John von Neumann (quotes and anecdotes)

> “Most mathematicians prove what they can, von Neumann proves what he wants”
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From: https://en.wikipedia.org/wiki/John\_von\_Neumann

### Examination and Ph.D.

He graduated as a chemical engineer from ETH Zurich in 1926 (although Wigner says that von Neumann was never very attached to the subject of chemistry), and passed his final examinations for his Ph.D. in mathematics simultaneously with his chemical engineering degree, of which Wigner wrote,

> “Evidently a Ph.D. thesis and examination did not constitute an appreciable effort.”
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### Mastery of mathematics

Stan Ulam, who knew von Neumann well, described his mastery of mathematics this way: “Most mathematicians know one method. For example, Norbert Wiener had mastered Fourier transforms. Some mathematicians have mastered two methods and might really impress someone who knows only one of them. John von Neumann had mastered three methods.” He went on to explain that the three methods were:

* A facility with the symbolic manipulation of linear operators;
* An intuitive feeling for the logical structure of any new mathematical theory;
* An intuitive feeling for the combinatorial superstructure of new theories.

Edward Teller 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. That is, I think, something unique.”

### Cognitive abilities

As a six-year-old, he could divide two eight-digit numbers in his head and converse in Ancient Greek. When he was sent at the age of 15 to study advanced calculus under analyst Gábor Szegő, Szegő was so astounded with the boy’s talent in mathematics that he was brought to tears on their first meeting.

### Hans Bethe on von Neumann

Nobel Laureate Hans Bethe said “I have sometimes wondered whether a brain like von Neumann’s does not indicate a species superior to that of man”, and later Bethe wrote that:

> “von Neumann’s brain indicated a new species, an evolution beyond man”.
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### Edward Teller

Edward Teller admitted that he “never could keep up with John von Neumann.”

Teller 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.”
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### George Dantzig

George Dantzig is the mathematician who thought that two problems on the blackboard were homework. He solved them and handed them, albeit a bit later, so he thought they were overdue.

Here’s the plot twist: They were two famous unsolved problems in statistics with which the mathematics community struggled for decades.

When George Dantzig brought von Neumann an unsolved problem in linear programming “as I would to an ordinary mortal”, on which there had been no published literature, he was astonished when von Neumann said “Oh, that!” before offhandedly giving a lecture of over an hour, explaining how to solve the problem using the hitherto unconceived theory of duality.

### Johnny as a student

“There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann” — George Pólya

### Nobel Prizes

Peter Lax wrote, “To gain a measure of von Neumann’s achievements, consider that had he lived a normal span of years, he would certainly have been a recipient of a Nobel Prize in economics. And if there were Nobel Prizes in computer science and mathematics, he would have been honored by these, too. So the writer of these letters should be thought of as a triple Nobel laureate or, possibly, a ​3 1⁄2-fold winner, for his work in physics, in particular, quantum mechanics”.

### von Neumann as a teacher

Von Neumann was the subject of many dotty professor stories. He supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious). One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, “Yes.”

*His fluid line of thought was difficult for those less gifted to follow. He was notorious for dashing out equations on a small portion of the available blackboard and erasing expressions before students could copy them.*

For a man to whom complicated mathematics presented no difficulty, he could explain his conclusions to the uninitiated with amazing lucidity. After a talk with him one always came away with a feeling that the problem was really simple and transparent.

### Henry Ford

Henry Ford had ordered a dynamo for one of his plants. The dynamo didn’t work, and not even the manufacturers could figure out why. A Ford employee told his boss that von Neumann was “the smartest man in America,” so Ford called von Neumann and asked him to come out and take a look at the dynamo.

Von Neumann came, looked at the schematics, walked around the dynamo, then took out a pencil. He marked a line on the outside casing and said, “If you’ll go in and cut the coil here, the dynamo will work fine.”

They cut the coil, and the dynamo did work fine. Ford then told von Neumann to send him a bill for the work. Von Neumann sent Ford a bill for $5,000. Ford was astounded — $5,000 was a lot in the 1940s — and asked von Neumann for an itemised account. Here’s what he submitted:

Drawing a line with the pencil: $1

Knowing where to draw the line with the pencil: $4,999

Ford paid the bill.

### David Blackwell

Blackwell did a year of postdoctoral research as a fellow at the Institute for Advanced Study in 1941 after receiving a Rosenwald Fellowship. There he met John von Neumann, who asked Blackwell to discuss his Ph.D. thesis with him. Blackwell, who believed that von Neumann was just being polite and not genuinely interested in his work, did not approach him until von Neumann himself asked him again a few months later. According to Blackwell,

> “He (von Neumann) listened to me talk about this rather obscure subject and in ten minutes he knew more about it than I did.”
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### Enrico Fermi

So Fermi had schematized the problem on his blackboard. Everybody knows that in the beginning stages of Taylor instability you assume a ripple on the surface, and instead of behaving sinusoidally in time it behaves exponentially in time with the same time behavior except it’s imaginary instead of real or vice versa. So there is a time in which the amplitude doubles; the next interval it quadruples; the next interval it gets to be eight times as big. And pretty soon, of course, this cannot go on because the energy in the instability exceeds the energy that was driving it; the velocity exceeds the velocity of light. And so the question is what happens at large amplitudes? So Fermi said, let me make a model; I’ll have a broad tongue which moves into the dense material; I’ll have a narrow tongue that moves away from it and I’ll just solve this numerically. So he did some of that but he wasn’t quite satisfied with the solution. One afternoon around 4:50 p.m. John von Neumann came by and saw what Fermi had on the blackboard and asked what he was doing. So Enrico told him and John von Neumann said “That’s very interesting.” He came back about 15 minutes later and gave him the answer. Fermi leaned against his doorpost and told me,

> “You know that man makes me feel I know no mathematics at all.”
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”You know, Herb, Johnny can do calculations in his head ten times as fast as I can. And I can do them ten times as fast as you can, so you can see how impressive Johnny is” — Enrico Fermi (Nobel Prize in Physics, 1938)

You know, Herb, how much faster I am in thinking than you are. That is how much faster von Neumann is compared to me. – Nobel Laureate Enrico Fermi to his former PhD student Herb Anderson[https://spartanideas.msu.edu/2013/08/31/another-species-an-evolution-beyond-man/]

### Eugene Wigner

“One had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch.” — Eugene Wigner (Nobel Prize in Physics, 1963)

#### von Neumann was the only genius

Von Neumann entered the Lutheran Fasori Evangélikus Gimnázium in 1911. This was one of the best schools in Budapest, part of a brilliant education system designed for the elite. Under the Hungarian system, children received all their education at the one gymnasium. Despite being run by the Lutheran Church, the majority of its pupils were Jewish. The school system produced a generation noted for intellectual achievement. Wigner was a year ahead of von Neumann at the Lutheran School. When asked why the Hungary of his generation had produced so many geniuses, Wigner, who won the Nobel Prize in Physics in 1963, replied that:

> von Neumann was the only genius.”
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### Eidetic Memory

At the age of six, he was able to exchange jokes with his father in classical Greek. The Neumann family sometimes entertained guests with demonstrations of Johnny's ability to memorise phone books. A guest would select a page and column of the phone book at random. Young Johnny read the column over a few times, then handed the book back to the guest. He could answer any question put to him (who has number such and such?) or recite names, addresses, and numbers in order.

This enabled him to accumulate an almost encyclopedic knowledge of what ever he read, such as the history of the Peloponnesian Wars, the Trial Joan of Arc and Byzantine history (Leonard, 2010). **A Princeton professor of the latter topic once stated that by the time he was in his thirties, Johnny had greater expertise in Byzantine history than he did (Blair, 1957).**

"One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how A Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes."

Excerpt, The Computer from Pascal to von Neumann by Herman Goldstein (1980)

### Quantum Mechanics

Quantum mechanics was very fortunate indeed to attract, in the very first years after its discovery in 1925, the interest of a mathematical genius of von Neumann's stature. As a result, the mathematical framework of the theory was developed and the formal aspects of its entirely novel rules of interpretation were analysed by one single man in two years (1927-1929)

### Two Trains Puzzle

Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time, a fly that travels at a steady 15 m.p.h. starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover?

There are two ways to answer the problem. One is to calculate the distance the fly covers on each leg of its trips between the two bicycles and finally sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly an hour after they start so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: “Oh, you must have heard the trick before!”

“What trick,” asked von Neumann, “all I did was sum the infinite series.”

Excerpt, A Beautiful Mind (Nasar, 1998)

### The Duties of John von Neumann’s Assistant in the 1930s

'Von Neumann lectured on operator theory. His lectures were on Mondays, Tuesdays and Wednesdays. Lorch writes that the task of keeping up with the brilliant professor on this task alone amounted to “consuming the entire energies of a younger person, who had to be not only well-meaning but sharp, fast, clever and tough.”'

“These notes ran to over 600 pages. Weekly.”

### Gymnasium

In the rest of Johnny’s education Ratz was every bit as good as his word. Johnny learned his Latin and his Greek and his history in the gymnasium classroom along with his fellows. Ratz went so far as to insist that Johnny scrupulously attend the courses in mathematics provided in the gymnasium curriculum, and Johnny dutifully put aside the work with which he was engaged at the university to direct his attention to beginner’s algebra and the like. William Fellner, one of his schoolmates, recalled with admiration that Johnny not only clearly enjoyed those classes but also was in his own fashion working to learn from them, although what he was learning was not what the courses were designed to teach. He had understood that already, before the age of ten.

—John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More

### "Unsolvable Questions"

One German professor praised the habit of asking Ph.D. students “unsolvable questions” at their oral exams.

If the student instantly said,“That’s unsolvable,” he was deemed to have the right sharp set of mind.

The professor put his favorite unsolvable equations on the blackboard as an illustration. Johnny muttered at the ceiling for a few minutes, and then solved some of them.

—John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More

### A Distaste for Arrogance

A more typical occasion was when one professor propounded a new discovery that was actually quite wrong. This wrongdoer handled all the questions at the seminar devastatingly well, and there was a discussion of his discovery at a private dinner that night. Johnny demolished the whole discovery by saying that he should have been asked *a*, *b*, and *c*. “Why didn’t you ask that?” said the seminar organizer desperately. Johnny intimated that he did not like to be publicly rude.

This later made him popular in America as a referee for papers that had been submitted to learned journals. On at least one occasion he commended a paper but said it could be made much stronger by inserting the following dozen lines of figures and equations. The paper was thereby transformed into a major one, and the young author was rather embarrassed to keep in his own name even as a joint work.

—John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More

### Peter Lax

It is a name that should be known to every American—in fact, every person in the world, just as the name of Einstein is. I am always utterly surprised how come he’s almost totally unknown. All people who had met him and interacted with him realized that his brain was more powerful than anyone’s they have ever encountered. I remember Hans Bethe even said, only half in jest, that von Neumann’s brain was a new development of the human brain. Only a slight exaggeration.

...People today have a hard time to imagine how brilliant von Neumann was. If you talked to him, after three words, he took over. He understood in an instant what the problem was and had ideas. Everybody wanted to talk to him.

https://infoproc.blogspot.com/2017/09/lax-on-vn-he-understood-in-instant.html

### Other (Quotes)

“When asked a question he would instantly jump ten steps ahead and solve a whole family of related questions.” — John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More

“He demonstrated theorems in 5 minutes, resolved master’s and doctoral problems in a conversation, and had more knowledge than specialized people on all kinds of topics.”

“The military needed to solve a difficult problem. They were going to build a multimillion dollar computer to find the solution. They hired von Neumann to help design the computer. They staged a seminar where experts on the problem would tell all they knew to von Neumann. Instead of designing the computer von Neumann solved the problem and no new computer was needed.”

“Someone was giving a presentation on sphere packing in a very high dimensional space. After looking at it, von Neumann said “I think there is space to fit another one in there” and it turned out to be true.”

“John von Neumann solved master and doctorate problems like most people solve first or second degree equations.”

It's difficult to overstate the sheer intelligence of Von Neumann. He was unfathomably intelligent. I work in a university. There are a lot of smart people here. None of them are anything close to Von Neumann.

—Dr\_Marxist (Reddit)

Most world-class geniuses felt like dumbasses compared to him... and in turn, those in the same field as those world-class geniuses felt like dumbasses compared to them. This makes most of us his great-granddumbass at best.

—NewFolgers, Reddit

Can Von Neumann solve most of the IMO/IPHO problems in no time?

https://qr.ae/pN5B8x

Passing of a Great Mind