Creativity continued

For my mechanical project I've been researching Leonardo Da Vinci, and one of the most interesting things I've found about him is how he managed to combine so many different skills and areas of interest.
Da Vinci was "an artist, architect, musician, scientist, geologist, physicist, designer, mechanic and inventor" as it says in the book I borrowed from the library. In the 1400s, artists weren't mainly hired for their artistic skills alone, but for their knowledge of engineering, which they acquired during their apprenticeship. In an age of changing warfare, new inventions and reworked traditional weapons were the key to success.
Learning about everything makes complete sense. It's what I thought my art foundation would be, being taught as many different ways of creating as possible, so you have more tools at your disposal. Unfortunately it didn't really work like that, which I think is a shame. For all I know, I could have some secret metalsmithing talent which will now forever lie dormant.

Things are split up far too much, especially when it comes to school subjects. History links to geography, which links to the sciences, and then maths, and then music and so on. Separating things so much makes sense from a teaching perspective, but also forces people to drive a wedge between their interests.

Is it wise to specialise? Does focusing on one subject specifically give you a deeper understanding, or should you widen your horizons and have a larger understanding of everything?

I've often wondered if it's best to train for something completely different to what you actually want for a career in life. That way when you do work your way there, you'll have a completely different outlook and set of skills to everybody else, and will maybe think in a more creative way about the tasks in hand. Having come from a wider employment circle, you'd also have more objectivity.

Perhaps we should all have an Ancient Greek style education, where we are apprenticed into as many different jobs as possible.