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No country for mediocre mathematicians

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Re: No country for mediocre mathematicians

#131

Post by wakawaka28 »

aleph_minus_one wrote: post #87
wakawaka28 wrote: post #80

Earlier quoted context omitted.

It's mighty pretentious to say that one needs all that theory to simply answer the question lol. For many questions, only the most rudimentary theory is plenty to get an answer, that is exactly the same answer as a more elaborate theory would yield.

If you just want to do some stupid computations: sure. But this is not what mathematics is centrally about. The central point is the kind of thinking about the respective topics (and understanding it) which these more abstract definitions encode. Understanding the topic just enough to do some elementary computations does not give you the kind of thinking that is often near a transcendental experience. Just to give on…

Those "stupid computations" comprise the bulk of useful work in the world. If one learns enough to do that, there may be no reason to go further. You're proving my point about the pretentiousness of insisting on the theory when one doesn't need it.

Nothing in your comment makes me want to go learn more theory, and I would argue that it's nonsense to anyone who is not a mathematician.

Imagine arguing that the only way to understand or appreciate basic set logic is to know all about infinite sets and ZF axioms... Most people, even mathematicians, will not understand all of that and have only heard about it in the most basics if at all.

A similar phenomenon happens with philosophy. Imagine arguing that simple logic is "stupid" and that one can only reason well if they have a total understanding of epistemology. I happen to think epistemology matters, and that people can benefit from at least being aware of it, but it is really a separate topic from actual mechanical logic and argumentation.

Re: No country for mediocre mathematicians

#132

Post by bluecheese452 »

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…

I thought we were adding 2 fractions? This seems completely unnecessary. It is like explaining how to kick a ball and you busting out string theory.

Re: No country for mediocre mathematicians

#133

Post by aleph_minus_one »

wakawaka28 wrote: post #131
aleph_minus_one wrote: post #87

Earlier quoted context omitted.

If you just want to do some stupid computations: sure. But this is not what mathematics is centrally about. The central point is the kind of thinking about the respective topics (and understanding it) which these more abstract definitions encode. Understanding the topic just enough to do some elementary computations does not give you the kind of thinking that is often near a transcendental experience. Just to give on…

Those "stupid computations" comprise the bulk of useful work in the world. If one learns enough to do that, there may be no reason to go further. You're proving my point about the pretentiousness of insisting on the theory when one doesn't need it. Nothing in your comment makes me want to go learn more theory, and I would argue that it's nonsense to anyone who is not a mathematician. Imagine arguing that the only way…

> Nothing in your comment makes me want to go learn more theory, and I would argue that it's nonsense to anyone who is not a mathematician.

You are free to ignore mathematics that is not completely trivial. I prefer (and would rather recommend) to understand it, and use this understanding to build a >1-billion-USD/EUR application out of it. :-)

Re: No country for mediocre mathematicians

#135

Post by photonemitter »

bmacho wrote: post #66
Terr_ wrote: post #44

Earlier quoted context omitted.

Terry Pratchett, The Science of Discworld : > As humans, we have invented lots of useful kinds of lie. As well as lies-to-children ('as much as they can understand') there are lies-to-bosses ('as much as they need to know') lies-to-patients ('they won't worry about what they don't know') and, for all sorts of reasons, lies-to-ourselves. > Lies-to-children is simply a prevalent and necessary kind of lie. Universities…

I don't get it? Nevertheless you don't have to lie to kids in any field, science, art or otherwise.

the earth is round, but not really quite. Gravity is 10 m/s*2, but not quite, it’s the same everywhere on earth, but not really. A day is 24 hours, but not actually. A year is 365 days, except it’s not, and the leap years correct for the disparity, but not exactly. Light travels at c, but not across all distances, or through all mediums. There’s no sound in space, but there is wind, and it does sort of carry vibrations in a way that roughly is what we mean by sound Space is really really cold, but it’s not actually cold, hot/cold doesn’t measure the same way

- it’s not about lying, that’s the wrong way to say it. We explain too simply. We lie by omission…

The point of Pratchett is to make fun of how the university humbles the students, trading their self-assurance in their knowledge for actual knowledge that is dried inside its books

Re: No country for mediocre mathematicians

#136

Post by photonemitter »

a_bonobo wrote: post #109

As an ex-academic (not mathematician), this really resonates. Every generation of researchers has to outperform the researcher generation before them - there are fully tenured profs out there who, with their track record, wouldn't get a postdoc nowadays. It's just a ratchet where every generation has to be more outstanding than the previous one, so yeah, you suddenly need 'triple the conferences'. Eventually that rat…

All research and progress boils down to Brownian Loop Soup. Someone/something having a result showing a connection does not mean they have explored "the way" to do it.

Not even the most elegant mathematically perfect solution is guaranteed to be the best way to crack a problem, or provide a definite answer.

Meandering paths through whatever we set our minds to do and serendipity is the way of human beings for the past few hundred millennia.

Re: No country for mediocre mathematicians

#137

Post by ofjcihen »

ACCount37 wrote: post #75
uptodatenews wrote: post #72

Earlier quoted context omitted.

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"

[flagged]

You seem to have one goal in every thread and that’s “rage boost” LLMs, often to the point of getting flagged multiple times. I’m honestly wondering if you aren’t just trolling HN.

Re: No country for mediocre mathematicians

#138

Post by [deleted] »

photonemitter wrote: post #135
bmacho wrote: post #66

Earlier quoted context omitted.

I don't get it? Nevertheless you don't have to lie to kids in any field, science, art or otherwise.

the earth is round, but not really quite. Gravity is 10 m/s*2, but not quite, it’s the same everywhere on earth, but not really. A day is 24 hours, but not actually. A year is 365 days, except it’s not, and the leap years correct for the disparity, but not exactly. Light travels at c, but not across all distances, or through all mediums. There’s no sound in space, but there is wind, and it does sort of carry vibratio…

[deleted]

Re: No country for mediocre mathematicians

#139

Post by jlev1 »

torginus wrote: post #120
randusername wrote: post #33

> We're all frustration addicts. We just want to bang our heads against problems we don't yet know how to solve. I've been tapering off AI lately. I think I've realized that conquering the struggle is the fun part, and accomplishments just don't hit the same if AI is smoothing over every friction and cordoning off all the pitfalls and rabbit-holes.

I hate struggling. I hate the realization that comes after the struggle about how easy was the problem I tried to solve. I hate realizing that I only reduced the number of problems from infinity + 1 to infinity, and have to do it again, forever. Yet I also hate when I get away from solving problems and feel like I'm wasting my life with nothing to show for it.

> I hate the realization that comes after the struggle about how easy was the problem I tried to solve.

You're far from the only one to feel this way, but I want to point out that this attitude is a choice, not an intrinsic feature of the problem. An equally valid perspective is that learning turns difficult problems into easy ones.

One advantage of the latter perspective is that it makes solving a problem a moment to enjoy and celebrate, whereas your perspective turns it (almost definitionally) into a moment of self-recrimination. "Hooray, I understand it!" vs "Why didn't I understand it sooner? (I'm so stupid!...)"

I actually suspect that there is natural selection for people with the more upbeat perspective to succeed at becoming mathematicians.

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