09/19/2014 04:10 pm ET Updated Nov 19, 2014

10 Game-Changing Ideas on Entrepreneurship from Peter Thiel

"What great business is nobody building?" is the question Peter Thiel, celebrity investor and veteran entrepreneur, asks entrepreneurs every day.

The brilliant PayPal cofounder, Facebook investor, creator of the Thiel Fellowship, and general partner of Founders Fund recently spoke at Columbia University on his book Zero to One: Notes on Startups, or How to Build the Future. The book, released Tuesday, shares his perspective of the future and the modern technological landscape. His first tip involved "learning to ask the questions that lead you to find value in unexpected places."

Thiel's talk heavily focused on the concept of zero-to-one innovations -- revolutionary inventions like the first airplane or home computer, which require "intensive, vertical, zero-to-one progress" -- and how to get there.

Here are 10 key takeaways from Thiel's talk and his book so you can start dreaming up the next big thing:

1. Question what you think you know about the past. To understand businesses and startups today, you have to do the truly contrarian thing: you have to think for yourself.

2. The usual narrative is that capitalism and perfect competition are synonymous. A better one frames capitalism and perfect competition as opposites: capitalism is about the accumulation of capital, whereas the world of perfect competition is one in which you can't make any money.

3. To build your company culture, it may be helpful to dichotomize two extreme personality types: nerds and athletes. Neither extreme is optimal. A company made up of nothing but athletes will be biased towards competing, while a company made up of nothing but nerds will ignore the fact that there may be situations where you have to fight. You have to strike the right balance.

4. Avoid being blinded by entrepreneurial optimism. The default thinking is seductive, but too simplistic: you've created something wonderful, venture capitalists (VCs) like to invest in wonderful things, and therefore VCs will be desperate to invest in your wonderful thing. That's wrong. VCs, as we've seen, have their own biases and motivations. The question is simply how you can exploit them to your mutual advantage.

5. Inspiration isn't all that counts. Dispel the belief that the best product always wins. There is a rich history of instances where the best product did not, in fact, win. An incredible product doesn't necessarily mean success -- but it might get you half way there.

6. Every company is different. But there are certain rules that you simply must follow when you start a business. A startup messed up at its foundation cannot be fixed. If you focus on the founding and get it right, you have a better chance at success.

7. For a company to own its market, it must have some combination of brand, scale cost advantages, network effects, or proprietary technology. Of these elements, brand is probably the hardest to pin down. The best kind of business is one where you can tell a compelling story about the future. The stories will all be different, but they take the same form: find a small target market, become the best in the world at serving it, take over immediately adjacent markets, widen the aperture of what you're doing, and capture more and more.

8. As a society, we now gravitate towards explaining things by chance and luck rather than skill and calculation. The internal narrative is that talented people got together, worked hard, and made things work. The external narrative chalks things up to right place, right time. But it's not all a matter of luck. And the part of it that is can be channeled and mastered.

9. No one knows for sure when the future will arrive. But that's no reason not to think about the question. It's easy to point to past predictions where people envisioned a very different future from the one they got. Knowing how and why things didn't quite unfold as people thought is important. You have to know how people in your shoes got it wrong if you hope to get it right.

10. Progress comes in two flavors: horizontal/extensive and vertical/intensive. Horizontal or extensive progress means copying things that work. Vertical or intensive progress, by contrast, means doing new things. The single word for this is "technology." Intensive progress involves going from zero to one.

His closing left us with some Thielspiration in the form of making the distinction between mysteries and secrets: "You have mysteries no one has a clue about, and there are secrets you could figure out. The truth seems to be the people that believe in secrets will find them. People that believe that they are all solved will not even try. Go against the conventional wisdom that everything has already been discovered."

For more enlightenment, be sure to grab your copy of Zero to One.