Daily Archives: March 26, 2009

A Mathematician’s Apology on the Anonymity of Mathematicians John von Neumann and Jack Schwartz

One of my favorite books about mathematics is the memoir by the British mathematician and number theorist G. H. Hardy, A Mathematician’s Apology. 1

Jack Schwartz was one of the Founding Fathers of the Computer Revolution. His only peers are John von Neumann, Seymour Cray, John Cocke, and Don Knuth. Only Knuth still lives.

Jack and von Neumann were among the greatest mathematicians of the last century.

Ten or so years ago I chanced upon a documentary about von Neumann that was being shown on television. He died around 1956. I learned that only two artifacts survived him other than his writings:

  • A wire recording of one of his lectures;
  • A recording of a science show for children. John is shown standing next to some children. He was asked by the host, a Mr. Wizard-like character, the following question:

    What are you holding, Professor?

    to which John replied:

    A battery.

    The only film showing John speaking contains just ONE word!

    It was then that I first appreciated that, as Hardy observed, mathematicians labor in obscurity.2

    Last week I attended my first Caltech Alumni Event in five years. At the end of the meeting I stood up and told the audience about Jack. There were sixty people in the audience. Perhaps forty were Caltech grads.

    I asked how many people recognized the name “Jacob Schwartz” or “Jack Schwartz”

    Only ONE raised his hand!

    Though I have been quite active at late, I am now near a state of exhaustion since I have spent most of the last four days trying to think of people who should be informed about the upcoming events so they be given the opportunity to attend.

    I was driven to this by that single raised hand.

    I know many others have been working in the same way.

    Well, I have what I could, and I look forward to meeting Jack’s family, friends, and colleagues at CIMS this weekend.

    Early on in this blog I listed the Five Smartest People I have ever worked with or seen in action:

    • Feynman
    • Murray Gell-Mann
    • Jack
    • John Cocke
    • Tom Friedman

    Tom is not a scientist, leaving four.

    I wrote then that Feyman’s mind was by far the best I have ever seen.

    I said that Gell-Mann’s was the most superficially brilliant. His mind lit up like a supernova.

    Feyman’s mind could light up a galaxy.

    I now believe that Jack was Feynman’s peer, for I only realized recently, when I read some of the writings of the most eminent of my mathematical brothers, MIT Prof. Gian-Carlo Rota, that Jack was a much, much better mathematician than I had ever guessed.

    I now consider Feynman and Jack to be peers, as I cannot make the case to favor one over the over. That I will leave to others.

    Feynman and Jack had many similarities. Both were born and raised in New York.

    Both had many interests. We’ve all seen the pictures of Feynman playing the drums, or heard him talk about his days cracking safes at Los Alamos, or heard him speak about taking drawing lessons. (I did. I also noted some years back that part of my sleeve can be seen in a picture taken while Feynman spoke of drawing in the Caltech Student Center.)

    Both also traveled widely. Feynman to Tuva; Jack to Argentina, China, Russia, Turkey, and so forth.

    The greatest similarity is that both were extremely modest men, almost to a fault.

    That is the truest measure of their character and their intelligence.

    – o –

    Jacob T. “Jack” Schwartz – May His Memory Be A Blessing.


    1. See for example the anecdote about the number 1729.

    1, Bloggers also labor in obscurity. See Security Through Obscurity. On the escape velocity from obscurity, and The Long March Up From Obscurity: Technorati Authority Now 40, Rank 199700.

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