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Math is way more automatable than programming. In math, a proof is a proof. We don't know if we can get there and so getting there is the hard part. In softwa

Math is way more automatable than programming. In math, a proof is a proof. We don't know if we can get there and so getting there is the hard part. In software, we always know that we can solve the problem. So HOW to solve the problem is the hard part. Because the type of solution involves maintainability, which involves planning, LLMs suck at it. This leads to "LLM slop code" whereby the LLM creates ad-hoc convoluted logic with redundancies and no reuse of existing standard library batteries. Unless you're a Grothendieck who gets mad at Deligne for not solving the Weil's conjecture "THE RIGHT WAY", software is fundamentally different than math in this respect. So I'll say it again, AI will win a fields medal for before managing a McDonald's simply because there are enough big problems within arms reach than their current capacity to plan over time

sashank_1509 3mo ago
> So I'll say it again, AI will win a fields medal for before managing a McDonald's simply because there are enough big problems within arms reach than their current capacity to plan over time AI can manage a McDonald’s already. If manage means directing humans to do something to ensure the store is running. If manage means running robots, then yes maybe that is 5 years away but just directing humans to run a store, that is possible right now.
- vatsachak 3mo ago
  No it can't. Show me a business which uses in context learning to manage a McDonald's
  - wanderlust123 3mo ago
    Well that’s a problem of incentives. Why would a manager outsource their own job to an AI?
    - vatsachak 3mo ago
      It's not a problem of incentives. Every executive wants to inject LLMs everywhere these days. If they haven't somewhere it means that it does not work.
      - wanderlust123 3mo ago
        Every executive wants to inject LLMs downstream from their own job. As you get away from execution and toward management the incentive to innovate gets less and less as management at the same level.
- fsmv 3mo ago
  Have you not seen vend bench?
fsmv 3mo ago
I think the difference is in math the problem is fully specified and easily verifiable and in programming it's not. I don't agree that we always know we can solve the problem.
- vatsachak 3mo ago
  Not always, sure but 90% of the time yes. For example, create a DFA for a regex, not too bad just use Thompson's algorithm and then NFA->DFA. But now we have to care about efficiency, user API, maintainability of definitions etc. Coding is more of a human problem than math
nicf 3mo ago
I've spent some time working both as a math researcher and as a software engineer, and I think this comment actually underrates the similarity between the two fields as they're actually practiced. Some math research does involve grabbing a single, fully specified conjecture off the shelf and hunting for a proof of it, and it's true that if you manage to solve a long-standing open problem, other mathematicians will be interested no matter how you did it. But this isn't all of what they do, probably not even most of what they do. Like in software engineering, it's not always obvious which question would be the most useful one to ask. A lot of mathematical work also goes into what we call "theory-building", where you could say that primary work goes into coming up with definitions rather than theorems. Mathematicians also care a great deal about how something is proved; a lot of them are some of the most aesthetically picky people I've ever met. Words like "ugly", "beautiful", "creative", and "boring" are used to describe both definitions and proofs all the time. From the outside, it can look like all they're doing is pumping out proofs at any cost. But I promise you that when I talk to mathematicians who don't have any experience building software, they have a similarly narrow view of that field as well! Both fields, from the inside, look a lot more human than you might expect.
- vatsachak 3mo ago
  I think that your take is quite optimistic. Having published in top tier journals my only experience is that mathematicians care about what other mathematicians worked on and failed to solve. Theory building papers are dime a dozen and don't get published in high tier journals unless they solve a problem. Math is such that most theories are built after solving a problem and actually don't solve a larger class of problems. Etale Cohomology is an example of a rare exception. Grothendieck was mad that Deligne used adhoc complex analysis techniques to prove Weil. But everyone else was thrilled. Whereas in CS, a good theory (library) solves a large class of problems. The reason being is that CS tackles general problems while math specific ones. Math on average solves problems that don't lead to solutions to other problems. To me at least, math is more of a game like chess and coding is more of an art. There are aspects which are a game, like performance engineering but I'm pretty sure that LLMs will become superhuman at that soon
  - 3mo ago

sashank_1509 3mo ago

> So I'll say it again, AI will win a fields medal for before managing a McDonald's simply because there are enough big problems within arms reach than their current capacity to plan over time AI can manage a McDonald’s already. If manage means directing humans to do something to ensure the store is running. If manage means running robots, then yes maybe that is 5 years away but just directing humans to run a store, that is possible right now.

vatsachak 3mo ago
No it can't. Show me a business which uses in context learning to manage a McDonald's
- wanderlust123 3mo ago
  Well that’s a problem of incentives. Why would a manager outsource their own job to an AI?
  - vatsachak 3mo ago
    It's not a problem of incentives. Every executive wants to inject LLMs everywhere these days. If they haven't somewhere it means that it does not work.
    - wanderlust123 3mo ago
      Every executive wants to inject LLMs downstream from their own job. As you get away from execution and toward management the incentive to innovate gets less and less as management at the same level.
fsmv 3mo ago
Have you not seen vend bench?

fsmv 3mo ago

I think the difference is in math the problem is fully specified and easily verifiable and in programming it's not. I don't agree that we always know we can solve the problem.

vatsachak 3mo ago
Not always, sure but 90% of the time yes. For example, create a DFA for a regex, not too bad just use Thompson's algorithm and then NFA->DFA. But now we have to care about efficiency, user API, maintainability of definitions etc. Coding is more of a human problem than math

nicf 3mo ago

I've spent some time working both as a math researcher and as a software engineer, and I think this comment actually underrates the similarity between the two fields as they're actually practiced. Some math research does involve grabbing a single, fully specified conjecture off the shelf and hunting for a proof of it, and it's true that if you manage to solve a long-standing open problem, other mathematicians will be interested no matter how you did it. But this isn't all of what they do, probably not even most of what they do. Like in software engineering, it's not always obvious which question would be the most useful one to ask. A lot of mathematical work also goes into what we call "theory-building", where you could say that primary work goes into coming up with definitions rather than theorems. Mathematicians also care a great deal about how something is proved; a lot of them are some of the most aesthetically picky people I've ever met. Words like "ugly", "beautiful", "creative", and "boring" are used to describe both definitions and proofs all the time. From the outside, it can look like all they're doing is pumping out proofs at any cost. But I promise you that when I talk to mathematicians who don't have any experience building software, they have a similarly narrow view of that field as well! Both fields, from the inside, look a lot more human than you might expect.

vatsachak 3mo ago
I think that your take is quite optimistic. Having published in top tier journals my only experience is that mathematicians care about what other mathematicians worked on and failed to solve. Theory building papers are dime a dozen and don't get published in high tier journals unless they solve a problem. Math is such that most theories are built after solving a problem and actually don't solve a larger class of problems. Etale Cohomology is an example of a rare exception. Grothendieck was mad that Deligne used adhoc complex analysis techniques to prove Weil. But everyone else was thrilled. Whereas in CS, a good theory (library) solves a large class of problems. The reason being is that CS tackles general problems while math specific ones. Math on average solves problems that don't lead to solutions to other problems. To me at least, math is more of a game like chess and coding is more of an art. There are aspects which are a game, like performance engineering but I'm pretty sure that LLMs will become superhuman at that soon
- 3mo ago