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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 e

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
> In my experience there is a strong correlation between depth of understanding and being able to communicate a topic effectively. I claim that I would be able to explain some rather deep results from my area of mathematical expertise quite effectively. But for the ordinary person to understand my explanations, we would have to start with a full-time course about elemetary basics that lasts for quite some months. On other words: just because you are able to communicate a topic effectively does not mean that the other side has the necessary background knowledge to understand your good explanations.
- Voultapher 2y ago
  I fully agree. However here we are not talking about laymen, we are talking about people with PHDs in related or exactly this field. If they can't understand it, who is left?
  - aleph_minus_one 2y ago
    > However here we are not talking about laymen, we are talking about people with PHDs in related or exactly this field. In particular in mathematics, research areas are quite isolated from each other, so even for a people from a related (sometimes even from the same) field, it typically takes a very serious effort to gain the necessary knowledge to understand a proof. This is also a reason why paper reviews take so much longer in mathematics than in many other academic disciplines.
    - Voultapher 2y ago
      Genuine question, does this level of complexity lead to higher rates of mistakes, such as faulty proofs passing review? I'm asking this because in my field of expertise it's a common correlation, that the more complex and arcane a piece of code is, the lower the chance is that issues will be discovered during review. In addition the chance of issues grows superlinear with complexity, as more control flow and invariants needs to be tracked in error prone human minds.
- lenkite 2y ago

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

> In my experience there is a strong correlation between depth of understanding and being able to communicate a topic effectively. I claim that I would be able to explain some rather deep results from my area of mathematical expertise quite effectively. But for the ordinary person to understand my explanations, we would have to start with a full-time course about elemetary basics that lasts for quite some months. On other words: just because you are able to communicate a topic effectively does not mean that the other side has the necessary background knowledge to understand your good explanations.

Voultapher 2y ago
I fully agree. However here we are not talking about laymen, we are talking about people with PHDs in related or exactly this field. If they can't understand it, who is left?
- aleph_minus_one 2y ago
  > However here we are not talking about laymen, we are talking about people with PHDs in related or exactly this field. In particular in mathematics, research areas are quite isolated from each other, so even for a people from a related (sometimes even from the same) field, it typically takes a very serious effort to gain the necessary knowledge to understand a proof. This is also a reason why paper reviews take so much longer in mathematics than in many other academic disciplines.
  - Voultapher 2y ago
    Genuine question, does this level of complexity lead to higher rates of mistakes, such as faulty proofs passing review? I'm asking this because in my field of expertise it's a common correlation, that the more complex and arcane a piece of code is, the lower the chance is that issues will be discovered during review. In addition the chance of issues grows superlinear with complexity, as more control flow and invariants needs to be tracked in error prone human minds.
lenkite 2y ago