I am reading “Thinking, Fast and Slow” now and I’ve just realized that a great amount of the events happening around are just random. It is just our brain that always tries to come up with a story to make some sense out of the environment.

This totally changes my perspective. So far I thought that patterns are everywhere and a well-designed neural network would solve almost every problem. I am wondering whether mathematicians have already come with a way to predict those random events.

This opens a really good discussion about what is random in real world.

If something is truly random, it is, by definition, impossible to predict. But even random number generators in common libraries (tf, numpy, etc) are not like that, but pseudo-random generators. That may be the case for a lot of the events that appear to be random but just have a very complicated and intricate explanation underneath. That is when a well-designed neural network, as you said, can come in handy.

Alvaro makes some great points here: it’s not that you can predict events that are inherently random, but you can have a mathematical model for the behavior. That’s a topic that is covered by the general field of Probability and Statistics. I’m sure you’ve heard of a Normal Distribution or maybe even a Poisson Distribution or Markov Chains. Those are different mathematical models that may describe a particular random phenomenon that you are studying. The general field of Game Theory is another area where mathematicians have studied how to model unpredictable behavior in various ways.