[gus_massa]

About 1:

Only a small groups of researches of mathematical history reads what exactly Pythagoras said about triangles, in mainstream mathematics people just have a general idea of the results of Pythagoras or some rehash of his ideas and a few later/former mathematicians. Moreover, most theorems names are misattributed. The name of Pythagoras is more a nice historical anecdote about triangles and the equation x^2+y^2=z^2. Moreover, IIRC none of his books have survived. It's just a mix of folklore and indirect sources.

A better example is the work of Euclid. He wrote some books and some copies survived and you can still read them. Anyway, most mathematician don't read them, they have only a general idea of what Euclid wrote. I'm not sure what parts of his books were original and what parts were only a recompilation of the common knowledge of his time. He had a very interesting idea. You can choose some sensible axioms and derive all the geometry from them. [Whatever sensible means.] This idea survived, but the axioms he choose were wrong. Some are confusing, there are some missing cases ... IIRC with the Euclid's axioms you don't get the "real plane" with all it's points of , you can use them in a smaller plane were x and y are algebraic numbers, like fractions and square roots, ... but the point (x=pi, y=e) doesn't exist. IIRC the modern versions of axiomatic geometry use about 20 axioms, and some are very technical.

With most people like Gauss or Euler gets a few theorems named after them and a few anecdotes, but most mathematicians don't read the original material.

In some cases, it's nice to see as a curiosity a copy of the original publication. IIRC there are some copies of the work of Newton, Leibnitz or Cauchy were you can see that the notation they used is very similar to the current notation.

In other cases, the following mathematicians buried completely the original work and only the original name remains but most of the intermediate steps and notation are not made by the original author. IIRC all what you usually study about Galois theory is actually the version that was written later by Artin and Noether.

[akvadrako]

I didn't read your whole post but I think I agree with your point which I would phrase as saying that:

In mathematics (and science) it doesn't matter much what the researchers thought; the ideas stand on their own. So we shouldn't study Plato, but it would be good to study his ideas which are still relevant and insightful.

[foldr]

I'm not a mathematician of physicist, but I suspect that these disciplines are ahistorical largely out of necessity. They now require the grasp of so much technical material that there simply isn't time to teach the history of the discipline. I see no reason to think that this is a particularly good thing.

[akvadrako]

Somehow you are implying that philosophy is so simple all the material can be covered, so there is time to study the history?

What's important is understanding. If studying the history aids understanding it might be worth the time.

I believe studying the history in physics impedes understanding, because it builds up mistaken ideas that become hard to tear down.

For philosophy I'm not sure but I suspect it's better to order learning so as to make a logical progression and that isn't the same as the historical order.

[foldr]

I didn't mean it as a dig at philosophy for being simple. But I think it's true that there is less "essential technical material" to cover in philosophy. There's no equivalent to spending 3 months practicing solving differential equations.

>I believe studying the history in physics impedes understanding, because it builds up mistaken ideas that become hard to tear down.

This can be true in some cases of course, but there are also good ideas that get forgotten about or become unfashionable. And without studying the history of the discipline, you will often end up rejecting straw man versions of historical ideas rather than the ideas themselves.