Great. They fail at that too. There have been a few studies that show that after 2 years of college, the difference in reading, writing, math, and critical thinking are negligible.
So if you're not good for the industry, you're terrible at what you're made for, what good are you?
This probably depends a lot on the course one is taking. I have a feeling (from observing the people around me) engineers are a lot better at critical thinking and logical reasoning after a couple years of college than they were coming out of high school.
From my observation it takes about ~4 years for the really observable differences to settle in ... it might also just be maturity. Difficult to say :)
It's definitely my experience that it's hard to find people with high levels of mathematical knowledge who don't have a 4-year, technical-field bachelor's degree. It's of course possible this is merely a correlation, but I would at least hypothetize that the students who've finished a four-year degree in an area like mathematics, computer science, electrical engineering, or physics, have more mathematical sophistication than they would have had if they had not finished that degree and taken/passed the mathematics classes it required.
It's not impossible to self-teach, but as far as I can tell, self-taught people usually don't self-teach mathematics, at least not successfully. Among self-taught programmers without CS degrees, for example, it's quite common to find people who are skilled coders, but much less common to find people who have a strong mathematical grounding.
Heck, if you want someone who really knows statistics and data mining, to take one example, I haven't met many people without grad-school experience who fit the bill. Masters degree is good, some PhD experience is better (finishing a PhD doesn't matter as much; ABD is fine).
So far for me 100% of candidates claiming self taught can barely code a for loop, much less explain at a high level how a compiler works or the difference between a heap and the heap. In most cases they don't even know the foundations of the language in which they are most efficient.
Most people I know are also self-taught and read a lot of the theory. If they are self-taught, what in God's name are they using to teach themselves?
So if you're not good for the industry, you're terrible at what you're made for, what good are you?