I would say that learning mathematics is virtually impossible without a teacher. Like, would you try learning Karate without a teacher? How about if you get with a bunch of friends and you all try to learn it together? No way.
Even the professionals try to find someone to learn a new concept from. There's something about mathematical writing that is too fragile/brittle for wetware.
One other strategy: I've noticed the really smart (arrogant?) people just don't bother reading new mathematics, they re-invent it themselves. It's actually worth trying if you can stomach it.
Even the professionals try to find someone to learn a new concept from. There's something about mathematical writing that is too fragile/brittle for wetware.
One other strategy: I've noticed the really smart (arrogant?) people just don't bother reading new mathematics, they re-invent it themselves. It's actually worth trying if you can stomach it.