Episode 6: The Monster Problem: Fibonacci’s Deepest Secrets (Part 2)

Ready for the next level? In Part 2, we dive into the monster problem.

Imagine you’re trying to figure out if prime numbers—those special numbers only divisible by 1 and themselves—hide a secret code when you write them using Fibonacci numbers instead of regular digits. It’s like asking: Do these two totally different worlds—primes and Fibonacci—talk to each other? The monster part comes in because it’s huge—it pulls in geometry, binary codes, even calculus, and it’s tricky to solve. Mathematicians use crazy tools like Gowers norms to zoom out and see the big picture, hunting for patterns that might explain how numbers and shapes fit together. It’s not just one puzzle; it’s a whole adventure into the wildest corners of math!

Discover how math bridges the discrete and continuous with tools like Gowers norms and explores patterns in engineering, finance, and even your sleep cycles. Missed Part 1? Watch it here: [https://youtu.be/4UJt391PMqY] Let’s unravel the universe’s hidden math—hit play now!

00:00 Introduction and Recap of Previous Topics
01:14 Exploring the Zeckendorf Expansion
02:16 Prime Numbers and Zeckendorf Digits
02:56 Gelfand's Problems and Sparse Sets
03:52 The Sarnac Conjecture and Möbius Function
04:39 Morphic Words and Inverse Carry Propagation
05:43 Continuous Approaches in Number Theory
07:02 Gowers Norms and Their Surprising Connections
10:47 Fibonacci-like Sequences and Their Variations
12:37 The Ultimate Goal of Tackling the Monster Problem
15:55 Fibonacci Sequence and Geometric Shortcuts
19:20 Binary Code and Cryptography
20:18 Exploring the Thumor Sequence
21:24 Understanding Modulo Arithmetic
22:53 Multiplicative Order and Fibonacci
25:24 Random Polynomials and Real-World Applications
30:18 Mathematical Patterns in Financial Markets
32:39 Mathematics in Our Daily Lives
36:32 The Interconnectedness of Mathematical Concepts
40:33 Conclusion: Embracing the Mathematical Lens

📚 Key Papers for Further Exploration:
Fibonacci Partial Sums Tricks (https://arxiv.org/abs/2409.01296)
Binary sequences meet the Fibonacci sequence (https://arxiv.org/abs/2412.11319)
Primes as sums of Fibonacci Numbers (https://arxiv.org/abs/2109.04068)
A note on the number of real roots of random polynomials (https://arxiv.org/abs/2408.09247)

Dive in, keep exploring, and enjoy the mathematical journey!

Видео Episode 6: The Monster Problem: Fibonacci’s Deepest Secrets (Part 2) канала Sethu Iyer