[Enrique]

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First off I think you misunderstood my original comment about math and logic. I didn't mean that advanced problems can be easily solved without recourse to advanced math. I meant that they could in theory be solved that way. After all advanced math is just a logical progression from less advanced math. (Which is why it is ridiculous to postulate someone who is extremely adept at everything through calculus could have more trouble with higher math than someone who wasn't.)


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I wonder if anyone doubts that with time and work, one can understand higher mathematics. The problem is that it is a lot of work and it needs a lot of time.

I am very adept at everything through calculus, and very adept at higher math, but there's a point where going to much higher math needs a serious time commitment. To get depth, you need a lot of time and work, and there are so many branches in mathematics, that one can't really go into all of them.

Here's an anecdote from Von Neumann:
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"It is often said that modern mathematics is so vast that no one can know more than a tiny fraction of it. Someone once asked von Neumann how much of mathematics he himself knew. Von Neumann went into one of his characteristic thinking trances. After a moment he had an answer. 'Twenty-eight percent.'"

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And that was one of the most versatile mathematicians and mathematics wasn't as broad as now.

(I probably went way off topic, but I don't understand what point you are trying to make).