Another Crisis in mathematics

What does mathematics mean to me? There were a lot of ideas that were revealed to me. I think that there is a clue that I was going to be more of a philosopher than a mathematician. Mathematical ideas didn’t excite me so much as the philosophical ideas which were inspired by mathematics. 

1. I was trying to study physics for the first time. I don’t know how long it was before we studied static / dynamics / mechanics. But one day something struck me: we use mathematics a lot in physics because there is a similarity in structure between mathematics and the physical laws that govern our world today. In many ways, they were coherent / non-contradictory, consistent over time and space. The world is a predictable one because we can use mathematics to analyse things. People would say that this is obvious. But it’s not a trivial statement. What is the alternative, were this not to be true? Everything would be a mess. 

2. The idea that things resembled orthogonal dimensions: that we could treat different aspects of our wealth like they were on different spatial dimensions. Intelligence / wealth / other numbers that you could see in a dungeons and dragons profile. 

3. The idea that you could analyse and break down intuitive concepts into a series of mathematical tests. The delta and epsilon definitions of a continuous function. How do you relate a continuous curve to something else. 

4. The idea of a proof showing that a principle is scale free: the notion of continuity applies when you’re looking at a function at a bird’s eye view, and also at a worm’s eye view. 

5. The idea that knowledge is something that doesn’t really open up possibilities, but rather forecloses possibilities. Knowledge tells you that this and that possibility cannot be true, and in doing so, narrows the scope of what is worth taking into consideration. It clarifies by removing the clutter in your mind. A knowledgeable person actually has to think less than a novice because his head is not full of crap. A vector field dynamic system either has fixed points, or it tends to infinity, or it has loops or it has strange attractors. 

6. The idea of using mappings to reason: an algebra equation can map to curves of different shapes, which may cross this other line or axis, or it may not. 

And that’s the part of learning mathematics which is the most rewarding, that some of the lessons that you learn in mathematics will translate into how it teaches you to reason and argue in real life, even in domains that don’t obviously have to do with mathematics. 

The AI way of mathematics doesn’t really teach you that. 

One of my favourite classes in mathematics is nonlinear dynamics and chaos. 

I see it slightly differently. This is not a crisis for applied maths. It is a crisis for pure math.

Pure math does not seem to have real world applications for me. With only a few exceptions. Somebody solves an elliptical curves problem and a voice in my head says “who gives a fuck”. AI being able to prove theorems will make this voice louder.

I think there is a crisis in pure maths. There is no raison d'etre for pure maths, and that's why it's pure maths.

For applied maths, there will always be OR or machine learning or AI, so applied maths is in good health. In pure maths, because of the lack of applications, it's more like athletics. Pure maths is more like athletics than labour that produces economic value, and I feel that the AI developments have made this more apparent.

This is on top of the crisis in mathematics of the 20th century that I was taught in Snowy Hill.