Most of history's great inventions weren't 'new' but a combination of technologies from varying fields that were combined in a unique way. People must have a vast knowledge base to be able to create truly unique products. I've combined artificially intelligent systems with kids toys, machine vision with apparel, computer science with gene therapy, the craziest had to be when I took apparel manufacturing techniques and an AI and applied them to food processing. Every solution came at the problem in a unique way, solving problems others thought impossible.
Sadly most people/start-ups look for the narrow skill set not the highly analytical individual that can solve any problem. This has driven away those that would have otherwise become polymaths. With the huge amount of knowledge available, a polymath today is someone who knows enough about every field so that when posed with a problem, they know where to go to create an answer.
Another problem in today's economy is that a polymath jumps between fields so they lack the 'years' of experience in any one field. This does lead to quite a few difficulties as people automatically leap to the 'jack-of-all-trades, master of none'. Most fail to realize that the difference between designing a kids toy or mobile app are small. They utilize the same skills and knowledge, just varying in the implementation due to different targeted demographics and sales channels.
I'd say there are tens or hundreds of thousands of "polymaths" running around. They are not hard to find; just go wherever people are inventing the future.
But someone who is recognised as a polymath. Jared Diamond for instance.
http://en.wikipedia.org/wiki/James_Franco
Read the "Personal Life" section.
Just-add-internet and all of those people with leisure time also can access lots of information easily.
