4 ms·

All jokes aside, Terry is writing to an audience where this is utterly elementary. The phrase "it is well known" is seldom misused. Yes, anyone who knows anythi

All jokes aside, Terry is writing to an audience where this is utterly elementary. The phrase "it is well known" is seldom misused. Yes, anyone who knows anything about the Fourier transform will know the Gaussian is a fixed point, or can easily verify it for themselves. It would actually look very amateurish if Terry provided a citation for that. In fact, it would look borderline cranky. Most of the cranky "proofs" of the RH begin by dedicating a whole section or two to elementary results, such as analytic continuation, followed by three or four sections of misunderstandings or utter gibberish.

meuk 9y ago
Agreed. "It is well-known" should be read as "It is well-known among specialists". On the other hand, I have some professors who abused the word "trivial" to mean "it can be proven by me". One professor spent the better half of an hour thinking about a question, only to declare that the answer was trivial. His explanation followed and filled the rest of the hour.
- WhitneyLand 9y ago
  That’s funny. I wonder if the origin of the concept of something being trivial only in hindsight can be dated, or has it always been a truism?
- vostok 9y ago
  I think trivial means that the proof requires no serious amount of creativity.
  - zeth__ 9y ago
    >Takes less than a week to complete.
- alphydan 9y ago
  Remember that problems in high school typically can take 1/2h to solve, in college a couple of hours ... as a PhD typically a couple of years and as a professional researcher ... many years. So for him, a problem where he was confused 20 minutes and solved it in 10 minutes is probably "trivial".
- contravariant 9y ago
  There's a reason there's a somewhat famous joke about a professor who, when asked to explain an step he claimed to be trivial, furrowed his brow deeply, spent the best part of an hour looking at notes and scribbling on the blackboard only to declare afterwards "Yes! It is trivial!'.
  - SAI_Peregrinus 9y ago
    Or the numerous results which are obvious in hindsight.
- ajkjk 9y ago
  (Not even specialists -- 2nd-3rd year undergraduates in engineering/math/physics!) In that case the word 'trivial' means it doesn't require complex machinery to solve. A simple consequence of arithmetic manipulations, say, may be extremely difficult to think of yourself, but once you know it it's trivial to see the validity of. I believe that counts as 'trivial' in mathematical terminology.
munificent 9y ago
> All jokes aside, Terry is writing to an audience where this is utterly elementary. One of the things I find fascinating about the Internet is the effect it has on writing when you have so little control over who your audience is. Every now and then, a blogger or Twitterer used to writing for some niche audience catches the larger eye of the Internet zeitgeist and all of the sudden momentarily finds themselves with a much larger, very different audience, who perceive their work entirely differently because they lack the context the author presumed. I wonder how much of the modern trends of political correctness, trigger warnings, etc. come from this experience where you can no longer safely make any assumptions about your audience. At the same time, it's not possible to write effectively when you assume the audience could be anyone, even a potentially malicious aggressor.
- msla 9y ago
  It's the result of opening all the echo chambers to the world, including parts of the world who, for whatever reason or none at all, simply don't like you, who you are, what you are, or what you do. It also opens them to people who are just not going to get it, but who still feel compelled to comment and get a reaction, whatever kind of reaction they can elicit, and will not stop until they get a reaction or are forced to leave/stop participating. So, can we recreate the good echo chambers, such as academia, but do it right this time, such that irrelevant characteristics no longer matter but the people inside of them no longer have to deal with nutballs and assholes coming in and disrupting anything?

meuk 9y ago

Agreed. "It is well-known" should be read as "It is well-known among specialists". On the other hand, I have some professors who abused the word "trivial" to mean "it can be proven by me". One professor spent the better half of an hour thinking about a question, only to declare that the answer was trivial. His explanation followed and filled the rest of the hour.

WhitneyLand 9y ago
That’s funny. I wonder if the origin of the concept of something being trivial only in hindsight can be dated, or has it always been a truism?
vostok 9y ago
I think trivial means that the proof requires no serious amount of creativity.
- zeth__ 9y ago
  >Takes less than a week to complete.
alphydan 9y ago
Remember that problems in high school typically can take 1/2h to solve, in college a couple of hours ... as a PhD typically a couple of years and as a professional researcher ... many years. So for him, a problem where he was confused 20 minutes and solved it in 10 minutes is probably "trivial".
contravariant 9y ago
There's a reason there's a somewhat famous joke about a professor who, when asked to explain an step he claimed to be trivial, furrowed his brow deeply, spent the best part of an hour looking at notes and scribbling on the blackboard only to declare afterwards "Yes! It is trivial!'.
- SAI_Peregrinus 9y ago
  Or the numerous results which are obvious in hindsight.
ajkjk 9y ago
(Not even specialists -- 2nd-3rd year undergraduates in engineering/math/physics!) In that case the word 'trivial' means it doesn't require complex machinery to solve. A simple consequence of arithmetic manipulations, say, may be extremely difficult to think of yourself, but once you know it it's trivial to see the validity of. I believe that counts as 'trivial' in mathematical terminology.

munificent 9y ago

> All jokes aside, Terry is writing to an audience where this is utterly elementary. One of the things I find fascinating about the Internet is the effect it has on writing when you have so little control over who your audience is. Every now and then, a blogger or Twitterer used to writing for some niche audience catches the larger eye of the Internet zeitgeist and all of the sudden momentarily finds themselves with a much larger, very different audience, who perceive their work entirely differently because they lack the context the author presumed. I wonder how much of the modern trends of political correctness, trigger warnings, etc. come from this experience where you can no longer safely make any assumptions about your audience. At the same time, it's not possible to write effectively when you assume the audience could be anyone, even a potentially malicious aggressor.

msla 9y ago
It's the result of opening all the echo chambers to the world, including parts of the world who, for whatever reason or none at all, simply don't like you, who you are, what you are, or what you do. It also opens them to people who are just not going to get it, but who still feel compelled to comment and get a reaction, whatever kind of reaction they can elicit, and will not stop until they get a reaction or are forced to leave/stop participating. So, can we recreate the good echo chambers, such as academia, but do it right this time, such that irrelevant characteristics no longer matter but the people inside of them no longer have to deal with nutballs and assholes coming in and disrupting anything?