MHO,
The best traders are the small business with the Math/Scientist type of mind.
It doesnt require rocket science math and science. But the Scientist type because of all the strategy testing and theory testing. Some Math skills are required.
Most importantly is the Small Business Entreprenuer type mind though. The type of person that knows there's no one else to do it. They are the ones that will be ultimately responsible for their own success and or failures. If there are no Entreprenuarials to hire look toward the solo Sports (the golfer/Wrestler) type of personalities instead of Entreprenuerial.
Now the whole Book smart vs street smart
UNiv degree not so much but always get the degree if you have the opportunity (it wont hurt) Cant teach drive and determination. And believe it or not some people werent even challenged in Univ to get their degree.
Respectfully, I'm gonna disagree with this. I think this is your concept of what a good trader is based on the path you have chosen in your own efforts to become succesul.
You seem to be coming from the angle of purely mechanical approaches to trading. I guess if a lot of people were making money from purely mechanical systems then I'd agree.
Quants are not traders and traders are not quants. There's a myth around that quants are employed to find complex mathematical patterns to trade - this is what most quants would like to be doing. What they actually do (in the main) is risk analysis and woking on software systems.
Now - of course, mathematical automated systems are used in things like arbitrage - but you also need a fair pot of cash to make money that way so it's out of the domain of traders like us who mostly go for directional trades & outright positions.
There are different styles of trading and I'd say that different styles take different types of people to be succesful.
On the one hand, you have the likes of Paul Rotter aka The Flipper who regularly fakes out the market and is pretty much a master of the tape. On the other hand you have Peter Lynch who brought shares in a company making tights because his wife told him l'egg was selling out all over the place. Both trade yet it is safe to say that neither could do what the other does.
So - let's say there are different styles and different personalities for each style. In the above 2 examples, I would doubt that either Rotter or Lynch have any background in the sciences, in fact I know Lynch doesn't, Rotter pretty much keeps himself to himself - but I would NOT play poker with him. I have a friend who runs a forex desk, he could best be described as "cockney barrow boy". I have seen no evidence that a physics Phd is an ideal qualification to trade.
For business skills - I doubt these are important either. I have been running a company for the last 9 and a half years, I have 35 employees and the company makes millions (sadly, I started it with OPM and they own it), yet trading doesn't come easy to me. Certainly - for short term trading i.e. Paul Rotter (or following a Paul Rotter), it is of absolutely no use at all. For the Peter Lynch types - perhaps it is.
I think the most important skills are - confidence, a set of balls, the ability to shrug things off easily and the ability to not let things go to your head.
As for golfers/wrestlers - I think you must have been drinking at that point. Are you saying that tiger woods, Big Daddy and Giant Haystacks could have been traders ???
Each genre of trading is a skill in itself. Just as beckham has footie skills, I think it's fair to say that people can have trading skills. Of course, I could practise football all I liked but never become Beckham. I don't think there's any reason to think that trading itself isn't a skill.
I personally think you could suck at everything else in life but be a good trader, although some people may call you a savant.