4 ms·

Mathematics is such an old field, older than anything except arguably philosophy, that it's too broad and deep for anyone to really understand everything. Even

Mathematics is such an old field, older than anything except arguably philosophy, that it's too broad and deep for anyone to really understand everything. Even in graduate school I often took classes in things discovered by Gauss or Euler centuries before. A lot of the mathematical topics the HN crowd seems to like--things like the Collatz conjecture or Busy Beavers--are 60, 80 years old. So, you end up having to spend years specializing and then struggle to find other with the same background. All of which is compounded by the desire to provide minimal "proofs from the book" and leave out the intuitions behind them.

ekjhgkejhgk 11mo ago
> A lot of the mathematical topics the HN crowd seems to like--things like the Collatz conjecture or Busy Beavers--are 60, 80 years old. Do you know the reason for that? The reason is that those problems are open and easy to understand. For the rest of open problems, you need an expert to even understand the problem statement.
scotty79 11mo ago
> Mathematics is such an old field, older than anything except arguably philosophy If we are already venturing outside of scientific realm with philosophy, I'm sure fields of literature or politics are older. Especially since philosophy is just a subset of literature.
- saithound 11mo ago
  > I'm sure fields of literature or politics are older. As far as anybody can tell, mathematics is way older than literature. The oldest known proper accounting tokens are from 7000ish BCE, and show proper understanding of addition and multiplication. The people who made the Ishango bone 25k years ago were probably aware of at least rudimentary addition. The earliest writings are from the 3000s BCE, and are purely administrative. Literature, by definition, appeared later than writing.
  - thaumasiotes 11mo ago
    > As far as anybody can tell, mathematics is way older than literature. That depends what you mean by "literature". If you want it to be written down, then it's very recent because writing is very recent. But it would be normal to consider cultural products to be literature regardless of whether they're written down. Writing is a medium of transmission. You wouldn't study the epic of Gilgamesh because it's written down. You study it to see what the Sumerians thought about the topics it covers, or to see which god some iconography that you found represents, or... anything that it might plausibly tell you. But the fact that it was written down is only the reason you can study it, not the reason you want to.
    - mkl 11mo ago
      > That depends what you mean by "literature". If you want it to be written down That is what literature means: https://en.wiktionary.org/wiki/literature#Noun https://en.wiktionary.org/wiki/literature#Noun
      - pfortuny 11mo ago
        Well, then poetry is not literature.
        thaumasiotes 11mo ago
        No, the argument is even dumber than that. The person who writes a poem hasn't created any literature. The person who hears that poem in circulation and records it in his notes has created literature; an anthology is literature but an original work isn't.
        baobun 11mo ago
        > No, the argument is even dumber than that. The person who writes a poem hasn't created any literature. Sure they have, by virtue of writing it down. It becomes literature when it hits the paper (or computer screen, as it were). (Unless you mean to imply that formulating an original poem in your mind counts as "writing", in which case I guess we illustrate the overarching point of value in shared symbols and language and the waste of time in stating our original definitions for every statement we want to make)
Davidzheng 11mo ago
actually a lot of minimal proof expose more intuition than older proofs people find at first. I find it usually not extremely enlightening reading the first proofs of results, counterintuitively.
bell-cot 11mo ago
I'll argue for astronomy being the oldest. Minimal knowledge would help pre-humans navigate and keep track of the seasons. Birds are known to navigate by the stars.
- nkrisc 11mo ago
  I would argue that some form of mathematics is necessary for astronomy, for “astronomy” as defined as anything more than simply recognizing and following stars.
adornKey 11mo ago
The desire to hide all traces where a proof comes from is really a problem and having more context would often be very helpful. I think some modern authors/teachers are nowadays getting good at giving more context. But mostly you have to be thankful that the people from the minimalist era (Bourbaki, ...) at least gave precise consistent definitions for basic terminology. Mathematics is old, but a lot of basic terminology is surprisingly young. Nowadays everyone agrees what an abelian group is. But if you look into some old books from 1900 you can find authors that used the word abelian for something completely different (e.g. orthogonal groups). Reading a book that uses "abelian" to mean "orthogonal" is confusing, at least until you finally understand what is going on.
- otoburb 11mo ago
  >>[...] at least gave precise consistent definitions for basic terminology. Hopefully interactive proof assistants like Lean or Rocq will help to mitigate at least this issue for anybody trying to learn a new (sub)field of mathematics.

ekjhgkejhgk 11mo ago

> A lot of the mathematical topics the HN crowd seems to like--things like the Collatz conjecture or Busy Beavers--are 60, 80 years old. Do you know the reason for that? The reason is that those problems are open and easy to understand. For the rest of open problems, you need an expert to even understand the problem statement.

scotty79 11mo ago

> Mathematics is such an old field, older than anything except arguably philosophy If we are already venturing outside of scientific realm with philosophy, I'm sure fields of literature or politics are older. Especially since philosophy is just a subset of literature.

saithound 11mo ago
> I'm sure fields of literature or politics are older. As far as anybody can tell, mathematics is way older than literature. The oldest known proper accounting tokens are from 7000ish BCE, and show proper understanding of addition and multiplication. The people who made the Ishango bone 25k years ago were probably aware of at least rudimentary addition. The earliest writings are from the 3000s BCE, and are purely administrative. Literature, by definition, appeared later than writing.
- thaumasiotes 11mo ago
  > As far as anybody can tell, mathematics is way older than literature. That depends what you mean by "literature". If you want it to be written down, then it's very recent because writing is very recent. But it would be normal to consider cultural products to be literature regardless of whether they're written down. Writing is a medium of transmission. You wouldn't study the epic of Gilgamesh because it's written down. You study it to see what the Sumerians thought about the topics it covers, or to see which god some iconography that you found represents, or... anything that it might plausibly tell you. But the fact that it was written down is only the reason you can study it, not the reason you want to.
  - mkl 11mo ago
    > That depends what you mean by "literature". If you want it to be written down That is what literature means: https://en.wiktionary.org/wiki/literature#Noun https://en.wiktionary.org/wiki/literature#Noun
    - pfortuny 11mo ago
      Well, then poetry is not literature.
      - thaumasiotes 11mo ago
        No, the argument is even dumber than that. The person who writes a poem hasn't created any literature. The person who hears that poem in circulation and records it in his notes has created literature; an anthology is literature but an original work isn't.
        baobun 11mo ago
        > No, the argument is even dumber than that. The person who writes a poem hasn't created any literature. Sure they have, by virtue of writing it down. It becomes literature when it hits the paper (or computer screen, as it were). (Unless you mean to imply that formulating an original poem in your mind counts as "writing", in which case I guess we illustrate the overarching point of value in shared symbols and language and the waste of time in stating our original definitions for every statement we want to make)

Davidzheng 11mo ago

actually a lot of minimal proof expose more intuition than older proofs people find at first. I find it usually not extremely enlightening reading the first proofs of results, counterintuitively.

bell-cot 11mo ago

I'll argue for astronomy being the oldest. Minimal knowledge would help pre-humans navigate and keep track of the seasons. Birds are known to navigate by the stars.

nkrisc 11mo ago
I would argue that some form of mathematics is necessary for astronomy, for “astronomy” as defined as anything more than simply recognizing and following stars.

adornKey 11mo ago

The desire to hide all traces where a proof comes from is really a problem and having more context would often be very helpful. I think some modern authors/teachers are nowadays getting good at giving more context. But mostly you have to be thankful that the people from the minimalist era (Bourbaki, ...) at least gave precise consistent definitions for basic terminology. Mathematics is old, but a lot of basic terminology is surprisingly young. Nowadays everyone agrees what an abelian group is. But if you look into some old books from 1900 you can find authors that used the word abelian for something completely different (e.g. orthogonal groups). Reading a book that uses "abelian" to mean "orthogonal" is confusing, at least until you finally understand what is going on.

otoburb 11mo ago
>>[...] at least gave precise consistent definitions for basic terminology. Hopefully interactive proof assistants like Lean or Rocq will help to mitigate at least this issue for anybody trying to learn a new (sub)field of mathematics.