3 ms·

The more pertinent question is not the binary "should we fund mathematicians or not?" It's "how many?" The money you dole out to them needs to come from someone

by bjt 14d ago

The more pertinent question is not the binary "should we fund mathematicians or not?" It's "how many?" The money you dole out to them needs to come from someone else. Easy yes: Let's impose a tax on everyone to support at least one mathematician. Easy no: Let's impose a tax on everyone to support one billion mathematicians. Where are you going to draw that line? How are you going to convince a majority of voters that you're drawing it at the right place?

trhway 14d ago
Do we support people who are intentionally not using GPS and are still using paper maps? Or even the people who do it without any maps, just from their memory? Do we support people who aren't using vaccines and are intentionally infecting themselves directly (measles parties)? Do we support people who are intentionally using axe instead of chainsaw? Police officers and stormtroopers who are intentionally using knife instead of a gun? With civilization and technology we do loose some mental capabilities - like say the part of the brain Amazonian people use for extremely skillful face recognition we do use for reading/writing while loosing that face recognition skill level that those people in the jungle have. So goes the medieval way of doing mathematics (it is a pity though - I liked it and hoped that mathematics will fall among the last, yet it happened to be among the firsts)
- xigoi 14d ago
  If GPS required you to pay hundreds of dollars per month to criminal companies, most people would still be using paper maps.
  - trhway 14d ago
    That exactly illustrates the way of technology - the first commercial GPS receivers cost $3000, and of course people used the paper maps back then, yet technology prices have always been going down (temporary RAM crunches notwithstanding :)
    - xigoi 14d ago
      The difference is that the inventors of GPS didn’t deliberately buy out the entire world’s supply of GPS receivers so that no more could be sold to ordinary people.
  - spacebanana7 14d ago
    Assuming paper maps were the only alternative - absolutely yes. I probably would, and least on a pro rata basis for bigger weekend trips in unfamiliar areas.
  - snapcaster 14d ago
    What is this based on? my view seems to be that people happily pay tons of money to criminal companies for pretty marginal utility
- defrost 14d ago
  Weird questions. > Do we support people who are intentionally not using GPS and are still using paper maps? Or even the people who do it without any maps, just from their memory? Yes. We do - it's a sport from way back and ongoing - a good many people want to retain non GPS navigational skills. > Do we support people who are intentionally using axe instead of chainsaw? Police officers and stormtroopers who are intentionally using knife instead of a gun? Yes. We do. Proficiency in multiple weapons and non weapon combat is a basic part of service training. Axes and wedges still have their place in tree felling.
- w4der 14d ago
  You are making your argument on the basis that LLMs and future AI system will be just as good or better as current mathematicians at all the relevant processes involved in academic math and mathematics in general. I'd like to see an experiment where an AI system was trained as a 1870s mathematician and see if it can come up with set theory, if that is not possible, then current AI systems are not fit to replace mathematicians.
  - trhway 14d ago
    >where an AI system was trained as a 1870s mathematician and see if it can come up with set theory a car or a future starship wouldn't climb a tree better than ancient human.
    - w4der 14d ago
      The hell is that reply? If we're obsoleting human mathematicians, which have fundamentally been the same thing brains-wise since forever, why shouldn't an AI system be able to replace a 1870s mathematician in the same way you are proposing it replace a 2020s mathematician?
      - trhway 14d ago
        >which have fundamentally been the same thing brains-wise since forever and you don't see any issue here? When it takes people 2 years to understand a proof it means that the old ways are done, they hit cul-de-sac. Like in many situations, it is the highest point as well as it is a crisis at the same time. >why shouldn't an AI system be able to replace a 1870s mathematician my point isn't that whether it would be able to replace - i think it would. My point is that it doesn't matter. The tool is needed for the 2020s math with those proofs taking 2 years, not for the 1870s math with proofs fitting a several pages letter. That is math of 1870s https://en.wikipedia.org/wiki/Cefn-coed-y-cymmer#/media/File:Cefn_Coed_Viaduct_near_Merthyr_Tydfil_-_geograph.org.uk_-_2023854.jpg https://en.wikipedia.org/wiki/Cefn-coed-y-cymmer#/media/File... and that is what we need in 2020 https://en.wikipedia.org/wiki/Huajiang_Canyon_Bridge#/media/File:Huajiang_Canyon_Bridge2.JPG https://en.wikipedia.org/wiki/Huajiang_Canyon_Bridge#/media/... Edit in response to the comment below as i hit my post limit : New mathematical fields require many years of work by many people. What seems to be coming is people would be able to explore various ideas in say days instead of those years. It means more fields will be discovered and built up. And by wider array of people, ie. by the less capable than the top dog people. Mathematics will be more like engineering. Including more practical applications - like exploring transformers trajectories mapped into manifolds in p-adic spaces and applying the dynamic systems chaos theory there - borderline gibberish that no human would spend meaningful time on, yet a one would be able to throw a couple bucks at Claude++ for it to play with it. That would mean more money into the math, not less.
true_religion 14d ago
We already have public support for the arts, and basic research, so going back to the fundamentals isn't necessary. We draw the line, where the voting public, and elected representatives decide. Our political system is squishy and doesn't require upfront reasoning, or absolutely correct decisions. We often make wrong, sometimes even horrifically wrong decisions, and adjust later.
- bjt 13d ago
  100%. You're at the place that I was trying to lead the parent comment. There's a wide range of reasonable positions on how much to invest in any given thing like science, the arts, etc. The public is generally bad at debates around taxing and spending, sadly. Voters struggle to accept the idea that more of X means less of Y. They want to believe they can have it all, for free, and there are plenty of politicians willing to tell them they can.
- kmijyiyxfbklao 13d ago
  If you trust the system and you think things are going to work out, then you have nothing to worry about. But people are saying this is a crisis, and to solve a crisis you have to have at least a vague plan.

by bjt 14d ago

trhway 14d ago

Do we support people who are intentionally not using GPS and are still using paper maps? Or even the people who do it without any maps, just from their memory? Do we support people who aren't using vaccines and are intentionally infecting themselves directly (measles parties)? Do we support people who are intentionally using axe instead of chainsaw? Police officers and stormtroopers who are intentionally using knife instead of a gun? With civilization and technology we do loose some mental capabilities - like say the part of the brain Amazonian people use for extremely skillful face recognition we do use for reading/writing while loosing that face recognition skill level that those people in the jungle have. So goes the medieval way of doing mathematics (it is a pity though - I liked it and hoped that mathematics will fall among the last, yet it happened to be among the firsts)

xigoi 14d ago
If GPS required you to pay hundreds of dollars per month to criminal companies, most people would still be using paper maps.
- trhway 14d ago
  That exactly illustrates the way of technology - the first commercial GPS receivers cost $3000, and of course people used the paper maps back then, yet technology prices have always been going down (temporary RAM crunches notwithstanding :)
  - xigoi 14d ago
    The difference is that the inventors of GPS didn’t deliberately buy out the entire world’s supply of GPS receivers so that no more could be sold to ordinary people.
- spacebanana7 14d ago
  Assuming paper maps were the only alternative - absolutely yes. I probably would, and least on a pro rata basis for bigger weekend trips in unfamiliar areas.
- snapcaster 14d ago
  What is this based on? my view seems to be that people happily pay tons of money to criminal companies for pretty marginal utility
defrost 14d ago
Weird questions. > Do we support people who are intentionally not using GPS and are still using paper maps? Or even the people who do it without any maps, just from their memory? Yes. We do - it's a sport from way back and ongoing - a good many people want to retain non GPS navigational skills. > Do we support people who are intentionally using axe instead of chainsaw? Police officers and stormtroopers who are intentionally using knife instead of a gun? Yes. We do. Proficiency in multiple weapons and non weapon combat is a basic part of service training. Axes and wedges still have their place in tree felling.
w4der 14d ago
You are making your argument on the basis that LLMs and future AI system will be just as good or better as current mathematicians at all the relevant processes involved in academic math and mathematics in general. I'd like to see an experiment where an AI system was trained as a 1870s mathematician and see if it can come up with set theory, if that is not possible, then current AI systems are not fit to replace mathematicians.
- trhway 14d ago
  >where an AI system was trained as a 1870s mathematician and see if it can come up with set theory a car or a future starship wouldn't climb a tree better than ancient human.
  - w4der 14d ago
    The hell is that reply? If we're obsoleting human mathematicians, which have fundamentally been the same thing brains-wise since forever, why shouldn't an AI system be able to replace a 1870s mathematician in the same way you are proposing it replace a 2020s mathematician?
    - trhway 14d ago
      >which have fundamentally been the same thing brains-wise since forever and you don't see any issue here? When it takes people 2 years to understand a proof it means that the old ways are done, they hit cul-de-sac. Like in many situations, it is the highest point as well as it is a crisis at the same time. >why shouldn't an AI system be able to replace a 1870s mathematician my point isn't that whether it would be able to replace - i think it would. My point is that it doesn't matter. The tool is needed for the 2020s math with those proofs taking 2 years, not for the 1870s math with proofs fitting a several pages letter. That is math of 1870s https://en.wikipedia.org/wiki/Cefn-coed-y-cymmer#/media/File:Cefn_Coed_Viaduct_near_Merthyr_Tydfil_-_geograph.org.uk_-_2023854.jpg https://en.wikipedia.org/wiki/Cefn-coed-y-cymmer#/media/File... and that is what we need in 2020 https://en.wikipedia.org/wiki/Huajiang_Canyon_Bridge#/media/File:Huajiang_Canyon_Bridge2.JPG https://en.wikipedia.org/wiki/Huajiang_Canyon_Bridge#/media/... Edit in response to the comment below as i hit my post limit : New mathematical fields require many years of work by many people. What seems to be coming is people would be able to explore various ideas in say days instead of those years. It means more fields will be discovered and built up. And by wider array of people, ie. by the less capable than the top dog people. Mathematics will be more like engineering. Including more practical applications - like exploring transformers trajectories mapped into manifolds in p-adic spaces and applying the dynamic systems chaos theory there - borderline gibberish that no human would spend meaningful time on, yet a one would be able to throw a couple bucks at Claude++ for it to play with it. That would mean more money into the math, not less.

true_religion 14d ago

We already have public support for the arts, and basic research, so going back to the fundamentals isn't necessary. We draw the line, where the voting public, and elected representatives decide. Our political system is squishy and doesn't require upfront reasoning, or absolutely correct decisions. We often make wrong, sometimes even horrifically wrong decisions, and adjust later.

bjt 13d ago
100%. You're at the place that I was trying to lead the parent comment. There's a wide range of reasonable positions on how much to invest in any given thing like science, the arts, etc. The public is generally bad at debates around taxing and spending, sadly. Voters struggle to accept the idea that more of X means less of Y. They want to believe they can have it all, for free, and there are plenty of politicians willing to tell them they can.
kmijyiyxfbklao 13d ago
If you trust the system and you think things are going to work out, then you have nothing to worry about. But people are saying this is a crisis, and to solve a crisis you have to have at least a vague plan.