Some people, including me, can get away with knowing much less and just figuring stuff out as we go along. I’m not sure if anyone can learn this ability, but for me personally it wasn’t inborn and I know exactly how I acquired it. Working through one math topic properly at school over a couple years taught me all the skills needed to fill any gaps I encountered afterwards. University was a breeze after that.
The method of study was this: we built one topic (real analysis) up from the ground floor (axiomatization of the reals), receiving only the axioms and proving all theorems by working through carefully constructed problem sets. An adult could probably condense this process into several months. It doesn’t sound like much fun—it’s extremely grueling intellectual work of the sort most people never even attempt—but when you’re done, you’ll never be afraid of math again.
I had to figure out ALL myself, without the help of anyone in meatspace. I’m lacking any formal education that be worth mentioning. The very language I’m writing in right now is almost completely self-taught. It took me half a decade to get here, irrespective of my problems. That is, most of the time I haven’t been learning anything but merely pondering what is the right thing to do in the first place. Only now I’ve gathered enough material, intention and the basic tools to tackle my lack of formal education.
Some people, including me, can get away with knowing much less and just figuring stuff out as we go along. I’m not sure if anyone can learn this ability, but for me personally it wasn’t inborn and I know exactly how I acquired it. Working through one math topic properly at school over a couple years taught me all the skills needed to fill any gaps I encountered afterwards. University was a breeze after that.
The method of study was this: we built one topic (real analysis) up from the ground floor (axiomatization of the reals), receiving only the axioms and proving all theorems by working through carefully constructed problem sets. An adult could probably condense this process into several months. It doesn’t sound like much fun—it’s extremely grueling intellectual work of the sort most people never even attempt—but when you’re done, you’ll never be afraid of math again.
I had to figure out ALL myself, without the help of anyone in meatspace. I’m lacking any formal education that be worth mentioning. The very language I’m writing in right now is almost completely self-taught. It took me half a decade to get here, irrespective of my problems. That is, most of the time I haven’t been learning anything but merely pondering what is the right thing to do in the first place. Only now I’ve gathered enough material, intention and the basic tools to tackle my lack of formal education.