The proper intellectual ambition of all humanity is to develop as a polymath. Of course most will completely disagree with me. Not only that most will couch their contributions in impenetrable language so as to obscure it from the casual reader.
Yet understand what i am saying. A polymath first develops a high level of mathematical skill. My own exposure was actually exceptional and perhaps unnecessary except to understand what had been done if one actually contributes there. Thus my work introducing third and forth order Pythagorean metrics. I really did have to know mathematical history and the full extent of the oeuvre of the foundations of mathematics.
What i am saying though, you are no polymath without a real facility with mathematics at the undergrad level and all that takes time and practice. Do notice that i mentioned practice. Lots of it and that is where the university typically falls short. It is why most polymaths are largely self taught. I regret most taking courses in which practice was invisible or even doing it over intensely as well.
What happens in all this is that your internal tool box expands and becomes sophisticated often in way you do not perceive.
Then we come to the hard part. You must feed your monkey scrutinized information and lots of it. I pick up a book to ferret out a single fact or insight and once attained, discard the rest. I have been doing this for sixty years and from that insight flows.
As an aside, focus on a specific topic will allow local mastery and that is good. Except it is obsolete in a decade or so and in our present world every tradition is been re engineered. Thus it is far better to be a polymath as you can leap farther into the maze of knowledge as i do in this blog..
If you want to stay successful, learn to think like Leonardo da Vinci
The redundancy of reality
A higher rate of learning
“Study the science of art. Study the art of science. Develop your senses—especially learn how to see. Realize that everything connects to everything else.”