Password making game: https://neal.fun/password-game/

AIME level FTW style game: https://mathblitz.herokuapp.com/

Ruler and compass construction game: https://www.euclidea.xyz/

Geometry game: Pythagorea

Cryptography game: https://cryptohack.org/courses/intro/enc2/

TeXnique: https://texnique.xyz/ A LaTeX reproducing game.

Real Analysis/Lean game: https://adam.math.hhu.de/#/g/AlexKontorovich/RealAnalysisGame

Permutations that avoid a pattern:
https://combos.org/jump

Music Composition:
flat.io

How would you define Bitcoin?
Bitcoin is a peer to peer network of distributed ledgers. Bitcoin utilizes cryptography. Bitcoin depends on trust in the Bitcoin core developers, and the general Bitcoin community to not vote against the ideals and core values of Bitcoin. Other than that, bitcoin is “trustless”. One can audit the Bitcoin source code. The fact that Bitcoin is developed by someone anonymous also can be of concern, as well as a 50 percent attack. Bitcoin provides an alternative to the traditional banking system, which is expensive (think of all of the buildings made for banks, folks working in banks, bank executive salaries)

Jameson Lopp’s Explanation of Bitcoin:
https://www.lopp.net/bitcoin-information/bitcoin-explained.html

What is an LLM?
The term AI can refer to several different things. An AI agent can be trained to play the game of Go or Starcraft at a high level. A Large Language Model predicts the next word in a sequence of words. Google Deepmind developed AlphaStar, an agent that can play starcraft as a result of imitation learning, reinforcement learning and deep neural networks. While both of these are AI’s, one is for natural language processing and one is for playing a video game.

Thoughts on AI:
If used incorrectly, AI (LLM’s) can become a tool that lets one degrade. Overreliance on AI can make you weak, not think analytically (i.e. solving math competition problems), not form a hypothesis and test it out (like in the scientific method), not conjecture something that is natural to consider after solving a problem.

If you are careful to not delegate critical thinking to an LLM, you can use AI to enhance you productivity possibly.

“What is my grade?” is not as important as “What did I learn?”

Your beliefs become your thoughts. Your thoughts become your actions. Your actions become your habits. Your habits become your values. Your values become your destiny. (Mohatma Gandhi)

Scientific truth does not becomes the truth by convincing its opponents and making them see the light, but rather because it’s opponents eventually die and a new generation grows up that is familiar with it.

Pulling hay out of a haystack (on describing finding Ramsey graphs. Almost all large graphs are Ramsey. We try to finding hay in a hay stack, but we always pull out a needle)