Hacker News Reader

Comment by sillysaurusx | Hacker News Reader

It took many years to understand that!

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.

View on HN

I agree entirely. Industrially, I work a role within an IT team. My work is, I hope, useful and strives towards a purpose - my employer's purpose/business model.

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

It doesn't matter yet. Applications of pure math happen downstream decades or centuries later. It's hard to predict the impact.

I don’t like this framing because it implies any piece of pure math becoming useful is just a matter of time, and I see no reason to suspect this is the case.

> I see no reason to suspect this is the case

Isn’t history enough reason?

No history actually tells you that only 1% of produced maths is useful. You only see the good stuff not the ugly stuff.

I don't know why people are throwing around percentages so much in these replies. Percentage of what? Plus, the body of work of mathematics continues to grow all the time.

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.

In addition to what the other commenter said, it’s important to understand the scale. Cutting edge research 600 years ago was solving cubic equations. Today, cutting edge research requires potentially years of advanced study to understand the objects involved.

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.

I've read lots of math papers that were a complete waste of time because they were banal. The only "innovation" was to use different words to describe the same thing. New mathematics is actually pretty damn hard I suspect.

I think it's more about being open minded to strange uses. Maybe 3% of strange pure math ends up being used for something bigger? But since nobody knows what it'll be, it's good to be curious about all sorts of nonsense. Riemannian geometry was OBVIOUSLY absurd useless pure math sophistry, but then it turned out we lived in it. I think a lot of the work on modular forms and elliptic curves has come across that way too, despite the crypto intersection. The general idea is that, even if it's been a century or two, it's too soon to tell if something is useless, that's solid. And formalization of infinity has been useful in some practical exploration of proof systems used by humans. It might be the future of programming, who knows?

To follow up on this comment, I think that math should be viewed as a giant tree structure or pyramid

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?

Reply on news.ycombinator.com