From an AMA on Reddit 4 years ago:
Three parts to Piketty:
1 He describes a world of greater inequality. I think this is happening and is an important phenomenon.
2 He explains the phenomenon as driven by high returns on capital. I think this explanation is incorrect (the real returns have been negative since 2008, with interest rates at 0% and inflation at 2% in the US).
3 He proposes much higher marginal tax rates and a wealth tax. I think this is very bad policy and almost impossible to implement, and will result in massive distortions as people try to shelter more income and wealth.
I think we need to find ways to grow the overall economy faster — without faster growth, inequality will be the least of our problems.
In general, Thiel is a fan of trickle-down economics, focused on wealth creation through the fast growth of new systems of value.