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As a math major, I would say that editing a textbook or even adding a few theorems or corrections would not make you a first-rate mathematician. The ceiling in

by jhp123 3y ago

As a math major, I would say that editing a textbook or even adding a few theorems or corrections would not make you a first-rate mathematician. The ceiling in math is very very high. If we're calling Theon first-rate then what do we say about Gauss?

dr_dshiv 3y ago
Gauss, you mean the guy who lived 1500 years later? Yeah, he definitely set a higher bar. But a “first-rate” restaurant does not mean “the best ever of all time.” Theon and Hypatia were probably some of the best mathematicians of their century. That is enough to be both “first rate” and “formidable” — and I’d be surprised if Gauss would talk smack about them.
- jhp123 3y ago
  You're talking about two people who don't seem to have contributed a single new theorem, proof, conjecture, or formula to mathematics. That bar is cleared by their contemporaries Pappus and Diophantus. I don't think your idea that being "one of the best of the age" makes you "first-rate" holds any water. A reenactor at a local Renaissance Faire who has never worn a suit of plate armor or ridden a war horse is probably one of the best jousters of the current age, because it's not really pursued any more, but I would never call them a "first-rate, formidable jouster". The medieval scribes who wrote dry annals of what happened each year were among the best writers of their age, because writing was rare, but I wouldn't call them "first-rate, formidable writers". There is an objective component to this kind of language.
boomboomsubban 3y ago
Is "first-rate" the top few mathematicians of all time or the top few mathematicians of their age? Or how many total "first-rate" mathematicians have their been? That ambiguity alone can explain this entire argument.
- yakubin 3y ago
  Nit: if it were top mathematicians of their age, then there wouldn’t be any ages without first-rate mathematicians, which is obviously wrong. That said, the “of all time” version also doesn’t sound right.
  - rcoveson 3y ago
    "First rank" is the phrase from OP's link, not "first-rate", but in both cases it is not obvious to me that it is wrong for there to be mathematicians with that descriptor in every age. They sound like relative adjectives; "first rank" undoubtedly so, "first-rate" to a lesser extent. "Who are the first-rate/first rank musicians of $YEAR" does not seem to me like it could be answered with "there were none in that year".
    - yakubin 3y ago
      I don’t know about “first-rank”. To me it sounds like an RPG term (“first-rank mage”). But in the case of “first-rate” I see nothing weird about the answer “there were none this year”. When quality is lower, that’s what I’d expect, since I think about this term a bit like the A1, A2, B1, B2, C1, C2 etc language proficiency certificates. They’re not assigned based on quantiles in current population, but based on a set of requirements applied to skill in absolute terms, not relative to skills of other people.
      - rcoveson 3y ago
        I think you'll find that if you set an absolute bar on most skills you'll end up with zero people above the bar in the past and a growing percentage of people above it in the future. The first person to run a four-minute mile was Roger Bannister in 1954. Now, that achievement is basically table stakes for college-level competitors. Similar effects can be observed in chess, piano performance, and just about any other activity you can measure. Making "first-rate" an absolute bar results in all sorts of crazy answers to the questions "who is first-rate now" and "who was first-rate 70 years ago". If you set the bar such that only the top 10 players of this year cut it, neither Bobby Fischer nor Michael Jordan would be first-rate.

by jhp123 3y ago

dr_dshiv 3y ago

Gauss, you mean the guy who lived 1500 years later? Yeah, he definitely set a higher bar. But a “first-rate” restaurant does not mean “the best ever of all time.” Theon and Hypatia were probably some of the best mathematicians of their century. That is enough to be both “first rate” and “formidable” — and I’d be surprised if Gauss would talk smack about them.

jhp123 3y ago
You're talking about two people who don't seem to have contributed a single new theorem, proof, conjecture, or formula to mathematics. That bar is cleared by their contemporaries Pappus and Diophantus. I don't think your idea that being "one of the best of the age" makes you "first-rate" holds any water. A reenactor at a local Renaissance Faire who has never worn a suit of plate armor or ridden a war horse is probably one of the best jousters of the current age, because it's not really pursued any more, but I would never call them a "first-rate, formidable jouster". The medieval scribes who wrote dry annals of what happened each year were among the best writers of their age, because writing was rare, but I wouldn't call them "first-rate, formidable writers". There is an objective component to this kind of language.

boomboomsubban 3y ago

Is "first-rate" the top few mathematicians of all time or the top few mathematicians of their age? Or how many total "first-rate" mathematicians have their been? That ambiguity alone can explain this entire argument.

yakubin 3y ago
Nit: if it were top mathematicians of their age, then there wouldn’t be any ages without first-rate mathematicians, which is obviously wrong. That said, the “of all time” version also doesn’t sound right.
- rcoveson 3y ago
  "First rank" is the phrase from OP's link, not "first-rate", but in both cases it is not obvious to me that it is wrong for there to be mathematicians with that descriptor in every age. They sound like relative adjectives; "first rank" undoubtedly so, "first-rate" to a lesser extent. "Who are the first-rate/first rank musicians of $YEAR" does not seem to me like it could be answered with "there were none in that year".
  - yakubin 3y ago
    I don’t know about “first-rank”. To me it sounds like an RPG term (“first-rank mage”). But in the case of “first-rate” I see nothing weird about the answer “there were none this year”. When quality is lower, that’s what I’d expect, since I think about this term a bit like the A1, A2, B1, B2, C1, C2 etc language proficiency certificates. They’re not assigned based on quantiles in current population, but based on a set of requirements applied to skill in absolute terms, not relative to skills of other people.
    - rcoveson 3y ago
      I think you'll find that if you set an absolute bar on most skills you'll end up with zero people above the bar in the past and a growing percentage of people above it in the future. The first person to run a four-minute mile was Roger Bannister in 1954. Now, that achievement is basically table stakes for college-level competitors. Similar effects can be observed in chess, piano performance, and just about any other activity you can measure. Making "first-rate" an absolute bar results in all sorts of crazy answers to the questions "who is first-rate now" and "who was first-rate 70 years ago". If you set the bar such that only the top 10 players of this year cut it, neither Bobby Fischer nor Michael Jordan would be first-rate.