Peter Thiel opens Zero to One with his foundational distinction between horizontal progress — copying and incrementally improving things that already work, going from one to many similar versions — and vertical progress, genuinely new creation, going from zero to one, which he argues represents the rarer, more valuable, and more difficult form of genuine innovation.

Thiel's foundational argument:

• He observes that globalization — spreading existing technologies and business models to new markets — represents horizontal progress, while genuine technological innovation — creating something new that didn't exist before — represents the considerably rarer vertical progress his book focuses on
• Thiel argues contemporary business and technology discourse has become excessively focused on horizontal, incremental competition within existing categories, while genuinely valuable business creation actually requires vertical, category-creating innovation
• This distinction sets up the book's overall project: examining what genuine, category-creating innovation actually requires, based on Thiel's own experience as a founder and investor across numerous highly successful technology companies

This foundational framing establishes the book's contrarian, provocative tone throughout — consistently challenging conventional startup and business wisdom in favor of Thiel's own, often counterintuitive, principles for building genuinely category-defining companies.