Its clear to me. The arc of human advancement is closely related to our cumulative knowledge.

But what is knowledge? If you look closer, it is the formal expression of a transformation.

Now if you start to define knowledge in these terms you can start to see the difference between knowledge and fact.

But why am I even saying all of this? If you look at the current events with AI and trace them back to the history of computation itself, where were the big breakthrough?

If you look at AI (LLMs) specifically the big breakthrough happened when we were mathematically able to represent language in a vector space and then perform all sorts of permutations on it through algorithms where we could finally create a probabilistic prediction engine of language itself.

The key point to note here is, ‘Mathematical Representation’. Now linking it back to my opening comment on knowledge is the formal representation of a transformation. We were able to formally represent the structure and interconnections present in human language(s) without using language itself as the base through mathematics.

It has made me realise that to truly master a domain in strict terms we must be able to represent a model of that domain/idea mathematically. To clearly be able to manipulate it and unlock it's true capacities.

Because even if you look at the things we haven't figured out perfectly like the weather, universal laws, the human brain and consciousness itself. It clearly points to the fact that we can't represent those concepts formally and in totality TODAY.

But we are getting close(r), with new unlocks in AI we are getting capabilities that allows us to understand complex systems like planetary weather patterns, quantum chemistry to design better drugs and so on and this excites me like nothing ever has before!

What a time to be alive. What do you think will be the next space we can perfectly mathematify?