdf2dUcTw74QZ5

Understanding Cryptography
https://www.youtube.com/watch?v=2aHkqB2-46k

Fundamentals
npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g
AverageGary
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In this episode, we dive deep into the fascinating world of elliptic curves and their significance in cryptography. We start by discussing the basics of elliptic curves, particularly focusing on the polynomial equation y² = x³ + 7, which is crucial for Bitcoiners. We explore how operations on these curves, like adding points, form a group and why this concept is important.
We then delve into the textbook by Neil Koblitz, which highlights the importance of elliptic curves in cryptography. The discussion transitions into the axioms of groups, such as closure, associativity, identity, and inverses, and how these relate to elliptic curves.
Our conversation takes a turn towards Fermat's Little Theorem and its application in cryptography, particularly in computing inverses in finite fields. We explore how this theorem simplifies calculations with large numbers and its implications for public key cryptography.
We also touch on the Diffie-Hellman key exchange, explaining how it enables secure communication over the internet by deriving a shared secret without exposing private keys.
Throughout the episode, we emphasize the importance of understanding these mathematical concepts to grasp the underpinnings of cryptographic systems, especially in the context of Bitcoin and other cryptocurrencies.

2^173(mod5) = (2^4)^43 * 2^1 = 1^43 * 2^1 = 1 * 2 = 2
 2^4(mod5) = 1 because 16(mod5) = 1
Fermat's Little Theorem
 https://mathworld.wolfram.com/FermatsLittleTheorem.html
Euler's Function
https://en.wikipedia.org/wiki/Euler's_totient_function
Elliptic Curves: Point Addition
https://www.rareskills.io/post/elliptic-curves-finite-fields
Diffie-Hellman Illustration
https://www.youtube.com/watch?v=NmM9HA2MQGI
Fundamentals
npub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99g
AverageGary
npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9
In this episode, we dive deep into the fascinating world of elliptic curves and their significance in cryptography. We start by discussing the basics of elliptic curves, particularly focusing on the polynomial equation y² = x³ + 7, which is crucial for Bitcoiners. We explore how operations on these curves, like adding points, form a group and why this concept is important.
We then delve into the textbook by Neil Koblitz, which highlights the importance of elliptic curves in cryptography. The discussion transitions into the axioms of groups, such as closure, associativity, identity, and inverses, and how these relate to elliptic curves.
Our conversation takes a turn towards Fermat's Little Theorem and its application in cryptography, particularly in computing inverses in finite fields. We explore how this theorem simplifies calculations with large numbers and its implications for public key cryptography.
We also touch on the Diffie-Hellman key exchange, explaining how it enables secure communication over the internet by deriving a shared secret without exposing private keys.
Throughout the episode, we emphasize the importance of understanding these mathematical concepts to grasp the underpinnings of cryptographic systems, especially in the context of Bitcoin and other cryptocurrencies.