[2021] Am I missing something about how penetration works, or is Path of Matth completely wrong in those 2 comments ?

also multiplies negative res (so it does, in fact not "increase" them, it just multiply them

This is untrue. It is an increase modifier, and is additive with any other "increased" or "reduced" modifiers applying to those resistances. Such modifiers are rare, but do exist.

This works exactly the same as any other "increased" modifier in the game. Increases mathmatically take a % of the value, and add that to the value. If the value is negative, this makes it more negative.

This is not preformed after "ele reduction", it is additive with any actual "reduced" modifiers to the resistance. People in this thread (and in general) are incorrectly using that term to refer to modifiers which subtract from resistance. In PoE, modifiers which add/subtract to the base value are always applied first, then all % increases and reductions to that value are summed and apply additively, (and each different "more" or "less" modifier applies separately multiplicative with other modifiers to the value, but I don't think there are any of those for resistance).

This is exactly the same as how +10 to maximum Life applies before 10% increased maximum Life (and thus also benefits from the increase).

Penetration inherently applies after all of those because it's impossible for it to not. Penetration is a modifier on you that lets you treat the enemy's resistance as a lower value than their actual resistance value. That fundamentally can't do anything before their actual resistance value is calculated, and is not part of the calculation of their resistance at all - they calculate their resistance from modifiers applying to them, and then later when you try to hit them, you look at their resistance value that they've calcualted and your penetration lets you pretend that number is lower.

I stand corrected.