7 ms·

It's not just that, people spend way more time going through mathematical proofs, finding, and formulating them. If you give programmers time to muse about ever

It's not just that, people spend way more time going through mathematical proofs, finding, and formulating them. If you give programmers time to muse about every function for weeks and write no more than 50-100 pages of program text per year or even less, then their programs will be almost bug free. You get what you pay for. Note: I'm not claiming that programmers should be treated like mathematicians or vice versa, I'm merely pointing out the differences of the activities. Edit: There is of course also a more trivial reason. On average, research mathematicians are probably more intelligent, skillful and diligent than typical programmers.

auggierose 9y ago
As I said, concepts don't fall out of thin air, it takes time to come up with the right ones. This is the major part of doing mathematics, once you got the right concepts nailed down, the proofs fall out basically automatically.
peoplewindow 9y ago
Programmers are less intelligent, skillful and diligent on average than research mathematicians? How do you figure that? This statement appears to rely on a circular definition of intelligence - maths is "hard" therefore people who do it must be "intelligent". Given the examples in the linked discussion of cases where not only did mathematicians write buggy proofs but it took years to figure out a mistake existed at all, let alone what it was, I find it hard to believe that. To the extent it may appear superficially to be true it's likely the result of the academic setting in which there is no connection to real world relevance and the only pressure that exists to get things done comes from peers and the need to publish papers - but if those papers achieve very little and your peers papers also achieve little, that's totally OK. Compare to the world of the working programmer who is judged not by how fast he writes code but by the real world positive impact of that code, and it is easy to see how the mathematician may come across as more diligent or intelligent. But it's just an artifact of the pressure-free environment. I was also surprised to learn that the idea of checking mathematical proofs using Coq is considered just as exotic or impractical as checking programs. I had thought that Coq and other proof assistants were in wide usage for this use case, as surely pure mathematics is simpler to reason about formally than entire programs ... but apparently not. The fact that maths proofs are still mostly checked by hand, whereas machine-checked proofs (like static type systems) are widely used by even novice programmers, is hardly reassuring.
- nerdponx 9y ago
  Research mathematicians are certainly more highly trained than non-research programmers, at least for the first few years of their career. A PhD, at least in the USA, is really intensive.
  - dfee 9y ago
    What’s the connection between being highly trained and being “intelligent, skillful and diligent”? Circus animals are definitely highly trained after all.
    - TheOtherHobbes 9y ago
      All math PhDs can become programmers. Some might be too bored to be good programmers, and some might have issues with corporate nonsense and workplace politics. But purely in terms of the ability to manipulate symbolic systems to useful effect, the base level is more than high enough for most programming jobs. Evidence: for a long time, math BSc/PhD quals were highly valued by software houses. This continues to be true to an extent, especially at the high end with FP/ML. The percentage of programmers who can become math PhDs is... lower.
      - deleted 9y ago
        [deleted]
      - pas 9y ago
        > All math PhDs can become programmers. First of all what does "can become" mean? If it means with sufficient training and supervision they can learn to be programmers, then that's also true for the inverse. Furthermore, we need only one counterexample to make it false, and I happen to know a few math PhDs that are not that great at programming even though one of them actually works as a programmer.
        SamReidHughes 9y ago
        > If it means with sufficient training and supervision they can learn to be programmers, then that's also true for the inverse. No way. Most programmers are genetically unfit to do research mathematics. Many programmers can't take in an idea and expel it back out without corruption because they've got some cosmic ray simulation device in their brain stem. Or they just don't have the creativity. For example, think of all the people that complain about interview warm-up questions or think they're something you'd memorize.
deleted 9y ago
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auggierose 9y ago

As I said, concepts don't fall out of thin air, it takes time to come up with the right ones. This is the major part of doing mathematics, once you got the right concepts nailed down, the proofs fall out basically automatically.

peoplewindow 9y ago

Programmers are less intelligent, skillful and diligent on average than research mathematicians? How do you figure that? This statement appears to rely on a circular definition of intelligence - maths is "hard" therefore people who do it must be "intelligent". Given the examples in the linked discussion of cases where not only did mathematicians write buggy proofs but it took years to figure out a mistake existed at all, let alone what it was, I find it hard to believe that. To the extent it may appear superficially to be true it's likely the result of the academic setting in which there is no connection to real world relevance and the only pressure that exists to get things done comes from peers and the need to publish papers - but if those papers achieve very little and your peers papers also achieve little, that's totally OK. Compare to the world of the working programmer who is judged not by how fast he writes code but by the real world positive impact of that code, and it is easy to see how the mathematician may come across as more diligent or intelligent. But it's just an artifact of the pressure-free environment. I was also surprised to learn that the idea of checking mathematical proofs using Coq is considered just as exotic or impractical as checking programs. I had thought that Coq and other proof assistants were in wide usage for this use case, as surely pure mathematics is simpler to reason about formally than entire programs ... but apparently not. The fact that maths proofs are still mostly checked by hand, whereas machine-checked proofs (like static type systems) are widely used by even novice programmers, is hardly reassuring.

nerdponx 9y ago
Research mathematicians are certainly more highly trained than non-research programmers, at least for the first few years of their career. A PhD, at least in the USA, is really intensive.
- dfee 9y ago
  What’s the connection between being highly trained and being “intelligent, skillful and diligent”? Circus animals are definitely highly trained after all.
  - TheOtherHobbes 9y ago
    All math PhDs can become programmers. Some might be too bored to be good programmers, and some might have issues with corporate nonsense and workplace politics. But purely in terms of the ability to manipulate symbolic systems to useful effect, the base level is more than high enough for most programming jobs. Evidence: for a long time, math BSc/PhD quals were highly valued by software houses. This continues to be true to an extent, especially at the high end with FP/ML. The percentage of programmers who can become math PhDs is... lower.
    - deleted 9y ago
      [deleted]
    - pas 9y ago
      > All math PhDs can become programmers. First of all what does "can become" mean? If it means with sufficient training and supervision they can learn to be programmers, then that's also true for the inverse. Furthermore, we need only one counterexample to make it false, and I happen to know a few math PhDs that are not that great at programming even though one of them actually works as a programmer.
      - SamReidHughes 9y ago
        > If it means with sufficient training and supervision they can learn to be programmers, then that's also true for the inverse. No way. Most programmers are genetically unfit to do research mathematics. Many programmers can't take in an idea and expel it back out without corruption because they've got some cosmic ray simulation device in their brain stem. Or they just don't have the creativity. For example, think of all the people that complain about interview warm-up questions or think they're something you'd memorize.

deleted 9y ago

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