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No country for mediocre mathematicians

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Re: No country for mediocre mathematicians

#141

Post by layer8 »

ventana wrote: post #2

It's interesting that this piece stands well enough if you replace mathematics with probably any other intellectual profession, including software development or pretty much anything else. And, I lie to anyone who asks me why I’m a mathematician. It is much easier to claim “I love learning the laws of life,” while literally handwaving, than it is for me to flashback to the twenty or so pivotal moments that lead to me…

> constant feeling of frustration caused by things not working or breaking for random reasons

That’s not a feature of software development, but a feature of working higher up in the stack and/or interfacing with lower-quality external systems. I am lucky to have been working on relatively self-contained systems for most of my career, where that experience hasn’t been a constant.

Re: No country for mediocre mathematicians

#142

Post by somesortofthing »

_carbyau_ wrote: post #117
somesortofthing wrote: post #115

Earlier quoted context omitted.

What happens when the thing they have to be responsible for takes multiple lifetimes to understand on even the most basic level, let alone know deeply enough to feel comfortable taking responsibility for it?

Again, engineers know what needs to be tested, how, to what degree, with which materials, and with what safety margin. Your widget that mankind may never understand. Well, that's just like anything else in the world. Engineers didn't understand building foundations to anywhere like the degree we do now. Or how to build earthquake proof buildings for a long time. It didn't stop stuff getting built. But it sure affecte…

You can write human-comprehensible regulations(and the AI will helpfully beat whatever it's building into the shape of those regulations, probably against the spirit of them, in ways you can't detect) and you can have humans go through the checklist, but it won't accomplish much.

To use your foundation example, it'd be like trying to make go/no go decisions using engineers that don't and can't understand why the foundations go below the building rather than on top of it. Past a certain complexity level, a human approval process is just noise.

Re: No country for mediocre mathematicians

#143

Post by RGamma »

bitwize wrote: post #47
lo_zamoyski wrote: post #27

Earlier quoted context omitted.

> 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…

This is why I still like solving software problems on my own. Because those solutions now live in my head, rather than being spit out by some agent and then disappearing from the Dixie Flatline's memory once the session shuts down. And they deepen and enrich my life, and my life deepens and enriches them. A brief example: When I was a teenager I had the most profound crush on a girl, as teenagers do. Gorgeous and gre…

That insight was then. The current insight is that robot girls' task schedulers are configurable.

Re: No country for mediocre mathematicians

#144

Post by 028363922092 »

kodoman wrote: post #57
paulpauper wrote: post #18

Earlier quoted context omitted.

mathematicians or physicists fall into this category of knowing a lot about many thing . Sabine videos for example . she knows everything it seems

She is just arrogant. And asserts a lot of silly opinion as fact, her stuff on philosophy and theology is generally terrible.The sort of atheist that never actually looks into theology but knows the thing that first came to her head is a definitely the most amazing point against classical theology that has never been considered before.

[dead]

Re: No country for mediocre mathematicians

#145

Post by _carbyau_ »

somesortofthing wrote: post #142
_carbyau_ wrote: post #117

Earlier quoted context omitted.

Again, engineers know what needs to be tested, how, to what degree, with which materials, and with what safety margin. Your widget that mankind may never understand. Well, that's just like anything else in the world. Engineers didn't understand building foundations to anywhere like the degree we do now. Or how to build earthquake proof buildings for a long time. It didn't stop stuff getting built. But it sure affecte…

You can write human-comprehensible regulations(and the AI will helpfully beat whatever it's building into the shape of those regulations, probably against the spirit of them, in ways you can't detect) and you can have humans go through the checklist, but it won't accomplish much. To use your foundation example, it'd be like trying to make go/no go decisions using engineers that don't and can't understand why the foun…

You are absolutely correct that the LLM vs Regulation relationship would be adversarial.

This is why there is the saying: regulations are written in blood.

Mankind has been on a blast improving the understanding and engineering of stuff in our society for a while now. The regulations are already written in an adversarial sense.

Will LLMs take it up a notch? Yeah.

And then the people making the regulations in their respective expert field, will have to deal with it. What they do?! I'm not qualified to say. The whole point is that engineers are the people we deem qualified in their field.

Whatever LLMs do, we will still need them.

Re: No country for mediocre mathematicians

#146

Post by lo_zamoyski »

skew-aberration wrote: post #79
lo_zamoyski wrote: post #27

Earlier quoted context omitted.

> 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…

'All truths are easy to understand once they are discovered; the point is to discover them' If knowing was the valuable part, then nobody would need a PhD. You could know more by just reading textbooks. Research mathematicians research, everybody else just learns.

> 'All truths are easy to understand once they are discovered; the point is to discover them'

There are plenty of things that are difficult to understand that have been known by others for a long time. The point is that you don't understand those things. Your understanding of something doesn't benefit from someone else understanding it, per se. I will agree that having a guide does make it easier.

> If knowing was the valuable part, then nobody would need a PhD. You could know more by just reading textbooks. Research mathematicians research, everybody else just learns.

Knowing is the most valuable part! It's the whole point of research!

And where knowledge is concerned, there isn't a sharp line between what constitutes "learning" and what constitutes "research". How do you know a claim in a book is correct? You can take it on authority and just believe it. Or, you can seek to verify it yourself. As far as your own mind is concerned, you've discovered something for yourself. And what is a researcher doing? He's inferring things and reasoning and verifying his inferences. These are activities you use both during learning and during research.

Re: No country for mediocre mathematicians

#148

Post by senderista »

aleph_minus_one wrote: post #125
senderista wrote: post #108

Earlier quoted context omitted.

It turned out she had more talent for being a science influencer than a scientist.

I don't think she is untalented as a researcher in physics. Where she did not have talent at (and which is why she became a science YouTuber) is in "playing the career game" in physics research. Being a great researcher in some science requires very different talents than climbing the career ladder in this area of academic research.

She chose to pursue fringe directions in physics which may or may not have been related to her lack of academic success.

Re: No country for mediocre mathematicians

#149

Post by a_bonobo »

perching_aix wrote: post #130
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…

> Just today I saw a Claude Science set of results that made my own work of the past 2 months completely superfluous Could you share more about that?

Sure! I was building a workflow that assesses human gene model accuracy. Which part is supported by what evidence? Important for drug development; if we want to change $THING it better exist in the first place.

I came up with a set of rules, collated external databases, and then slowly (Claude-code assisted) built a Nextflow pipeline that gives me an automated report, which I then manually expand by 'human' assessment of the evidence.

Claude Science prompted with 'assess this gene' came up pretty much with the same rules, built a report, and did the manual assessment of evidence pitfalls for about 10% of a Claude Max subscription's tokens in about 15 minutes. Some details differ from my report - a different tool here or there - but overall, what we needed out of these reports is in the Claude Science report.

Re: No country for mediocre mathematicians

#150

Post by jgerrish »

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.

What a coincidence this came up today.

I'm not a mathematician. I minored in math, but even the undergrad work was honestly difficult for me.

For most people, this might be nonsense. But it doesnt have to be.

I'm trying to learn about Fast Fourier Transforms because they're relevant for an embedded device system I'm investigating. I'm also not an Electrical Engineer so it is mostly new to me.

To understand the language of FFTs, linear bases and the like, I've started working through Axler's Linear Algebra Done Right.

First, just learning more theory shows me we can learn and grow in our old age.

This week I worked through linear spaces. I'm actively asking myself questions and working with other fields besides the reals and complex numbers so I can understand coding theory in general more.

And the parent's comment about quotient fields and rings is directly related to a question I asked myself about the

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