The Dark Night of Mathematics

I have two strong reactions to pieces like this:

First, this is about not just a job or career, but someone's identity. And we must have compassion that they are losing something that is fundamental to who they are. To them, it doesn't just feel like they're losing it, it is being taken by these companies that have so often acted in ways we despise

And that is a tragedy! And there are so many tragedies like this that will happen regularly as the technology advances

But my second reaction is one of this great shared experience. I studied math. Many of my friends are mathematicians. And it is now possible for anybody to access mathematical insights or think deeply about strange conjectures and theorems that were previously incomprehensible to anyone who hadn't at least studied mathematics in college

I don't know if 3b1b's Grant Sanderson considers himself a mathematician or science communicator, but I think of him as both. And while I expect he is someone with the mental capacity to find and prove new things in the world, I am grateful for the time he spends instead understanding things at a fundamental level and explaining and celebrating those concepts with his audience.

Not every mathematician can be or wants to be _that_ kind of mathematician. But for the moment, it is enough for me that higher mathematics is more accessible than ever.

And with some trepidation, I predict that the "traditional" job of a mathematician will change (of course it will). And it will change in big obvious ways and also subtle little ones. How will it change, though?

Importantly, math is actually going to be one of the fields where the fundamental things we thought we knew are shaken, because in the next five years we are going to start to see connections between things that were previously considered completely separate.

And so one way the job will change is that anyone who discusses math regularly will need to learn new things.

To me, this is exciting. It's almost like finding a bunch of new dinosaur fossils that fundamentally reshape our understanding. There's going to be a lot of work to do!

But "value provided to your customer" is not in itself what the society need. Or at least, it is a matter of opinion and you can probably find theoretical situations where even you would admit that maximizing actions based on the customer needs is not a good thing.

Same here: the value for the society may be more about "making art" than "being a cog in the paperclip factory".

> For me, the affective quality of learning mathematics is empathetically tethered to an act of discovery and creation. It is social. We are conversant with another mathematician—perhaps long dead. If we follow the chain of communication we arrive at a mathematician who enjoyed some original discovery. Human mathematics is Talmudic. It is a lively discourse of philosophical and religious richness spanning thousands of years.

This is really beautiful. And no matter what happens, two things have to be true: some form of lively philosophic and religious richness will keep being a core part of our history and will touch every person in some way; and it will change enormously over time (maybe with math continuing to be a small part, maybe not).

There is a part of math that is like that. There's also another part (as Vladimir Arnold provocatively said):

> All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like) hydrodynamics (supported by manufacturers of atomic submarines) celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).

> Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.

> Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.

> Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.

Those parts can just be delegated to AI the same way they used to be delegated to mathematicians. But Arnold continued:

> The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics (having no rational explanation).

An impressive number of things don’t make sense about this thought experiment. Whatever the genie says wouldn’t have much to do with the life you live afterwards, since your life changes after hearing the info. One persons careers worth of discovery work is not that much. A lot of work is dependent on the state of the world and can’t be moved into the past, even language changes. Someone could still do a craft or science or whatever afterwards— assuming life continues to have surprising complexity, the genie could only ever just scratch the surface.

I guess I don't follow admitting to a religious dimension in mathematics, and then eschewing the religious answer to the existential problem cited: prayer.

"Lord, this situation bites."

Potential reply: "Tell me about it."