- Person
- John von Neumann
- Lived
- 1903–1957
- Field
- Mathematics & computing
- From
- Hungarian-American
The story
By the early 1930s John von Neumann, born in Budapest in 1903 to a Jewish family, was already one of the most productive mathematicians in the world. He had lectured at the University of Berlin, where he was the youngest Privatdozent in its history, and from 1929 he was teaching at Princeton, publishing nearly one major paper a month.
Ergodic theory asks a deceptively simple question: if a system such as a gas evolves over a long time, does the average of some quantity over time equal its average over all possible states? The idea, rooted in Ludwig Boltzmann's ergodic hypothesis, sits at the heart of statistical physics, which explains the behaviour of heat and gases from the motion of countless particles.
In 1932 John von Neumann proved his mean ergodic theorem, giving the first rigorous mathematical results on the question, and argued that they were sufficient for the physical applications Boltzmann had in mind. He drew on his earlier work on operators in Hilbert space, the same mathematics he was using to put quantum mechanics on a rigorous footing. George David Birkhoff proved a closely related theorem in 1931, and the two results are counted among the most important in the field.
Later that year von Neumann published another influential paper that began the systematic study of ergodicity, including a decomposition theorem showing how complicated systems can be built from simpler ergodic pieces. He also pointed out what had not yet been achieved and marked it out for future work, and with Paul Halmos he later produced further results with significant applications in other areas of mathematics.
The mathematician Paul Halmos, once his assistant, wrote that even if von Neumann had never done anything else, those papers would have been sufficient to guarantee him mathematical immortality. Ergodic theory went on to grow into a major field, with connections to probability, geometry, harmonic analysis and number theory.
Why it matters
Ergodic theory became a major branch of mathematics, with applications in statistical physics, probability, geometry and number theory.
About John von Neumann
Budapest-born mathematician whose 1945 EDVAC report set out the stored-program design behind almost every computer, and who helped found game theory and modern quantum mechanics.
More about John von Neumann
- Von Neumann warned of CO2 warming in 1955In 1955 John von Neumann noted that carbon dioxide from burning coal and oil might already have changed the atmosphere enough to cause general warming.
- Von Neumann launched computer weather forecastingIn 1950 John von Neumann and Jule Charney used ENIAC to make the first numerical weather forecasts; in 1955 routine computer forecasting began in the US.
- John von Neumann founded game theoryJohn von Neumann proved the minimax theorem in 1928 and, with Oskar Morgenstern, published Theory of Games and Economic Behavior in 1944, founding game theory.
- Von Neumann's IAS computer was copied worldwideThe IAS machine John von Neumann built in Princeton from 1946 became the blueprint for early computers worldwide, and its design shaped IBM's first scientific computers.
- John von Neumann invented merge sort in 1945In 1945 John von Neumann invented merge sort, one of the most widely used methods for putting data in order, in what Donald Knuth called his first computer program.
- Von Neumann helped create the Monte Carlo methodWith Stanislaw Ulam, John von Neumann helped develop the Monte Carlo method, using random numbers on computers to solve problems too complex for direct calculation.
- Von Neumann gave quantum mechanics its mathematicsIn his 1932 book Mathematical Foundations of Quantum Mechanics, John von Neumann set out the first rigorous mathematical framework for quantum theory.
- Von Neumann designed a machine that copies itselfIn the late 1940s John von Neumann designed a self-reproducing 'universal constructor' and, with Stanislaw Ulam, created the field of cellular automata.
- John von Neumann wrote the blueprint for modern computersJohn von Neumann's 1945 report on the EDVAC gave the first published description of the stored-program computer, the design behind almost every computer since.
Sources
- John von Neumann Wikipedia
- Ergodic theory Wikipedia
Another act of tikkun olam. This is part of tikkun olam, the Jewish idea of repairing the world, and every one of us can add to it.