The Mathematical Foundations of Quantum Mechanics ‐ John von Neumann and his Impact on Physics in 2025

John von Neumann’s scientific impact ranges from quantum mechanics to economics and computer programming. He must be considered one of the most universal, creative, and influential scientists of the 20th century. This seminar focuses, from today’s perspective, on the role of the early seminal contributions by John von Neumann in quantum mechanics.

Already in 1927 von Neumann published a series of articles in which he clarified “The Mathematical Foundations of Quantum Mechanics”. This is the title of his core paper, his well-known book from 1932 and, appropriately, of our seminar.  His work, including the notion of Hilbert space, the role of operators, and the statistical interpretation of quantum ensembles, is still the basis for every student of the subject. His further work on quantum logic and, especially, operator algebras has developed into active current research fields. Nevertheless, von Neumann's role as one of the founding fathers of quantum theory is often not appreciated.

In addition, von Neumann revolutionized economic theory with his thinking in terms of game strategies, and was a key figure in the theory and construction of early computers. This topic connects again with quantum mechanics via the current endeavours of building a quantum computer. Accordingly, the best way to appreciate the work of this towering genius is to outline current research, while retracing its roots in von Neumann's ideas. An excellent array of active scientists in the fields shaped by von Neumann till today is ready to make these connections, and will attract the attention of scientists from the junior to the senior stage.

The topic of the seminar fits perfectly into the IYQST, the International Year of Quantum Science and Technology proclaimed by the United Nations in June 2024, and the imminent centennials of quantum mechanics. 

The conference language will be English. The Wilhelm and Else Heraeus-Foundation bears the cost of full-board accommodation for all participants.