[vjk800]

> If you read a few books on mathematics you think you're easily going to become one of the top mathematicians? Many ambitious people try to study math and decades later are disappointed by how they are still mediocre in their field or simply fail to make it into an academic career. Many PhDs in general, actually.

I don't know about being one of the top mathematicians, but I'd argue that actually, fully reading a few graduate level technical books is more than even most PhDs do.

I was once a PhD student in theoretical physics myself and I'd say that we mostly skim over the books or read only the sections that are immediately and obviously relevant to us.

I once did read one of the shorter known-to-be-difficult books of my field fully from cover to cover, and worked out most of the exercises in the book. After this exercise, I realized that I immediately had much better understanding of the somewhat foundational things described in the book than many of the more senior researchers had. And this was a book that everyone in my field knows, but apparently no-one actually reads it.

The reason why no-one reads actually the difficult books, even when half of their job is reading them, is because it's harsh, gruelling work.

So yeah, maybe you won't become the next Terence Tao by reading three or four graduate level mathematics books, but you can get pretty good if you actually seriously do it without any cheating or skimming.

[Tainnor]

While what you said may be true simply by the virtue of graduate level textbooks being so dense, I think GP wanted to imply that "just reading a moderate amount of mathematics" isn't sufficient to get anywhere. I would say that 3-4 entire graduate level textbooks (which you wouldn't understand anyway without having done the undergraduate stuff beforehand) is much more than "a moderate amount".