Do I 'go home' - leave my home office - and think about it? No. Do I muse on how to solve a work-related issue when I'm showering? Also no. Will I forget almost everything about this job as or when I move onto the next? Definitely yes.
But academically, I'm interested, and actively publish albeit modest, low-impact research, in relational databases. I love the set-based approach to all matters SQL and after many years in the field still fool around trying to embellish, attack, improve and invent the core ideas.
Why bother? Even if I come up with some magical new improvement to RDBMSs, it doesn't matter. If I fork MySQL and try out my ideas, no one cares. I'll never get the traction or the FOSS community support, I'll spend more time playing politics and managing collaborators than I'd like (zero) and I enjoy the independent thought that my interests bring.
So my academic work is pointless. But it's meaningful to me. And I think that's what matters. I don't understand one-tenth of the ideas in this article, but that doesn't matter. What matters is that it's interesting to somebody.
It doesn't matter yet. Applications of pure math happen downstream decades or centuries later. It's hard to predict the impact.
Isn’t history enough reason?
The core of the original comment that started this chain was:
> Applications of pure math happen downstream decades or centuries later.
My argument was that history shows that a surprising amount of mathematics does eventually trickle down into applications. I don't think anyone is arguing all of mathematics eventually sees an application.
Again, my point was that history does indeed seem to show that "applications of pure math happen downstream decades or centuries later". As the original commenter said, it's hard to predict what will be the next thing to be applied.
There are more mathematicians alive today than at any point in human history, and their work has become specialized to a tremendous degree. Gone are the days where one mathematician could do substantial new work in a dozen diverse areas.
So, in short, the fact that historically lots of pure math has not found use, the specialized nature of modern research math, the volume of work being out out, and an irreverence for applications(again, this is _pure_ math) leads me to be doubtful that even a moderate amount of modern pure math research will ever be useful in any practical sense.
At the bottom are all sorts of applications of linear algebra and optimization (calculus) are related to machine learning, deep learning (AI), physics, engineering etc.
One level up there are all sorts of ideas in algebra and mathematical analysis that are leading to new ideas in linear algebra and optimization (calculus)
Going one level higher, there are ideas in mathematical logic and set theory that are improving our understanding our algebra and analysis.
If you look at a specific result at the very top of the pyramid as ask why does it matter? It is difficult to give a good answer. Clearly we want to base of the pyramid, but do we need to keep building it up? Should we stop at a certain level?
It’s not a flippant question at all.
The answer is, it doesn’t matter. And that’s the joy of it.
It wasn’t until I got into ML that I learned the value of doing unimportant work. When you’re free to think about inconsequential matters very seriously, you end up discovering so many useful things. It was how I independently rediscovered what is apparently called the Discrete Hartley Transform.
You have a vague notion that what you’re doing might be important, but it’s not the focus. It matters because it’s fun in a way that nothing else can be.
Of course, the more serious folk won’t admit it’s fun. It’s serious work. And they’re not wrong; nobody’s fooling around. Our time is every bit as precious as an executive’s.
But their goal is to change the world. Ours — or mine, at least — is to know the truth of a thing that most people don’t know.