2

Looking up at the work of very good young researchers, I have found that very early, they know a lot of stuff. I wonder if they learned all of this by reading or if there is another way of learning because sometimes, it's just too much.

Is there another -more efficient- way of learning math instead of reading (with pen and paper) and filling gaps in proofs?

HeMan
  • 3,119
  • Look here: https://math.stackexchange.com/questions/62264/efficient-ways-to-read-and-learn-a-new-topic?rq=1 – LeviathanTheEsper Jun 21 '17 at 06:22
  • 1
    I don't think he's representative of all mathematicians, but Pierre Deligne started reading Bourbaki when he was a teenager: http://www.abelprize.no/c57681/binfil/download.php?tid=57756 – user49640 Jun 21 '17 at 06:33
  • 1
    Obviously this question will demand some opining to answer, but it strikes me as a very valid concern. Furthermore, questions such as what book is good for what and why often appear, and are also somewhat opinion based. No big deal, but it strikes me that seeking tips from more experienced practitioners should be encouraged. Peace! – Robert Lewis Jun 21 '17 at 17:47

1 Answers1

1

Solve problems. Solve a lot of problems. Try every problem that interests you, even if you can't complete a solution.

One good way do do this is to hang out here on MSE. Surf problems and try your hand. Read the linked citings.

Solving problems is different than completing proofs, although I would consider proof completion as a branch of problem solving.

I'm not the first person to suggest this; indeed, far better mathematicians than Yours Truly have recommended this method.

This sure as hell worked for me, and keeps on working.

I'd be interested in hearing back how this works out for you, should you choose to give it a go.

Best of Good Fortune (Luck) with it!

Robert Lewis
  • 71,180