Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

No country for mediocre mathematicians

garvvee.substack.com

Post reply on HN
Print view View original

151–159 of 159 posts

Re: No country for mediocre mathematicians

#151

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 rings is directly related to an active learning question I asked myself about whether the set with only the zero element is a linear space. I don't think it is a field if 0 is the multiplicative identity, 0 can't be 1, so it can't be a linear space, right?

But it works. I guess the set of the field for the scalar in a linear space is always assumed to contain more elements. It's a different set than the linear space. It seems like, duh, of course it is. But you don't see it until you work through it. And I'm guessing my experience can inform teaching others.

It's confusing to me, maybe because the notation is sparse in explicitly defining the set of the linear space and the set of the associated linear space.

But this helps me truly understand linear codes down the line, and Linear Feedback Shift Registers and FFTs. It's not just theory to me, I can now understand what my peers are saying and contribute my own thoughts.

Re: No country for mediocre mathematicians

#152

Post by Waterluvian »

dhosek wrote: post #71
arjie wrote: post #65

Really enjoyable read. I escaped a career in Mathematics by being sufficiently bad at it that I only have a Masters. Fortunately, I escaped to a field immune to AI: CS and then a software engineering career. Well, not really, but I did get a good 15 years out of it so thank god for that. About half of my friends are founders of various startups and the rest are executives of and almost all of them have the view that…

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…

Being an artist has always been a pretty difficult career path. But lots of people do it because they love creating art. If AI actually does what people fear it will to programming, people like your son and mine can choose to be an artist as a hobby or make a go of it as a profession.

Re: No country for mediocre mathematicians

#153

Post by wakawaka28 »

aleph_minus_one wrote: post #133
wakawaka28 wrote: post #131

Earlier quoted context omitted.

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. :-)

I often ignore mathematics that is not completely useful to me these days lol. I get the appeal of learning neat theories and feeling like you got it all figured out, but I'd rather limit my studies to topics that are likely to bear fruit in my life. Complication and abstraction does not necessarily deter me, but it has been my observation that overly complicated or abstract ideas rarely pay off in my endeavors.

Re: No country for mediocre mathematicians

#154

Post by wakawaka28 »

jgerrish wrote: post #151
wakawaka28 wrote: post #131

Earlier quoted context omitted.

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 relev…

OK now you're getting into some more useful topics. Linear algebra is a great one with tons of applications. But if you want my advice, prioritize useful stuff and spend less time on theoretical baubles or bedrock-level boilerplate. This is unless, of course, you enjoy puzzles and hard work with little application.

Re: No country for mediocre mathematicians

#155

Post by vuurmot »

Waterluvian wrote: post #152
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…

Being an artist has always been a pretty difficult career path. But lots of people do it because they love creating art. If AI actually does what people fear it will to programming, people like your son and mine can choose to be an artist as a hobby or make a go of it as a profession.

the arts is crashing harder than programming

many schools have shuttered since ~2022

artist gigs are at an all time low

if you practice artistry as a craftsman in niches like carpentry, maybe you could make a living..

Re: No country for mediocre mathematicians

#156

Post by x-complexity »

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.

> Nevertheless you don't have to lie to kids in any field, science, art or otherwise.

...if and only if the kid in question has the mental capacity to take on the whole truth without confusion.

Some kids have the potential to go hog wild on multivariable calculus, and they should be given the chance to handle it all. But they shan't be the benchmark that others with differing capabilities must hit to understand a concept.

Re: No country for mediocre mathematicians

#157

Post by ebiester »

a_bonobo wrote: post #149
perching_aix wrote: post #130

Earlier quoted context omitted.

> 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' assessmen…

Consider that if this was ran from your machine - it would have all of your memories and might be relying on the past 2 months. I'd be curious what would happen if it was run independently.

(I am assuming they didn't train on your prompts, which is always a worry)

Re: No country for mediocre mathematicians

#158

Post by jgerrish »

wakawaka28 wrote: post #154
jgerrish wrote: post #151

Earlier quoted context omitted.

> 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 relev…

OK now you're getting into some more useful topics. Linear algebra is a great one with tons of applications. But if you want my advice, prioritize useful stuff and spend less time on theoretical baubles or bedrock-level boilerplate. This is unless, of course, you enjoy puzzles and hard work with little application.

> This is unless, of course, you enjoy puzzles and hard work with little application.

Wouldn't that be great? If we could teach our kids that learning for the sake of learning is awesome? If only that was all this world was.

But you're right, you and the thousands of others posting, it's not. You have that voice, and the hundreds of online stories about college losing value have that political voice.

In the post-AI future I can imagine recreational mathematics being a socially approved past time. It helps with age-related cognitive decline, etc.

But I can also understand people in that post-AI future who had smart political ideas that were more important to them than smart math ideas.

Impactful ideas.

Just getting snapshots and puzzling out that post-AI future I don't know if we'll have the right space to encourage positive care for our mental and physical landscapes.

Re: No country for mediocre mathematicians

#159

Post by wakawaka28 »

jgerrish wrote: post #158
wakawaka28 wrote: post #154

Earlier quoted context omitted.

OK now you're getting into some more useful topics. Linear algebra is a great one with tons of applications. But if you want my advice, prioritize useful stuff and spend less time on theoretical baubles or bedrock-level boilerplate. This is unless, of course, you enjoy puzzles and hard work with little application.

> This is unless, of course, you enjoy puzzles and hard work with little application. Wouldn't that be great? If we could teach our kids that learning for the sake of learning is awesome? If only that was all this world was. But you're right, you and the thousands of others posting, it's not. You have that voice, and the hundreds of online stories about college losing value have that political voice. In the post-AI f…

I'm not making any political statement here, or at least that was not my intention. Life is short and there are infinite things we could be learning about. The advanced math I'm talking about avoiding here is not recreational math, but you could potentially apply the same logic to recreational math. Personally I see a big difference between "routine" abstract/advanced math and recreational math, though there can be some overlap. People have written books about what makes a pleasant puzzle, for example. Some puzzles are deceptively simple to state and impossible to solve without elite level theories. I think one of the characteristics of a good puzzle is that it can be solved with reasonable effort and not consume your whole life. Another is that it not be so contrived and abstract, that you need to be heavily initiated to even understand it. The worst are the ones that require a ton of mechanical computations even after you figure out the key insight. I don't think those are very fun either. But then again, there are people who don't get tired of Sudoku lol...
Post reply on HN