By the way, I don’t think climate denial has (or at least should, though I know Americans like to politicise everything under the sun) anything to do with ‘conservatism’.

We were told in 2023 that there’d be no more jobs within months and the singularity was here. At some point you have to realise it’s not happening.

Let me know when the other (much harder) millennium problems get resolved, let alone explained in a satisfactory way.

The whole point of mathematics is to vastly exceed that natural ceiling by gradually building a framework for understanding. In fact it’s wrong to speak of a ceiling altogether. If there were a ceiling, we’d have hit it long ago.

AIs have already swallowed the entire history of human thought, but apparently they’re ’just getting started’. I can only assume you don’t know what mathematicians actually do.

Most pure mathematicians are no more interested in ‘producing commodities’ than any other academic is. That’s not what the subject is about — at all. The confusion arises because mathematics turns out to be extremely useful (no surprise; it’s quite useful to have a detailed understanding of the basic principles of reality).

Again, this seems to be an alarmingly common fallacy here on HN. As a commenter above observed, pure mathematics (and that is what we’re talking about here) is in important ways closer to the humanities than it is to other sciences.

Thanks for providing a (much needed!) correction.

Unfortunately, it is actually surprisingly hard to pin down, and I think mathematicians (and, as a student, I count myself as one to some degree at least) now have the task of making this a lot clearer. If we want to justify our existence in the face of new machines that can seemingly ‘do our work for us’ (so far in a restricted context), we should give a robust defence of our practice. If we can’t do this, we simply don’t deserve the funding (which, by the way, again contrary to some misguided statements here, isn’t very much anyway!). I think all of this will become clearer to outsiders as time passes, but for now it’s not easy to give a quick answer — though I can try.

Mathematics is about understanding things. Isn’t that what every subject is about? Well, I suppose so, but mathematics more specifically does something like the following:

(1) observe some phenomenon in ‘reality’.

(2) attempt to formalise that phenomenon in such a way that it can be manipulated purely symbolically.

(3) use this (perhaps fairly arbitrary; remember that we can invent as many formal systems as we like) system to deduce from our initial assumptions new facts that would otherwise have been very non-obvious.

It seems like outsiders have a decent grasp of (3) and the application of AI to it, but have very little idea about the other two steps. It seems to be widely assumed among non-mathematicians that problems are essentially god given and that the job of a mathematician is therefore to chug away on these problems, manipulating symbols and trying out tools, in the hope of learning a yes/no answer to each one.

The first two steps are by far the hardest and most important, and they’re also the parts that AI seems currently unable to help with.

NOTE: this is not a deeply insightful description of what the subject is about, and there are many better characterisations out there. I think Tao and various others have written recently about why complicated and inscrutable AI-generated proofs aren’t nearly as valuable as one might imagine. (That’s not to say there’s no value to such proofs; perhaps in time, as technology improves, mathematicians will come to accept AI as part of the process.)

If you want to understand all of this issues better, reading the recent slew of guest posts on Tao’s blog would be a very good start.

Unfortunately, mathematics (especially pure mathematics) is by its very nature very, very poorly understood by those who haven’t worked as a mathematician. Even worse, those who don’t understand are seemingly not at all aware of their misunderstanding and are entirely confident in their (very wrong) characterisation of the subject.

Not sure quite what animates the absurd hatred of one of the least greedy groups of people on the planet, but it certainly isn’t experience. To anyone with any, it just looks like absurd derangement.

Otherwise you just sound like a jaded bitter washup.

Also, in the usual ZF set theory, it's empty.

Comments URL: https://news.ycombinator.com/item?id=47621251

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