How has Peter Thiel's approach to business influenced the success of PayPal and Palantir?

Zero to One, written by Peter Thiel and Blake Masters, is a book that emphasizes the importance of innovative thinking in business. The authors argue that the most valuable businesses are those that create something new and unique, going from "zero to one" rather than copying what's already been done, or going from "one to n".

The book also presents seven questions that every business must answer to determine if they are truly unique:
1. Can you create breakthrough technology instead of incremental improvements?
2. Is now the right time to start your particular business?
3. Are you starting with a big share of a small market?
4. Do you have the right team?
5. Do you have a way to not just create but deliver your product?
6. Will your market position be defensible 10 and 20 years into the future?
7. Have you identified a unique opportunity that others don’t see?

These principles guide entrepreneurs to think differently and to strive for creating monopolies in untapped markets.

The 'zero to one' concept has significantly influenced the way investors evaluate startups. It encourages investors to look for startups that are creating something truly unique, rather than those that are simply iterating on existing ideas. This is because unique startups have the potential to create entirely new markets, leading to massive returns on investment. Therefore, investors are now more interested in startups that can demonstrate they are going from 'zero to one', rather than from 'one to n'.

Some potential challenges in implementing the 'zero to one' approach in a business could include the difficulty in creating something truly unique, the risk of failure, the need for a high level of creativity and innovation, and the potential for resistance from stakeholders who are comfortable with the status quo.