Probably none of them. You may want to invent a new knowledge skill; the ones in the game are the 'practical' options to cover most active areas of concern for adventurers. Nothing stops a player and GM from inventing new ones or getting rid of/combining existing ones.
Knowledge (Engineering) covers a large amount of the practical aspects of Mathematics. It's not going to cover pure maths, but much of the mathematical focus of the ancienct world in real life was on geometry and aspects that would be.
Science is an odd one in a magical world. Mind you "Science" is a bit too broad a category to apply to knowledge in the real world. Craft (Alchemy), Knowledge (Engineering), Knowledge (Nature) and Heal all cover parts of the whole. But then that's the case in real life. A Rocket Scientist doesn't necessarily know much about Brain Surgery and vice versa.
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The existing Knowledge Skills seem sufficient for this to me. Knowledge (Engineering) for math seems both logical and sufficient, for example. Adding skills is also a bad call for many reasons, since any expansion of the skill list devalues skill points and makes the game more complicated in a way that's seldom useful.
And, partially for that reason, a lot of skills (including all Knowledge skills) involve multiple disparate fields of study. Arcana includes an exhaustive knowledge of dragons along with spells and magic, while Religion includes an exhaustive knowledge of the undead along with information on various churches and theology, and Linguistics includes forgery along with knowing many languages.
That said, one way to decouple particular skills from fields like math without adding skills is allowing multiple skills to be used for them. For example, the Trait that references being a math prodigy is tied to two Knowledge skills (Arcana and Engineering), so you could say that people could use either of those for math.
Additionally, the forthcoming Technology Guide will have additional, tech-based, skill uses for a number of skills, which might help codify which skills are used with which fields in areas like this.
I agree with Corvino. Expand KN: Engineering to KS: Science ... I also say this because it's very rarely taken, this might encourage it.
Keep in mind that the knowledge skills are incredibly broad. Someone who is good at knowing about bears also knows an equal amount about trees and pixies and minotaurs and giant spiders and hurricanes. If I want to be good at knowing about dragons, I also have to be good at knowing about golems, griffons, glyphs. I assume you get my point. No sense in making a new "rope use" level skill in "mathematics". Call it "engineering" and go from there.
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I think making characters "waste" skill points in made up skills isn't good. For the most part, the game is balanced around expecting characters to be "of a certain height". If they're not tall enough to get on the ride because they've been investing in "imaginary height" then some things will be more challenging than they're actually supposed to be. Whether or not this is a problem is up for you and your gaming group to decide. And, of course, if this is a completely custom scenario, it may not be an issue at all, but still devalues the existing skills.
I'd say any "learned" character would already have the basics of understanding most of this stuff anyways. For example, anyone trained in architecture (or most engineering degrees) has to take calculus (in real life, I mean). Anyone that has Kn Engineering should be more than sufficient for math (as you've already pointed out). But I wouldn't go so far as to make up a new knowledge skill for it, I'd let it be just a straight int roll with probably a not too high DC. Also, I'd say Arcana would probably cover it, too, just based off of the "learnedness" of the character.
For your examples:
Where the stone in a room came from: Type of Stone would be knowledge(dungeoneering) or Knowledge(geography.) Where a certain type of stone comes from would be Knowledge(geography) or Profession(merchant.) Of course when you are dealing with powerful teleportation effects, you are also likely dealing with all sorts of other powerful magics that make knowing the above fairly useless for figuring out where you are.
Alien Technology: If you want to allow this, this is probably a very good case for a custom skill. However, realistically it probably has really now practical value for a character. Even with perfect knowledge of an advanced technology you probably can't make or even repair a high tech item. You would have to make the tools to make the tools to make the tools that you need.
Investigating Magic: The theory of magic is covered by spellcraft.
Unless you want to add something 'new' to your world, and have it understandable by PCs, you don't really need any new skills.
One of my favorite houserules is allowing all players an additional skillpoint per level that must be spent in either a Craft or Profession skill. Both of these have broad RP appeal but are rarely taken unless as specific prerequisites for something else. It also allows players to choose something like Profession (Astromomer) which can be really useful in niche circumstances without penalising them elsewhere.
I'll go out on a limb here.
In the case of characters encountering Actual Science, I think it's fine for them to simply be unable to make knowledge checks.
Something like, say, renormalizing a quantum electrodynamical state function, or understanding UNIX code, or understanding the molecular biology of cell membranes, is just flat-out beyond the capabilities of Medieval-level fantasy world characters.
Now, once they encountered it, they could - possibly - begin learning about it, and certainly knowledge: engineering, arcana, nature, and so on could be leveraged a bit, but ultimately they'd simply have to invest in new skills (like mathematics, science (being generous here!), computer programming, and so on.) Is it a big skill tax? Yes! Of course! It's an entirely new world hithertoo unknown to the characters!
Another (possibly more generous) approach would be to allow players to use existing skills, but with DC caps which could evolve with exposure: for example, maybe be say that K: arcana provides the tools necessary to understand, say, quantum logic, but we cap it at DC 5 or 10... as the character is exposed to radical new ideas (maybe we need a sanity mechanic here as well!), he can make harder and harder checks.
Example: I ran a campaign in which the PCs were stranded (forever) on an alien world - the campaign was them learning to survive, meeting the natives, etc. until they could eventually set themselves up with a stronghold to thrive. The PCs were scientists, engineers, soldiers, and other types who might survive a crash of a research vessel. As the PCs encountered new life forms, technologies, and phenomena, their attainable DCs were capped, but as they explored, did research, and so on, they could access higher and higher caps - indeed, I treated it like "treasure": maybe the biologist managed to sequence an alien genome, so I'd give him a "+2" to his k:biology DCs concerning exozoological or other planetary matters.
That said, there *were* situations necessitating a new skill, K:psionics, since the planet was sentient (and psionic). Over time, the characters were allowed to buy ranks in K:psionics (no one could level and suddenly take 8 ranks and be a huge expert... ability to buy skill points was limited), and when their collective understanding of it was great enough, they could even take levels in a psionic prestige class.
Key point is that no one can master a wholly alien field (physics for wizards, magic for scientists) overnight - expertise should be meted out over time.
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Who is to say which areas of math and science have progressed in Golarion?
The existence of magic doesn't completely negate the need, or desire, to explore these subjects.
The realm of Golarion is vast, with many lands, planets, and planes of existence, all with varying degrees of societal, and scientific progress, access to magic, and other varied factors.
Even in the less fantastical regions, science and math are studied subjects.
Look, it is mentioned right in the available trait, Numerologist, and many other sources.