[johngossman]

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]

> 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.

[bell-cot]

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]

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]

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]

>>[...] 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.

[Davidzheng]

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.

[scotty79]

> 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]

> 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]

> 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]

> 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

[pfortuny]

Well, then poetry is not literature.

[thaumasiotes]

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.

[nkrisc]

If it’s not written down, then that’s true.

Once someone writes it down, it is.

[threatofrain]

Sure in the context that you mean it’s an oral tradition.

[dragonwriter]

> Literature, by definition, appeared later than writing.

Literature, by strict defintion, appeared no earlier than writing, but it is only a tentative conclusion from which surviving writing has been found and understood that it appeared later than writing.