Wang Hao (1921-1995), a student of Jin Yuelin and later W.V.O. Quine and Paul Bernays. was an important logician, philosopher, and mathematician who taught at Harvard, Oxford and Rockefeller University. His many contributions include pioneering the practice and theory of automated deduction, the use of tiling methods in the foundations of computation which influenced the theory of computational complexity, and the philosophy of mathematics where he became an authoritative interpreter and propagator of Gödel’s philosophical ideas, while also developing his own “substantial factualism” in between theoretical foundations and everyday discourse.

In a collaboration with the Yau Mathematical Sciences Center, the Institute for Interdisciplinary Information Sciences, and the Department of Philosophy at Tsinghua University, the center has started a Wang Hao Distinguished Lecture Series which will bring prominent international visitors to Tsinghua in the fields of mathematical and computational logic on a annual basis. The first Wang Hao lecturers will be Professor Hugh Woodin (Harvard) and Professor Moshe Vardi (Rice) in September of 2023.

##### Wang Hao lectures 2023

Is all mathematical truth simply the product of formal calculations, more precisely the result of formal proofs from formal axioms? This is arguably the most basic question in the Philosophy of Mathematics.

The incompleteness theorems of Gödel argue that the answer is no. But the extent to which this is actually a compelling answer is debatable.

However, there are new proofs of the incompleteness theorems which are based on computational complexity, and which definitively show that mathematical truth transcends mathematical proof.

Nowhere is the issue of truth versus proof more central than in Set Theory, which is the mathematical study of Infinity. Here many of the most basic questions, such as that of Cantor’s Continuum Hypothesis (CH), are known to be beyond the reach of proofs from the accepted ZFC axioms of Set Theory. So any resolution of the problem of CH must involve truth beyond proof.

One of the most famous questions in the philosophy of mathematics is whether mathematics is discovered or invented. As Timothy Gowers wrote: “It has been asked over and over again, and it is not clear what would constitute a satisfactory answer.” In this talk I will address this question from the perspective of a computer scientist. I will argue that the developments of mathematics and computung has dovetailed each other for thousands of years: Computing begat math, and math begat computing. Furthermore, both are connected to the real world via one of the most amazing faculties of the human mind: the capacity to abstract.