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The Amish tend to be pretty insular communities that have had the same extended families for generations, so being truly accepted might take a few years. Most "English" people who join tend to return to ordinary life within that time after the charm of the rustic lifestyle wears off. You'd also be required to learn Pennsylvania Dutch, as well as abide by all the other community rules, of course. Some Mennonite communities live pretty similar lifestyles, but are a little more relaxed in terms of strictness, so you may find them more forgiving, especially if it's to continue studies.
Dang you make it sound like some kind of religious cult.
😳
For real though, they aren't unlike many other fundamentalist sects across different religions, so one going in should expect pretty strict adherence to their interpretation of biblical doctrine. That's one of the things they're famous for, besides the no technology, raising barns, and building quality wooden furniture. Nowadays, there's a bit of flexibility regarding technology depending on which Amish community you live in, especially if it's to promote an Amish business, but there are still limits. All that being said, most newcomers who leave do cite the religious aspects as growing tiresome over time.
But it's not like the Amish are the kind of people who won't let you leave or anything, they're actually pretty big on the idea that one has to want to be a part of the Amish church and that it can't be forced on anyone; they even have that Rumspringa thing where kids are sent out into modern society at 16 until they decide whether they want to formally join the church or not. They don't believe in evangelism of any kind. I can't claim to be any kind of expert, though, I've just had a personal fascination with them for awhile.
I didn't intend for my first comment to come off that way, but I believe everything I've said is factual.
P.S.
I'll add for OP that I'm not sure how your goal of continuing your math studies would mesh with the Amish community. Assuming you'd be attending some sort of higher education outside of the community to earn a degree, I'm not sure how they'd perceive that. The Amish do their own schooling and don't offer classes at that level because they're actually against higher education in most communities, plus a university would probably be too far for a horse and buggy, so you'd most likely need a car. In fact, it was actually by Supreme Court decision that allowed the Amish to stop education at 8th grade. They might feel you weren't fully committed to the lifestyle.
If you were to stay after you earned your degree, what would you use it for? You'd likely have a job making furniture, doing some other handicraft, or farming. Your only option to use your advanced math skills would be to get a job in the non-Amish world, which might also ruffle some feathers. Hard to say for sure, though. I think even the more orthodox Mennonites are also a little more open to higher education, though, but I could be wrong.
Then again, you could still totally just get a degree, join whatever church you want, and live however rustically you choose.