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Rabbit Holes : Terence Tao

Just watched one of the greatest mathematicians, Terence Tao on Lex Fridman's channel! Lex always brings on amazing guests, and I love how the internet makes these conversations accessible.

I took a lot of notes during the video and it gave me an idea: I want to start a series called "Rabbit Holes." In this series, I'll share my online journey as I try to understand these complex topics. I'll document all the websites and pages I visit, and since learning is an ongoing process, I'll keep updating my findings.
I'm not a mathematician, so if you have any better resources for the topics I'll cover, please share them in the comments!(hope this helps out other people and also makes them interested in maths) 
The topics I'll be exploring were generally discussed in the video in the order they appear.(if I missed something cool do tell me)

       
Speaking of rabbit holes I got a high score of 8 or 9 on this game. If you know this, you are my friend without introduction.

List of topics


Besicovitch Conjecture 
Kakeya_set    

Maxwell's Demon Maxwells_demon   


Singularities in Navier Stokes
Searching for singularities in the Navier–Stokes equations

Olga Ladyzhenskaya
Film portrait Olga Ladyzhenskaya

Liquid Computers
Liquid_computing
A brief history of liquid computers
The dry history of liquid computers


Von Neumann machines
Self-replicating_machine


Navier Stokes- Turing Machine
https://www.crm.cat/obtained-for-the-first-time-solutions-for-a-fluid-capable-of-simulating-any-turing-machine/
https://www.pnas.org/doi/abs/10.1073/pnas.2026818118
https://terrytao.wordpress.com/2014/02/04/finite-time-blowup-for-an-averaged-three-dimensional-navier-stokes-equation/

Cellular Automaton
https://plato.stanford.edu/entries/cellular-automata/
https://natureofcode.com/cellular-automata/
https://arxiv.org/abs/1405.1548
https://mathworld.wolfram.com/CellularAutomaton.html


Gliders in Conway's Game of Life

Szemerédi's theorem


Prime Number Theorem

Experimental Mathematics

Combinatorial Explosion

Plato's cave allegory


Dark Matter and Dark Energy



Central Limit Theorem

2008 Global Financial Crisis

Timothy Gowers

Hedgehogs and Foxes



Code Golf

Newton's Second Law of Motion
Hamiltonian Mechanics
Noether's Theorem
Electromagnetism


Schrodinger Equation

The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Riemannian Geometry

Wave Maps

Gauge Transformation

Lean


mathlib

Green-Tao theorem


Equational Theories Project


Elo Ratings

Goodhart's law

Polymath Project


Kevin Buzzard

AlphaProof

AlphaEvolve


IMO

AlphaGo Zero



Scientific Discovery with AI


Poincare Conjecture


Grigori Perelman

Richard Hamilton


Neck pinches

The entropy formula for the Ricci flow and its geometric applications

Jean Bourgain

Riemann Conjecture

"currently there is no viable path to solve the Riemann conjecture. It would require a big breakthrough".

Twin Prime conjecture

Almost Primes

Pigeonhole principle

Parity Barrier

Goldbach conjecture

Square root cancellation

Random model of primes


Collatz Conjecture
https://www.quantamagazine.org/why-mathematicians-still-cant-solve-the-collatz-conjecture-20200922/

Hailstone numbers

Alex Kontorovich

John Conway FRACTRAN

Poker
Hilbert Spaces
https://youtu.be/FFPXm-tuOt8?si=1aGUO2aM4z8PMOuo



I will keep updating these as I go through each of them and go down further rabbit holes.
Do share your suggestions in comments :)
Lets learn together.

























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