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I find this for a lot of maths - I have often wondered why they don't include the intuition and the process that led them to the result.

grenoire 7y ago
It is taken granted that if you are reading a high level maths paper, you are capable of deriving the authors' working intuitively. Papers would be excessively bloated without that assumption; besides, how far in detail do you go with the process and intuition?
- JadeNB 7y ago
  > It is taken granted that if you are reading a high level maths paper, you are capable of deriving the authors' working intuitively. I don't think that many research mathematicians expect that the readers of their papers will be able to derive their work intuitively. I know that I don't expect this, and my papers are no works of high-flown genius, just highly specialised and domain-specific so that even the people most interested in using the results probably won't be as interested in the techniques.
JadeNB 7y ago
> I find this for a lot of maths - I have often wondered why they don't include the intuition and the process that led them to the result. On the most basic levels, because journals don't want it and many referees want it taken out. (There's still the mindset that physical space on paper is a bottleneck, since most of the big journals also have printed versions.) On a less cynical level, intuition is highly non-transferrable. What gives me the intuitive understanding of my result probably won't help you (https://byorgey.wordpress.com/2009/01/12/abstraction-intuition-and-the-monad-tutorial-fallacy https://byorgey.wordpress.com/2009/01/12/abstraction-intuiti...). I think that the established school of thought is therefore that, rather than my giving you my useless esoteric intuition, better to give you the results of crystallising that intuition into a transferrable formalism, and then allow you to decode that formalism into your own custom-built intuition.
- chongli 7y ago
  On a less cynical level, intuition is highly non-transferrable. This is a fantastic insight. I have been so frustrated trying to reach people monads over the years. People complain that Haskell is only intelligible for those with a math background. Now I understand why! It’s not because Haskell requires you to know the underlying abstract algebra and category theory to grok monoids (in the category of endofunctors). It doesn’t! It’s because people who have studied math in undergrad have developed the skills to take a bare, abstract definition and work through a few examples on their own to build an intuition for the concept. Regular people for the most part do not do this! Most people are used to having everything explained to them and not used to learning anything really abstract which requires effort to understand. This is where their frustration comes in, just as it does for first year math majors at a rigorous school.
xamuel 7y ago
On a practical level, for much of mathematics, the intuition and the process often involve complicated hand-drawn diagrams that would be really difficult to typeset (and completely ad hoc, too).

grenoire 7y ago

It is taken granted that if you are reading a high level maths paper, you are capable of deriving the authors' working intuitively. Papers would be excessively bloated without that assumption; besides, how far in detail do you go with the process and intuition?

JadeNB 7y ago
> It is taken granted that if you are reading a high level maths paper, you are capable of deriving the authors' working intuitively. I don't think that many research mathematicians expect that the readers of their papers will be able to derive their work intuitively. I know that I don't expect this, and my papers are no works of high-flown genius, just highly specialised and domain-specific so that even the people most interested in using the results probably won't be as interested in the techniques.

JadeNB 7y ago

> I find this for a lot of maths - I have often wondered why they don't include the intuition and the process that led them to the result. On the most basic levels, because journals don't want it and many referees want it taken out. (There's still the mindset that physical space on paper is a bottleneck, since most of the big journals also have printed versions.) On a less cynical level, intuition is highly non-transferrable. What gives me the intuitive understanding of my result probably won't help you (https://byorgey.wordpress.com/2009/01/12/abstraction-intuition-and-the-monad-tutorial-fallacy https://byorgey.wordpress.com/2009/01/12/abstraction-intuiti...). I think that the established school of thought is therefore that, rather than my giving you my useless esoteric intuition, better to give you the results of crystallising that intuition into a transferrable formalism, and then allow you to decode that formalism into your own custom-built intuition.

chongli 7y ago
On a less cynical level, intuition is highly non-transferrable. This is a fantastic insight. I have been so frustrated trying to reach people monads over the years. People complain that Haskell is only intelligible for those with a math background. Now I understand why! It’s not because Haskell requires you to know the underlying abstract algebra and category theory to grok monoids (in the category of endofunctors). It doesn’t! It’s because people who have studied math in undergrad have developed the skills to take a bare, abstract definition and work through a few examples on their own to build an intuition for the concept. Regular people for the most part do not do this! Most people are used to having everything explained to them and not used to learning anything really abstract which requires effort to understand. This is where their frustration comes in, just as it does for first year math majors at a rigorous school.

xamuel 7y ago

On a practical level, for much of mathematics, the intuition and the process often involve complicated hand-drawn diagrams that would be really difficult to typeset (and completely ad hoc, too).