6 ms·

I don't know what a phd in "algebra" means but I don't understand how anyone with a phd in any part of mathematics can find this unintelligibility surprising. I

by zyklu5 2y ago

I don't know what a phd in "algebra" means but I don't understand how anyone with a phd in any part of mathematics can find this unintelligibility surprising. I have a phd in what could be said to be the langlands program itself and I am not at all surprised I can't follow this result.

TheNewsIsHere 2y ago
I’ve always been amused that the The Princeton Companion to Mathematics, edited by Timothy Growers, amusingly notes in the introduction that for the mathematician reader it may come to pass that they may not easily understand the works of others on different areas of mathematics. Not unlike IT, medicine, or parts of software development.
- YeGoblynQueenne 2y ago
  Yeah, well, if anyone could understand something, there would be no point in having a PhD in it.
  - lupire 2y ago
    That's it true at all. A PhD is someone capable of doing research. Research requiring training doesn't mean results must be inscrutable.
    - YeGoblynQueenne 2y ago
      It's a joke. I'll make sure to add a suitable smiley from now on :P
YeGoblynQueenne 2y ago
I think "a phd in algebra" is shorthand for "I did my doctoral research on an apocryphal subject that is only understood by a sub-sub-sub field of the mathematics research community and I wrote a thesis with a title that would simultaneously melt your brain and mean nothing to you, so I'm saying it in a way that you would kind of get more or less what my PhD was approximately about ish, with caveats". In the same sense, I "have a PhD in AI". You have a PhD in "what could be said to be the Landlands problem itself". It happens.
Voultapher 2y ago
Is that a good thing? In my experience there is a strong correlation between depth of understanding and being able to communicate a topic effectively. I have encountered many technical papers that drape simple concepts in needless complexity. My area of expertise is software design and it's usually the least skilled people that produce the highest complexity. I find there is a lot of value in solving things in a way that is easy to understand.
- QuesnayJr 2y ago
  Mathematicians could do a better job of conveying their topics, but this is really not the case. Some things are just genuinely hard, and the research frontier in mathematics is one of these. If you could produce a 5-page proof of an important theorem that currently has a 100-page proof, you would be hailed as a hero.
  - User23 2y ago
    There’s really a lot more to it than that. There is a notion of “polite mathematics” which is independent of the difficulty of the proof. If every step clearly follows from the prior steps it’s rather immaterial how long the proof is. Similarly a short proof with enough rabbits can achieve a kind of incomprehensibility.
    - lupire 2y ago
      What is "polite mathematics"? That sounds like "logic". What's a "rabbit"?
      - User23 2y ago
        A rabbit is when the mathematician presents the next step in a proof as a magician pulls a rabbit from a hat; leaving his reader to puzzle out how the trick was performed. For shorter proofs this can be delightful, but for longer ones it becomes tedious or even unmanageable.
- aleph_minus_one 2y ago

by zyklu5 2y ago

TheNewsIsHere 2y ago

I’ve always been amused that the The Princeton Companion to Mathematics, edited by Timothy Growers, amusingly notes in the introduction that for the mathematician reader it may come to pass that they may not easily understand the works of others on different areas of mathematics. Not unlike IT, medicine, or parts of software development.

YeGoblynQueenne 2y ago
Yeah, well, if anyone could understand something, there would be no point in having a PhD in it.
- lupire 2y ago
  That's it true at all. A PhD is someone capable of doing research. Research requiring training doesn't mean results must be inscrutable.
  - YeGoblynQueenne 2y ago
    It's a joke. I'll make sure to add a suitable smiley from now on :P

YeGoblynQueenne 2y ago

I think "a phd in algebra" is shorthand for "I did my doctoral research on an apocryphal subject that is only understood by a sub-sub-sub field of the mathematics research community and I wrote a thesis with a title that would simultaneously melt your brain and mean nothing to you, so I'm saying it in a way that you would kind of get more or less what my PhD was approximately about ish, with caveats". In the same sense, I "have a PhD in AI". You have a PhD in "what could be said to be the Landlands problem itself". It happens.

Voultapher 2y ago

Is that a good thing? In my experience there is a strong correlation between depth of understanding and being able to communicate a topic effectively. I have encountered many technical papers that drape simple concepts in needless complexity. My area of expertise is software design and it's usually the least skilled people that produce the highest complexity. I find there is a lot of value in solving things in a way that is easy to understand.

QuesnayJr 2y ago
Mathematicians could do a better job of conveying their topics, but this is really not the case. Some things are just genuinely hard, and the research frontier in mathematics is one of these. If you could produce a 5-page proof of an important theorem that currently has a 100-page proof, you would be hailed as a hero.
- User23 2y ago
  There’s really a lot more to it than that. There is a notion of “polite mathematics” which is independent of the difficulty of the proof. If every step clearly follows from the prior steps it’s rather immaterial how long the proof is. Similarly a short proof with enough rabbits can achieve a kind of incomprehensibility.
  - lupire 2y ago
    What is "polite mathematics"? That sounds like "logic". What's a "rabbit"?
    - User23 2y ago
      A rabbit is when the mathematician presents the next step in a proof as a magician pulls a rabbit from a hat; leaving his reader to puzzle out how the trick was performed. For shorter proofs this can be delightful, but for longer ones it becomes tedious or even unmanageable.
aleph_minus_one 2y ago