“A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.” — John von Neumann, Address to Princeton Alumni, 1954
Considered the greatest mathematician of the 20th century, John von Neumann has sometimes been described as even smarter than his contemporary Albert Einstein. Both of them were employed at the Institute for Advanced Study at Princeton University. Unlike Einstein, whose major discoveries stopped around 1920 and who died at age 76 in 1955, von Neumann was highly productive until his untimely death at age 53 in 1957. He published over 150 papers: about 60 in pure mathematics, 20 in physics, and 60 in applied mathematics. During World War II, he developed mathematical models of explosive lenses used in the implosion-type (Nagasaki) atom bomb. His analysis of self-replication in 1948 preceded the discovery of DNA in 1953. Another area of his research is in something we use every day, even while reading this post.
Although von Neumann’s mind was extremely fast, his atom bomb equations needed digital computers to solve the explosive lenses, which had to be within 5% tolerance to work. The earliest computers used a Harvard Architecture, which separates the Program (Instruction Memory in the drawing) from the Data Memory. The computers were very difficult to program, originally using paper tape or a plugboard for the program instructions. Because fast memory was very expensive, a trade-off is needed to allocate physical memory storage between the program and data storage. Once so determined, it limited the flexibility of the computer.
A more general approach, now called the Von Neumann Architecture, has one fast memory for both program and data storage, which greatly simplifies this tradeoff. During the 1950’s and 1960’s, this architecture was the basis for commercial Mainframes and Minicomputers. For cost, power drain, and size considerations, early single chip microprocessors used Read Only Memory (ROM) for program storage and Random Access Memory (RAM) for data storage, but these memories used the same Von Neumann memory bus architecture. Extra RAM is used for debugging the program, but once verified, it is replaced by ROM.
Calling the architecture “Von Neumann” has lead to some hard feelings from others. In the summer of 1944, von Neumann was drawn to the EDVAC machine, and wrote an incomplete “First Draft of a Report on the EDVAC.” His colleague Herman Goldstine circulated it with only von Neumann’s name on it. Along with the designers of EDVAC, the brilliant Alan Turing had similar ideas, but due to the wartime conditions, he was not able to publish. Later, von Neumann recommended a magnetic drum for the IBM 701, which was the basis for the commercially successful IBM 704.
John von Neuman’s mind was so quick that his colleagues were amazed. Atom bomb expert Hans Bethe speculated: “I have sometimes wondered whether a brain like von Neumann’s does not indicate a species superior to that of man.” Likewise, Edward Teller said he “never could keep up with him”, and also said “von Neumann would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us.” Teller also wrote that “Nobody knows all science, not even von Neumann did. But as for mathematics, he contributed to every part of it except number theory and topology.”
In September 1930, Von Neumann went to a conference where the brilliant Kurt Gödel announced his first theorem of incompleteness. Less than a month later, von Neumann came up with the second theorem. Gödel sent von Neumann a preprint of his article containing both incompleteness theorems. Von Neumann acknowledged Gödel’s priority, and never thought much of “the American system of claiming priority for everything.” This and other examples probably rubbed off on colleague Richard Feynman, who quoted von Neumann in his 1985 book as saying “You don’t have to be responsible for the world that you’re in.”
While the initial quote is true for mathematics in general, John von Neuman’s many discoveries (e.g., quantum mathematics, game theory, linear programming, etc.) generally had very short times between formulation and practical use. Maybe the speed of his brain could also calculate how fast his ideas would become useful.
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