As you have defined the terms here, what you say makes no sense to me. It seems to imply as a direct corollary that solving deep problems does not make you any better at deep problems, whereas solving shallow problems does make you better at deep problems. I can believe the last half so long as it is only a supplementary form of training (a crude analogy might be of a virtuoso musician practicing scales), but the first statement beggars belief and is contrary to all my experience.

Of course, intelligent people are drawn to "deep" problems. Being willing and able to solve "deep" problems is practically the definition of academic intelligence. Actually, most people like "deep" problems more than shallow ones, but only intelligent people have the mastery of the basic techniques required to takle the deeper problems.

I'll admit this is all very much [citation needed] stuff, though. I'm not certain.

Citation? Wiles proved FLT at age 40. Perelman proved Poincare at age 39. Richard Hamilton was 50 at the time.

But even with that great mathematicians START doing deep problems early in life. By the time their 25 they've been doing deep problems for a decade at least. Terrence Tao, for example, was doing calculus at age 7. He got a gold at IMO at age 13. These great mathematicians like Tao, Goedel, Neuman have long gone beyond grill and drill math before age 20. So the notion that they just recently stopped solving shallow questions is absurd.

This is a ridiculous myth. As a truism, person's creative intellectual output is greatest when they are working hardest and have the greatest number of tools of creation available to them. I could go down a long list of mathematicians (famous and not famous) whose most influential work was done later in their careers.

I agree that cognitive scientists say that extensive background knowledge is necessary for a solid foundation, however having background knowledge does not necessitate drills. I haven't seen any studies that specifically say that pure drilling is good, and instead have seen the complete opposite. All I have read also enforce my beliefs that mindless drilling necessary isn't good.

tl;dr: The drill work is fine, as long as its motivated. Though it's obviously much more nuanced than that.

"An extension of this argument is that excessive practice will also drive out understanding. This criticism of practice (called "drill and kill," as if this phrase constituted empirical evaluation) is prominent in constructivist writings. Nothing flies more in the face of the last 20 years of research than the assertion that practice is bad. All evidence, from the laboratory and from extensive case studies of professionals, indicates that real competence only comes with extensive practice (e.g., Hayes, 1985; Ericsson, Krampe, Tesche-Romer, 1993). In denying the critical role of practice one is denying children the very thing they need to achieve real competence. The instructional task is not to "kill" motivation by demanding drill, but to find tasks that provide practice while at the same time sustaining interest. Substantial evidence shows that there are a number of ways to do this; "learning-from-examples," a method we will discuss presently, is one such procedure that has been extensively and successfully tested in school situations."

...

"Real competence only comes with extensive practice. The instructional task is not to "kill" motivation by demanding drill, but to find tasks that provide practice while at the same time sustaining interest. There are a number of ways to do this, for instance, by "learning-from-examples.""

Thanks for the source.

Statements like this immediately throw the bozo bit. And then the rest of your statement confirms it.