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> it's also true that typically mathematicians fix a logic or universe before getting down to work This is true for programmers, it's not true for mathematicia

> it's also true that typically mathematicians fix a logic or universe before getting down to work This is true for programmers, it's not true for mathematicians. You can say programming is a subset of mathematics but mathematics is more than programming so proof search does not exhaust all the activities of a mathematician but it does exhaust all the activities of a programmer.

ants_everywhere 1y ago
> it's not true for mathematicians It actually is true for mathematicians. Most of us work in ZFC. Some people choose to work in constructive logic. Some people choose to only use countable choice. But we always know what logic we're working in and which theorems we can invoke. E.g. if you choose not to accept the axiom of choice you also have a sense of which results depend on Zorn's lemma and have to work around them. All of this is normal background for mathematicians. So there's no need to allow the foundations of mathematics to vary unless you're working in logic and need to quantify over foundational systems or compare them. You would certainly never start a problem and then switch the logic midway through. That sort of thing wouldn't even be coherent.
- measurablefunc 1y ago
  You seem to have a very limited understanding of mathematics. You're welcome to stick to it but I'd recommend learning what mathematics is actually about before thinking you can reduce it all to proof search in a single & fixed finite axiomatic system.
  - ants_everywhere 1y ago
    > You seem to have a very limited understanding of mathematics. You're welcome to stick to it but I'd recommend learning what mathematics is actually about You'd think I'd know what mathematics is about since I have a Ph.D. in it... > fixed finite axiomatic system ZFC is not a finite axiomatic system. nowhere did we specify that axiomatic systems have to be finite > single...fixed As I said above, there are people who study different logics. However the topic of conversation is individual problems. An individual problem does not switch logics mid stream and anyone working on a problem works in the context of a logic.
    - measurablefunc 1y ago
      You don't need a degree to understand mathematics but plenty of people w/ degrees think they understand what it's all about. Seems a bit odd you have a degree in mathematics but lack the basic understanding of what counts for mathematical activity. I don't think you should be proud of that but then again I don't know what they teach in PhD departments these days so maybe that's what they told you you needed to think to get the degree.
      - ants_everywhere 1y ago
        I see. It sounds like you're coming at this from an outsider perspective as someone who hasn't formally studied math and doesn't know what research level mathematicians are taught. There's nothing wrong with taking an interest in a subject as an amateur. I thoroughly support it. But knowing what is taught in PhD departments and what mathematicians do is a precondition for understanding whether what AlphaEvolve is doing is similar to it. If I wanted to know whether some AI tool was doing what humans do for, say, song writing, the first thing I'd do is figure out how song writing is taught, how professionals think about song writing, etc. And this is true regardless of the fact that I enjoy, support and often prefer outsider musicians.
        measurablefunc 1y ago
        I think you're making too many assumptions. Something they should have taught you while you were getting your degree but again, I'm not sure what they teach these days b/c it's been a while since last time I was listening to a graduate lecture on mathematics in a classroom.

ants_everywhere 1y ago

> it's not true for mathematicians It actually is true for mathematicians. Most of us work in ZFC. Some people choose to work in constructive logic. Some people choose to only use countable choice. But we always know what logic we're working in and which theorems we can invoke. E.g. if you choose not to accept the axiom of choice you also have a sense of which results depend on Zorn's lemma and have to work around them. All of this is normal background for mathematicians. So there's no need to allow the foundations of mathematics to vary unless you're working in logic and need to quantify over foundational systems or compare them. You would certainly never start a problem and then switch the logic midway through. That sort of thing wouldn't even be coherent.

measurablefunc 1y ago
You seem to have a very limited understanding of mathematics. You're welcome to stick to it but I'd recommend learning what mathematics is actually about before thinking you can reduce it all to proof search in a single & fixed finite axiomatic system.
- ants_everywhere 1y ago
  > You seem to have a very limited understanding of mathematics. You're welcome to stick to it but I'd recommend learning what mathematics is actually about You'd think I'd know what mathematics is about since I have a Ph.D. in it... > fixed finite axiomatic system ZFC is not a finite axiomatic system. nowhere did we specify that axiomatic systems have to be finite > single...fixed As I said above, there are people who study different logics. However the topic of conversation is individual problems. An individual problem does not switch logics mid stream and anyone working on a problem works in the context of a logic.
  - measurablefunc 1y ago
    You don't need a degree to understand mathematics but plenty of people w/ degrees think they understand what it's all about. Seems a bit odd you have a degree in mathematics but lack the basic understanding of what counts for mathematical activity. I don't think you should be proud of that but then again I don't know what they teach in PhD departments these days so maybe that's what they told you you needed to think to get the degree.
    - ants_everywhere 1y ago
      I see. It sounds like you're coming at this from an outsider perspective as someone who hasn't formally studied math and doesn't know what research level mathematicians are taught. There's nothing wrong with taking an interest in a subject as an amateur. I thoroughly support it. But knowing what is taught in PhD departments and what mathematicians do is a precondition for understanding whether what AlphaEvolve is doing is similar to it. If I wanted to know whether some AI tool was doing what humans do for, say, song writing, the first thing I'd do is figure out how song writing is taught, how professionals think about song writing, etc. And this is true regardless of the fact that I enjoy, support and often prefer outsider musicians.
      - measurablefunc 1y ago
        I think you're making too many assumptions. Something they should have taught you while you were getting your degree but again, I'm not sure what they teach these days b/c it's been a while since last time I was listening to a graduate lecture on mathematics in a classroom.