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No country for mediocre mathematicians

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Re: No country for mediocre mathematicians

#91

Post by ndriscoll »

aleph_minus_one wrote: post #58
bananamogul wrote: post #51

Earlier quoted context omitted.

I don’t remember us getting to fractions in kindergarten, but maybe the curriculum has radically changed since the early 70s. What exactly is the lie? 1/4 and 3/8 equals 5/8. Is there’s something more to that? Is that fundamentally wrong?

> Is there’s something more to that? Yes: this is about building the quotient field (field of fractions) [1] for some integral domain, or more generally, building the localization ([2], [3]) of a commutative ring with respect to some given set that is closed under multiplication (the special case of the quotient field for a ring R is obtained when one chooses R\{0} as such a set). -- [1] https://en.wikipedia.org/w/in…

Don't we still teach kids that e.g. 3/4=6/8, that they need to make a common denominator to add, and that they should cross multiply to check equality? I suppose we don't teach zero divisors, but otherwise, jargon aside, I'd be hard pressed to explain how we don't teach kids that fractions are members of ZxZ* mod (ad-bc).

Lies to children are like... time-reversal symmetry.

Re: No country for mediocre mathematicians

#93

Post by dhosek »

uptodatenews wrote: post #72
dhosek wrote: post #71

Earlier quoted context omitted.

Yeah, I’m pretty much on a trajectory of building up as much retirement savings as possible before AI completely kills my career. The sweet spot seems to be about three years out. I honestly don’t know how to guide my 12-year-old son who loves math¹ and coding. ⸻ 1. Which at his age essentially means solving computation problems, although he figured out how to take something like 0.3535… and turn that back into a rat…

Im going with this... scifi stuff still requires engineers. Its laughable and insulting to think these billionaire owners are going to make robots and llm loops to get real shit done https://rcsnyder.github.io/open-frontier-curriculum/ Ya "claude can you build me the next cern Thanks"

From what I’ve seen of what AI can do for coding, the part of software engineering that I like is going to be automated out of existence, much like the ability to do serious calculations by hand got automated out of existence with the development of computing. Writing code by hand will be as marketable as factoring 5-digit numbers in your head.¹

⸻

1. I enjoy doing both, but I doubt that anyone will pay me what I’ve been paid in the past for this five years from now.

Re: No country for mediocre mathematicians

#94

Post by 11101010010001 »

waterheater wrote: post #84
dhosek wrote: post #71

Earlier quoted context omitted.

Yeah, I’m pretty much on a trajectory of building up as much retirement savings as possible before AI completely kills my career. The sweet spot seems to be about three years out. I honestly don’t know how to guide my 12-year-old son who loves math¹ and coding. ⸻ 1. Which at his age essentially means solving computation problems, although he figured out how to take something like 0.3535… and turn that back into a rat…

As someone who's also thinking about their child's future, I've come to the conclusion that building their capacity for precise language by expanding their vocabulary and grammar in an array of domains and subdomains is the best way forward. Not only will they have a more detailed understanding of what's out there, but using specialized, narrow terminology with AI provides vastly better solutions than general prompt…

It was this way before AI.

Re: No country for mediocre mathematicians

#96

Post by adrianN »

uptodatenews wrote: post #72
dhosek wrote: post #71

Earlier quoted context omitted.

Yeah, I’m pretty much on a trajectory of building up as much retirement savings as possible before AI completely kills my career. The sweet spot seems to be about three years out. I honestly don’t know how to guide my 12-year-old son who loves math¹ and coding. ⸻ 1. Which at his age essentially means solving computation problems, although he figured out how to take something like 0.3535… and turn that back into a rat…

Im going with this... scifi stuff still requires engineers. Its laughable and insulting to think these billionaire owners are going to make robots and llm loops to get real shit done https://rcsnyder.github.io/open-frontier-curriculum/ Ya "claude can you build me the next cern Thanks"

If you want AI-proof careers it seems risky to go into knowledge work at all. Robotics lag behind mere computation, so something where you do awkward work in places designed around human bodies seems a lot safer. Plumbing, landscaping or something like that perhaps.

Re: No country for mediocre mathematicians

#98

Post by esafak »

whattheheckheck wrote: post #86
esafak wrote: post #82

Earlier quoted context omitted.

How many CERNs are there? Enough to build careers on?

No, what do you think about the book Four Futures?

I have not read it but I can't imagine a book written before the current explosion of AI can be accurate. What do you think of it?

Re: No country for mediocre mathematicians

#99

Post by JoshGG »

throwway120385 wrote: post #68
azan_ wrote: post #56

Earlier quoted context omitted.

> My physicist friend once asked me what the point of doing research was if someone like Terence Tao could have figured out everything in my dissertation in a tenth of the time. That's really mean thing to say

It's actually a really dumb thing to say and OP's response is the best one because it's a microcosm about how the world works. For every Terence Tao there's probably 20 more people cranking out high-quality work that's just a little less inspired. Their work is valuable and important, and asking that question is devaluing the entire endeavor of human knowledge. It's essentially positing that nobody else can contribut…

Very true but you can go even further than that. Advancing knowledge is a community endeavor. Consider where the field of mathematics would be if everyone except Terrence Tao and a handful of other luminaries stopped doing math research. It would die.

Re: No country for mediocre mathematicians

#100

Post by a2ff6eeb0 »

lo_zamoyski wrote: post #27
derangedHorse wrote: post #6

> My physicist friend once asked me what the point of doing research was if someone like Terence Tao could have figured out everything in my dissertation in a tenth of the time. I answered by pointing out that Terence Tao didn’t. Terence Tao did not find a small open problem posited by my advisor and publish a bite sized result making incremental progress. He has only so much time and so many other fish to fry. This…

> what the point of doing research was if someone like Terence Tao could have figured out everything A similar question is now being asked: what is the point of doing research, etc. if something like AI can figure out everything? The question betrays the parochial way in which many people think about knowledge. For them, knowledge is merely an instrument or an effect. It does not occur to them that knowing is a valua…

Yes, I think we will continue to have hobbyist learners as we advance AI, but it's going to be a niche, and not a commercially viable one.
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