7 ms·

No country for mediocre mathematicians

ventana 1mo ago
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 walking out of Gainesville with a PhD in Arithmetic Geometry. Since “normal” people mostly don't understand what the software development job is about, handwaving in response to regular questions: “what do you do at work?”, “what do you like about your job?” – is pretty normal. I think that most of us have some prepared answers ready to use. Mathematics is the thing you try to understand, don’t, get frustrated about, and then do. Just like the software development. I truly believe that the only people who can survive a software job are those who can tolerate the constant feeling of frustration caused by things not working or breaking for random reasons, and persevere in this environment to do the things you need to do.
- marcosdumay 1mo ago
  > “what do you like about your job?” For software development, normal people will just assume it's money and probably not even ask...
  - pwdisswordfishq 1mo ago
    They would not even be wrong.
    - binary0010 1mo ago
      Yeah seems like most programmers just do it for the money. I imagine only like 20% of us do it just because we enjoy it.
      - geodel 1mo ago
        I'd just say there are scores of people who like programing. But that's about it.
      - axus 1mo ago
        I feel like the number is higher for software work where I'm at, and lower for every other profession. Scary when you think that your doctor is in it for the money
        SoftTalker 1mo ago
        You can be a software developer without any formal training and without any licensure. Not so for an MD. It's going to attract more people who have the mentality of artists or musicians, i.e. people who do it for the love of the craft and as a creative outlet.
        ventana 1mo ago
        > You can be a software developer without ... any licensure. Don't jinx it. We are extremely lucky in this regard, and it actually looks like a rare exception.
        inanutshellus 1mo ago
        hopefully the MD that passes all the tests is still worth his salt even if he only chose the profession for the paycheck. but as one of the nearby professors is famous for saying: "C students gotta go somewhere." ( and since this is HN - he didn't mean the programming language :D )
        nkrisc 1mo ago
        There are plenty of easier ways to make money than becoming a doctor.
        Marsymars 1mo ago
        They tend to be higher risk though. If you've got the capacity for memorizing all the stuff you need to become a doctor, there's not much risk involved in attaining your doctor salary.
  - doctorpangloss 1mo ago
    For mathematicians in the US, it's because their parents like money.
- paulpauper 1mo ago
  A PhD in Arithmetic Geometry and a publication in a top tier journal is hardly mediocre in and of itself, as far the author is concerned. The equivalent for a software engineer is probably a leading AI engineer, with a strong publication count. I think a lot of people who are not mediocre are unaware of what mediocrity actually is. Yeah if you're only in the top .1% and comparing yourself to the literal best in the world, you will feel mediocre in that sense . A mid mathematician maybe publication in worse journals, teaching community college.
  - bananaflag 1mo ago
    > A PhD in Arithmetic Geometry and a publication in a top tier journal is hardly mediocre in and of itself, as far the author is concerned. It kinda is (sadly) because unlike engineering there aren't thousands of postdoc jobs in arithmetic geometry. And ofc in a year because of AI all math PhDs will be mediocre by definition.
  - p1esk 1mo ago
    As a professional mathematician, if you’re not advancing your subfield of research consistently you are mediocre.
    - fn-mote 1mo ago
      If you say so. Saying most tenured faculty at research 1 institutions are mediocre seems to be stretching the definition, though.
      - p1esk 1mo ago
        Who’s saying that?
  - kcexn 1mo ago
    It's still impressive, but it's not enough.
- bananaflag 1mo ago
  > And, I lie to anyone who asks me why I’m a mathematician. I prefer to say "I liked a girl" (because it's the truth)
  - sheafification 1mo ago
    My go-to is “It’s the only thing I was good at in school, I was hopeless at everything else,” which is only a slight exaggeration.
- layer8 1mo ago
  > 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.
hyperhello 1mo ago
Hobbies aren’t as fun when you have an overbearing friend who constantly shows off how much more they know and how quickly they can switch to talking about anything you want but in greater depth than you.
- MostlyStable 1mo ago
  I do not have a single hobby where I'm very far beyond the median hobby-haver in skill (that is to say: if you took all other humans who share my hobby, I'm likely somewhere near median for all of them). This may put me in top whatever percentile among all humans, since most humans don't share my hobbies and so are terrible at those things, but there are enough humans out there, and enough humans who share my hobbies, that I have always known that there are people who are vastly better at them than I am. Now yes, if I was constantly being followed around by one of the top 10 hobby-havers, pointing out to me all the mistakes or sub-optimal decisions I was making, that would indeed be annoying and reduce my enjoyment in the hobby. But why do you expect AI to be like this? I would love if I had one of those top 10 hobby-havers on call to answer every one of my (often inane) questions with infinite patience (and who would only talk about the hobby when I specifically initiated the topic). I'm already under no illusions that I'm the best, but it's now easier than it has ever been (for some hobbies, I expect others to join them over time) to get better at them....if one so desires.
- paulpauper 1mo ago
  mathematicians or physicists fall into this category of knowing a lot about many thing . Sabine videos for example . she knows everything it seems
  - jplusequalt 1mo ago
    Sabine is a crank who likes to wax poetically about fields she has no creds in.
    - BoredomIsFun 1mo ago
      She is a grifter, not crank.
derangedHorse 1mo ago
> 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 reminds me of a post I saw recently, although I can't remember the platform. It said something along the lines of assessing the limits of AI by finding the dumbest questions it can't solve. I think that pairs well as an additional way to view meaning through one's work. The linked post points out constrained attention as a way to bring meaning to novel work that no one else took on. With AI, this can still be applied to compute. I'm just wondering if there are a class of problems that humans, at least in the short-term, where humans need to be in the loop to solve more efficiently.
- pdm55 1mo ago
  I have just started reading this Gates Notes about reserving some jobs for humans: https://www.gatesnotes.com/a-turbulent-ai-era-and-critical-choices-to-make https://www.gatesnotes.com/a-turbulent-ai-era-and-critical-c...
- lo_zamoyski 1mo ago
  > 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 valuable thing in itself, that understanding is valuable and desirable. Yes, some knowledge has merely practical value, but theoretical knowledge is primarily sought for its own sake, because we desire to know reality. So, even if Terrence Tao, an AI agent, or who or whatever arrives at some bit of new knowledge, it doesn't benefit you as a knowing subject unless you understand it yourself and make it your own.
  - bitwize 1mo ago
skavi 1mo ago
[flagged]
karmakurtisaani 1mo ago
That was well-written and interesting, thanks!
arunix 1mo ago
Related: Does one have to be a genius to do maths? https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/ https://terrytao.wordpress.com/career-advice/does-one-have-t...
- lambdaone 1mo ago
  He's right, of course, for those people who already have a mathematical gift, but the problem with that is that Tao has never experienced not being a mathematical genius, and is no more capable of understanding what it's like to not be a genius as an ordinary person is capable of understanding what it's like to be one.
aslprt 1mo ago
These AI ads are getting better and better by the day.
- NeOchenHorosho 1mo ago
  Could you elaborate, please? Does your point imply that mathematical discoveries achieved with LLM's aren't real?
bhouston 1mo ago
I have some bad news for the non-mediocre mathematics. Given it another year or two or so and there won't be much need for non-mediocre mathematics either. Instead everyone will have on call a near magic mathematician who can push the state of the art for their needs. Math is actually a perfect fit for AI because it is possible to express everything in terms of written language and you can write formal verifications of things. It is just a set of abstract rules, perfect for a computer. And remember computer science was initially a sub-discipline of mathematics. So after Claude/Codex conquer writing code, it makes sense to move on to mathematics.
- paulpauper 1mo ago
  Whenever there is a breaking AI-generated proof, it's the job of actual leading mathematicians to formalize/check it . Laypeople are not checking or writing these AI-assisted proofs. Even when Lean is used, it's mathematicians writing these proofs and checking if the formalization was done right. Terrance Tao's career trajectory has reached new highs due to AI. He's more relevant than ever. This is the exact opposite of Ai making mathematicians obsolete.
  - asib 1mo ago
    To the credit of the original commenter, that is why they said "give it one or two years". _Right now_ we need the experts to formalize/check. They're saying they think LLMs will reach a point in the near future where that won't be necessary.
    - pfdietz 1mo ago
      All we need experts for right now is verifying the formalization of the statement of the problem is correct. The proof itself, that formalization is checked automatically.
      - paulpauper 1mo ago
        So there is no getting around the fact that someone has to verify something. my point still stands.
cammasmith 1mo ago
Really enjoyed reading your perspective. I am a recent math PhD graduate, and I also find it both exciting and terrifying to see what AI is doing to the field of math.
throwaway_7274 1mo ago
Dear Garvy. You and your writing are wonderful. Sincerely, someone.
randusername 1mo ago
> 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.
- torginus 1mo ago
  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.
  - jlev1 1mo ago
    > 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.
emil-lp 1mo ago
> Lying is a core part of communicating mathematics. We lie to kindergarteners when explaining fractions. We lie to fourth graders when approaching limits... Hard disagree. Lying is with intention to deceive. Teaching is simplifying with the intention that they understand and get the correct intuition. Math is not about lying, that's just silly.
- Terr_ 1mo ago
  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 are very familiar with bright, qualified school-leavers who arrive and then go into shock on finding that biology or physics isn't quite what they've been taught so far. 'Yes, but you needed to understand that,' they are told, 'so that now we can tell you why it isn't exactly true.' > Discworld teachers know this, and use it to demonstrate why universities are truly storehouses of knowledge: students arrive from school confident that they know very nearly everything, and they leave years later certain that they know practically nothing. Where did the knowledge go in the meantime? Into the university, of course, where it is carefully dried and stored.
  - amosj 1mo ago
    Brilliant
  - bmacho 1mo ago
    I don't get it? Nevertheless you don't have to lie to kids in any field, science, art or otherwise.
    - photonemitter 1mo ago
      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
underlipton 1mo ago
[flagged]
- uptodatenews 1mo ago
  Yeah this just means 1000x more people can become phds if theyre willing
  - lupire 1mo ago
    PhD in naturalism (stamp-collecting AI proofs), not a PhD in math. The AI is the one earning the PhD in math.
Vgoose 1mo ago
I wish I could write this well. What an enjoyable read.
arjie 1mo ago
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 it’s better for everything to be a failure than to be in the “it could make it” category for half a decade or more. In that way, I am glad I found that it wasn’t for me. I had the curiosity, but not the doggedness to face difficulty (not enough curiosity perhaps?) or the ability to not encounter such difficulty. And fortunately that meant I was never in the “I could make it” category. God bless clear and present boundaries and may the devil take the grey zone.
- dhosek 1mo ago
  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 rational number without any guidance at all.² 2. I want to see how close to the general solution he’s gotten on his own, but given that he’s not had any formal algebra, it’s damned impressive and bodes well for his future development.
  - uptodatenews 1mo ago
    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/ https://rcsnyder.github.io/open-frontier-curriculum/ Ya "claude can you build me the next cern Thanks"
    - ACCount37 1mo ago
      [flagged]
asdf_snar 1mo ago
An incredibly enjoyable read, with a distinct voice.
dmix 1mo ago
This author has a natural talent for writing. That was interesting throughout.
globalnode 1mo ago
> Comparison is the thief of joy, and I don’t lock my doors There we have it, one of the many secrets to happiness.
wwarner 1mo ago
so well written
m3kw9 1mo ago
I'd think AI can help him even out the score a little, or a lot.
txhwind 1mo ago
Funded positions are much less than PhD number. However, people can fund themselves with a job. In a country, if it's easy to to get a part-time job with enough payment, mathematicians can continue work.
jazzpush2 1mo ago
This is the best thing I've read in years.
a_bonobo 1mo ago
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 ratcheting reflects on your self-worth and you start calling yourself mediocre, even though you vastly outperform the previous generation. It's an extremely unfair game designed by careless people. Throw AI into the mix and your self-worth crashes. Just today I saw a Claude Science set of results that made my own work of the past 2 months completely superfluous, and I sit here and wonder what's the point.
- perching_aix 1mo ago
  > 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?
  - a_bonobo 1mo ago
    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.
    - ebiester 1mo ago
      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)
contubernio 1mo ago
As a middle-aged mathematician, AI is provoking a serious crisis among the better mathematicians I know. Many are only half jokingly talking about retiring. We use AI a lot in research already and it's obvious that whoever doesn't will fall behind fast. At the very least it gives access to the full library in a few minutes, serving as a kind of knowledge oracle generally more useful than the expert who ought to be in the office next door but isn't. And we see what can happen when it is effectively coupled with lean to automate theorem proving and discovery. We aren't dumb enough to see this as the end of the profesión - Esther it's clearly a shift in how we will work - but we like doing computations and playing around with examples and how one does that just changed a lot. The other problem is we know we don't have the energy of youth to learn to use AI as effectively as the kids, although we are wiser and have better judgment and do know some things. Mathematicians who are not taking seriously how to adapt to AI are deluding themselves.
deleted 1mo ago
[deleted]

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 walking out of Gainesville with a PhD in Arithmetic Geometry. Since “normal” people mostly don't understand what the software development job is about, handwaving in response to regular questions: “what do you do at work?”, “what do you like about your job?” – is pretty normal. I think that most of us have some prepared answers ready to use. Mathematics is the thing you try to understand, don’t, get frustrated about, and then do. Just like the software development. I truly believe that the only people who can survive a software job are those who can tolerate the constant feeling of frustration caused by things not working or breaking for random reasons, and persevere in this environment to do the things you need to do.

marcosdumay 1mo ago
> “what do you like about your job?” For software development, normal people will just assume it's money and probably not even ask...
- pwdisswordfishq 1mo ago
  They would not even be wrong.
  - binary0010 1mo ago
    Yeah seems like most programmers just do it for the money. I imagine only like 20% of us do it just because we enjoy it.
    - geodel 1mo ago
      I'd just say there are scores of people who like programing. But that's about it.
    - axus 1mo ago
      I feel like the number is higher for software work where I'm at, and lower for every other profession. Scary when you think that your doctor is in it for the money
      - SoftTalker 1mo ago
        You can be a software developer without any formal training and without any licensure. Not so for an MD. It's going to attract more people who have the mentality of artists or musicians, i.e. people who do it for the love of the craft and as a creative outlet.
        ventana 1mo ago
        > You can be a software developer without ... any licensure. Don't jinx it. We are extremely lucky in this regard, and it actually looks like a rare exception.
      - inanutshellus 1mo ago
        hopefully the MD that passes all the tests is still worth his salt even if he only chose the profession for the paycheck. but as one of the nearby professors is famous for saying: "C students gotta go somewhere." ( and since this is HN - he didn't mean the programming language :D )
      - nkrisc 1mo ago
        There are plenty of easier ways to make money than becoming a doctor.
        Marsymars 1mo ago
        They tend to be higher risk though. If you've got the capacity for memorizing all the stuff you need to become a doctor, there's not much risk involved in attaining your doctor salary.
- doctorpangloss 1mo ago
  For mathematicians in the US, it's because their parents like money.
paulpauper 1mo ago
A PhD in Arithmetic Geometry and a publication in a top tier journal is hardly mediocre in and of itself, as far the author is concerned. The equivalent for a software engineer is probably a leading AI engineer, with a strong publication count. I think a lot of people who are not mediocre are unaware of what mediocrity actually is. Yeah if you're only in the top .1% and comparing yourself to the literal best in the world, you will feel mediocre in that sense . A mid mathematician maybe publication in worse journals, teaching community college.
- bananaflag 1mo ago
  > A PhD in Arithmetic Geometry and a publication in a top tier journal is hardly mediocre in and of itself, as far the author is concerned. It kinda is (sadly) because unlike engineering there aren't thousands of postdoc jobs in arithmetic geometry. And ofc in a year because of AI all math PhDs will be mediocre by definition.
- p1esk 1mo ago
  As a professional mathematician, if you’re not advancing your subfield of research consistently you are mediocre.
  - fn-mote 1mo ago
    If you say so. Saying most tenured faculty at research 1 institutions are mediocre seems to be stretching the definition, though.
    - p1esk 1mo ago
      Who’s saying that?
- kcexn 1mo ago
  It's still impressive, but it's not enough.
bananaflag 1mo ago
> And, I lie to anyone who asks me why I’m a mathematician. I prefer to say "I liked a girl" (because it's the truth)
- sheafification 1mo ago
  My go-to is “It’s the only thing I was good at in school, I was hopeless at everything else,” which is only a slight exaggeration.
layer8 1mo ago
> 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.

hyperhello 1mo ago

Hobbies aren’t as fun when you have an overbearing friend who constantly shows off how much more they know and how quickly they can switch to talking about anything you want but in greater depth than you.

MostlyStable 1mo ago
I do not have a single hobby where I'm very far beyond the median hobby-haver in skill (that is to say: if you took all other humans who share my hobby, I'm likely somewhere near median for all of them). This may put me in top whatever percentile among all humans, since most humans don't share my hobbies and so are terrible at those things, but there are enough humans out there, and enough humans who share my hobbies, that I have always known that there are people who are vastly better at them than I am. Now yes, if I was constantly being followed around by one of the top 10 hobby-havers, pointing out to me all the mistakes or sub-optimal decisions I was making, that would indeed be annoying and reduce my enjoyment in the hobby. But why do you expect AI to be like this? I would love if I had one of those top 10 hobby-havers on call to answer every one of my (often inane) questions with infinite patience (and who would only talk about the hobby when I specifically initiated the topic). I'm already under no illusions that I'm the best, but it's now easier than it has ever been (for some hobbies, I expect others to join them over time) to get better at them....if one so desires.
paulpauper 1mo ago
mathematicians or physicists fall into this category of knowing a lot about many thing . Sabine videos for example . she knows everything it seems
- jplusequalt 1mo ago
  Sabine is a crank who likes to wax poetically about fields she has no creds in.
  - BoredomIsFun 1mo ago
    She is a grifter, not crank.

derangedHorse 1mo ago

> 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 reminds me of a post I saw recently, although I can't remember the platform. It said something along the lines of assessing the limits of AI by finding the dumbest questions it can't solve. I think that pairs well as an additional way to view meaning through one's work. The linked post points out constrained attention as a way to bring meaning to novel work that no one else took on. With AI, this can still be applied to compute. I'm just wondering if there are a class of problems that humans, at least in the short-term, where humans need to be in the loop to solve more efficiently.

pdm55 1mo ago
I have just started reading this Gates Notes about reserving some jobs for humans: https://www.gatesnotes.com/a-turbulent-ai-era-and-critical-choices-to-make https://www.gatesnotes.com/a-turbulent-ai-era-and-critical-c...
lo_zamoyski 1mo ago
> 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 valuable thing in itself, that understanding is valuable and desirable. Yes, some knowledge has merely practical value, but theoretical knowledge is primarily sought for its own sake, because we desire to know reality. So, even if Terrence Tao, an AI agent, or who or whatever arrives at some bit of new knowledge, it doesn't benefit you as a knowing subject unless you understand it yourself and make it your own.
- bitwize 1mo ago

skavi 1mo ago

[flagged]

karmakurtisaani 1mo ago

That was well-written and interesting, thanks!

arunix 1mo ago

Related: Does one have to be a genius to do maths? https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/ https://terrytao.wordpress.com/career-advice/does-one-have-t...

lambdaone 1mo ago
He's right, of course, for those people who already have a mathematical gift, but the problem with that is that Tao has never experienced not being a mathematical genius, and is no more capable of understanding what it's like to not be a genius as an ordinary person is capable of understanding what it's like to be one.

aslprt 1mo ago

These AI ads are getting better and better by the day.

NeOchenHorosho 1mo ago
Could you elaborate, please? Does your point imply that mathematical discoveries achieved with LLM's aren't real?

bhouston 1mo ago

I have some bad news for the non-mediocre mathematics. Given it another year or two or so and there won't be much need for non-mediocre mathematics either. Instead everyone will have on call a near magic mathematician who can push the state of the art for their needs. Math is actually a perfect fit for AI because it is possible to express everything in terms of written language and you can write formal verifications of things. It is just a set of abstract rules, perfect for a computer. And remember computer science was initially a sub-discipline of mathematics. So after Claude/Codex conquer writing code, it makes sense to move on to mathematics.

paulpauper 1mo ago
Whenever there is a breaking AI-generated proof, it's the job of actual leading mathematicians to formalize/check it . Laypeople are not checking or writing these AI-assisted proofs. Even when Lean is used, it's mathematicians writing these proofs and checking if the formalization was done right. Terrance Tao's career trajectory has reached new highs due to AI. He's more relevant than ever. This is the exact opposite of Ai making mathematicians obsolete.
- asib 1mo ago
  To the credit of the original commenter, that is why they said "give it one or two years". _Right now_ we need the experts to formalize/check. They're saying they think LLMs will reach a point in the near future where that won't be necessary.
  - pfdietz 1mo ago
    All we need experts for right now is verifying the formalization of the statement of the problem is correct. The proof itself, that formalization is checked automatically.
    - paulpauper 1mo ago
      So there is no getting around the fact that someone has to verify something. my point still stands.

cammasmith 1mo ago

Really enjoyed reading your perspective. I am a recent math PhD graduate, and I also find it both exciting and terrifying to see what AI is doing to the field of math.

throwaway_7274 1mo ago

Dear Garvy. You and your writing are wonderful. Sincerely, someone.

randusername 1mo ago

> 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.

torginus 1mo ago
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.
- jlev1 1mo ago
  > 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.

emil-lp 1mo ago

> Lying is a core part of communicating mathematics. We lie to kindergarteners when explaining fractions. We lie to fourth graders when approaching limits... Hard disagree. Lying is with intention to deceive. Teaching is simplifying with the intention that they understand and get the correct intuition. Math is not about lying, that's just silly.

Terr_ 1mo ago
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 are very familiar with bright, qualified school-leavers who arrive and then go into shock on finding that biology or physics isn't quite what they've been taught so far. 'Yes, but you needed to understand that,' they are told, 'so that now we can tell you why it isn't exactly true.' > Discworld teachers know this, and use it to demonstrate why universities are truly storehouses of knowledge: students arrive from school confident that they know very nearly everything, and they leave years later certain that they know practically nothing. Where did the knowledge go in the meantime? Into the university, of course, where it is carefully dried and stored.
- amosj 1mo ago
  Brilliant
- bmacho 1mo ago
  I don't get it? Nevertheless you don't have to lie to kids in any field, science, art or otherwise.
  - photonemitter 1mo ago
    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

underlipton 1mo ago

[flagged]

uptodatenews 1mo ago
Yeah this just means 1000x more people can become phds if theyre willing
- lupire 1mo ago
  PhD in naturalism (stamp-collecting AI proofs), not a PhD in math. The AI is the one earning the PhD in math.

Vgoose 1mo ago

I wish I could write this well. What an enjoyable read.

arjie 1mo ago

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 it’s better for everything to be a failure than to be in the “it could make it” category for half a decade or more. In that way, I am glad I found that it wasn’t for me. I had the curiosity, but not the doggedness to face difficulty (not enough curiosity perhaps?) or the ability to not encounter such difficulty. And fortunately that meant I was never in the “I could make it” category. God bless clear and present boundaries and may the devil take the grey zone.

dhosek 1mo ago
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 rational number without any guidance at all.² 2. I want to see how close to the general solution he’s gotten on his own, but given that he’s not had any formal algebra, it’s damned impressive and bodes well for his future development.
- uptodatenews 1mo ago
  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/ https://rcsnyder.github.io/open-frontier-curriculum/ Ya "claude can you build me the next cern Thanks"
  - ACCount37 1mo ago
    [flagged]

asdf_snar 1mo ago

An incredibly enjoyable read, with a distinct voice.

dmix 1mo ago

This author has a natural talent for writing. That was interesting throughout.

globalnode 1mo ago

> Comparison is the thief of joy, and I don’t lock my doors There we have it, one of the many secrets to happiness.

wwarner 1mo ago

so well written

m3kw9 1mo ago

I'd think AI can help him even out the score a little, or a lot.

txhwind 1mo ago

Funded positions are much less than PhD number. However, people can fund themselves with a job. In a country, if it's easy to to get a part-time job with enough payment, mathematicians can continue work.

jazzpush2 1mo ago

This is the best thing I've read in years.

a_bonobo 1mo ago

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 ratcheting reflects on your self-worth and you start calling yourself mediocre, even though you vastly outperform the previous generation. It's an extremely unfair game designed by careless people. Throw AI into the mix and your self-worth crashes. Just today I saw a Claude Science set of results that made my own work of the past 2 months completely superfluous, and I sit here and wonder what's the point.

perching_aix 1mo ago
> 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?
- a_bonobo 1mo ago
  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.
  - ebiester 1mo ago
    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)

contubernio 1mo ago

As a middle-aged mathematician, AI is provoking a serious crisis among the better mathematicians I know. Many are only half jokingly talking about retiring. We use AI a lot in research already and it's obvious that whoever doesn't will fall behind fast. At the very least it gives access to the full library in a few minutes, serving as a kind of knowledge oracle generally more useful than the expert who ought to be in the office next door but isn't. And we see what can happen when it is effectively coupled with lean to automate theorem proving and discovery. We aren't dumb enough to see this as the end of the profesión - Esther it's clearly a shift in how we will work - but we like doing computations and playing around with examples and how one does that just changed a lot. The other problem is we know we don't have the energy of youth to learn to use AI as effectively as the kids, although we are wiser and have better judgment and do know some things. Mathematicians who are not taking seriously how to adapt to AI are deluding themselves.

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