[paulpauper]

keep the salary. if the goal it to change the world, to understand reality, to have an impactful life, have a good standard of living, etc. math is one of the hardest ways of achieving that. It's such a saturated field. Almost everything you can imagine has been done to the highest possible degree of abstraction. Every stone overturned except for things which may take a lifetime to even try to understand. Writing a blog post is probably way more fulfilling and also a doable challenge. A top mathematician may spend years working on a result that maybe if he is lucky be worthy of a footnote somewhere.

As a field I think math is well past its diminishing returns imho. It's like 'what was the last big philosophical discovery'...yeah...hard to think of one. Maybe the P zombie concept or the simulation hypothesis. But new and important books, fiction and non fiction, are being written all the time.

[ratzkewatzke]

I'm not going to gainsay your experience, but it doesn't match mine. Much of what you do in graduate school is to discover where the accessible areas of research are--where do we have a foothold, and are making progress, and what are some achievable results?

There are big and hairy problems that are bad investments for a young mathematician. I would steer students clear of the Collatz conjecture. But once you get up to speed in your research area, you usually find interesting problems thick on the ground.

Tenure-track positions are competitive, but I don't think there are a lack of interesting things to work on.

[paulpauper]

when I worked on math I found that no matter what problem I was working on, someone had already solved it completely or to high level of abstraction than I had. got discouraging after while.

[bombcar]

I think the whole point would be to retire and do math for fun, not desiring anything more than the joy of discovery, no footnotes, no recognition, just math.

99.99% of everyone won't be remembered for their "contributions" so why not do something you enjoy?

[lupire]

Even if no one remembers you, your work is a contribution. Learning for its own sake is a hobby for yourself, like watching TV or reading a book.

[eyelidlessness]

Let me be remembered for watching TV. I would be utterly delighted if that’s my long term legacy. “They finally rested and enjoyed the most banal show imaginable. It was relaxing. Any other lasting contributions will be in other records should you care.” There I’ve written my eulogy.

[formerkrogemp]

My grandfather's last 10 years were spent developing diabetes, watching those three shows, and playing Microsoft solitaire until death. If that's what you want, then, sure, you can be remembered that way.

[lordnacho]

This is why I'm happy to simply read the well established facts of a variety of fields. There's more than enough to learn for a lifetime, and from what I read about research there's a heck of a lot of BS in the way for small incremental gains.

Having said that, if something does come along that interests someone, they should try it. A friend of mine is doing his 2nd PhD 40 years after his first, having found his way into it via a love of jazz music.

[nextos]

I totally agree with what you say, but there's a lot of low hanging fruit in mathematizing biology.

It's not easy, but it's certainly very impactful.

[07121941]

can you expand on that? sounds really interesting

[nextos]

Drop me an email, contact info in profile :)

Otherwise, I will try to come back to this comment in a few days. I'm a bit busy with an urgent deadline, but I'm glad to expand on this later on!

[xphos]

This is what a imagine late stage security after OS mature there stacks and such. The advent/widespread use of robost memory protections like PAC and Cheri are going to be so depressing for those on the offensive.

I wish I just had more time to do math like the OP but the saturation of the field especially with people who can deeply understand the abstraction is very very intimidating.

[andi999]

About the simulation hypothesia, how is that different from Descartes evil demon?

https://en.m.wikipedia.org/wiki/Evil_demon

(apart from saying that the evil demon is a future type computer)

[postingposts]

The simulation stuff is just “Plato’s Cave”:Reloaded for people who never understood the concept of the cave in the first place. At a basic level you can interpret it from Gödel’s incompleteness theorems, which state that systems of logic need some form of observer to function. That observer concept reaches way back across different philosophical domains and authors as well.

[hither_shores]

That is not at all what the incompleteness theorems say.

The first incompleteness theorem says that for any consistent formal system T (with a recursively enumerable set of axioms) capable expressing of elementary arithmetic, T can express a statement which it can neither prove nor disprove.

The second incompleteness theorem says that T can't prove the statement "T is consistent". (I've still glossed over a number of technical details here; pick up a book on model theory if you want all the messy internals.)

First order logic is notably not capable of expressing elementary arithmetic. And observers aren't involved in any way.

[postingposts]

Yes, it is.

Sorry if you can’t read deeply into it or something. I’m not posting for grad students. I can sense you just like to correct people. Ahhhh I’m so wrong, you’re right?

[dang]

We've banned this account for continuing to break the site guidelines after we asked you to stop.

https://news.ycombinator.com/newsguidelines.html

[Agingcoder]

Godel's theorems mean something quite specific, and rely on an equally specific set of hypothesis.

It's tempting to try to apply them (or rather the same kind of conclusions) in other (non math) contexts, but it's very not obvious that you'll get something sensible. While you can play with the ideas, invoking Godel's theorem outside of its specific context doesn't make much sense.

[MichaelBurge]

I usually think of logics as search algorithms, since that's how the semantics for the meta-language describing them are defined.

I guess you could call a Turing Machine implementing the search algorithm for proofs implied by a logic an "observer", since it produces "reachability observations" i.e. proofs.

[jamesrcole]

just a minor thing to note here: there's the foundations of mathematics... questions like, what are numbers and other mathematical structures? How is it that math, any math at all, can potentially accurately describe parts of reality? Symbolic representations of math are just squiggily lines... why should squiggily lines have any special relationships to the nature of the universe? Details like that are far from being understood.

[Idiotfucker]

maybe I'm misunderstanding you, it sounds like you're just describing abstract algebra. See linear algebra or group theory as topic titles.

[ffhhj]

I couldn't wait that much, started researching stochastic processes a few years ago and been developing a theory for supertasks.

[DecentAI]

What was this utter gibberish I just read? I’m absolutely positive you have the least idea of what modern mathematical research entails or is even about. Please refrain from sharing your opinions on subject matters which you clearly lack any understanding of.