Monday, February 13, 2017

Raymond Smullyan: Logician, Recreational math writer, Philosopher, passed away

Raymond Smullyan was born on May 25 1919 and passed away recently at the age of 97.  He was a logician (PhD from Princeton under Alonzo Church in 1959) who did serious,  recreational, and philosophical work. I doubt he invented the truth-teller/liar/normals and knight/knave/Knormal  problems, but he popularized them and (I suspect) pushed them further than anyone before him.

He was active all of his life:

His last book on Logic Puzzles, The Magic Garden of George B and other Logic Puzzles was published in 2015. Wikipedia lists 14 books on logical puzzles, from 1978 untl 2015.

His last book classified (on Wikipedia) as Philosophy/Memoir, A Mixed Bag: Jokes, Riddles, Puzzles, and Memorabilia was published in 2016. Wikipedia lists 8 books in this category, from 1977 until 2016.

His last Academica book, A beginners further guide to mathematical logic was published in 2016. (It was a sequel to his 2014 A beginners guide to mathematical logic.) Wikipedia lists 8 books in this category, from 1961 to 2016.

Recreational Work:

His recreational work was of the Knights/Knaves/Knormals/Sane/Insane/ variety.a

Knights always tell the truth.

Knaves always lie,

Knormals may tell the truth or lie.

Insane people only believe false things,

Sane people only believe true things.

He also added a complication: a species that says ALPHA and BETA for YES and NO but
you don't know which of ALPHA, BETA means YES and which one means NO.

Note that a truth teller Insane Knight will answer YES to 1+1=3.

He invented  (discovered?) the so called hardest logic puzzle ever. He wrote many books on recreational math. We mention four of them that show the line between recreational and serious mathematics is thin.

To Mock a Mockingbird. This book has logic puzzles based on combinatory logic. Is that really recreational?

Forever Undecided. This book introduces the layperson to Godel's theorem.

Logical Labyrinths. This is a textbook for a serious logic course that uses puzzles to teach somewhat serious logic. It was published in 2009 when he was only 89 years old.

A Personal Note: I read the following, from his
The Lady or the Tiger, when I was in high school, and I still don't know the answer!:

My brother told me he would fool me on April Fools Day. I lay awake that night wondering how he would fool me. All day I was worried how he would fool me. At midnight I asked him Hey, you said you would fool me but you didn't He replied April Fools!. To this day I don't know if I was fooled or not.

Serious Math Work. His serious work included the Double Recursion Theorem.  (you can write two programs that know both their indices and each others indices) and other theorem in logic. (ADDED LATER: Lipton and Regan have a blog post with lots of great information about Ray S's serious math work here.)

Philosophy. I'm not qualified to comment on this; however, it looks like he did incorporate his knowledge of logic.

Looking over his books and these points it seems odd to classify his books as the recreational books had some serious logic in them, and the academic books had some math that a layperson could understand

I think its rarer now to do both recreational and serious mathematics, though I welcome intelligent debate on this point.

Before he died, was he the oldest living mathematician? No- Richard Guy is 100 years old. wikipedia claims that Guy is still an active math Guy. Is he the oldest living mathematican? The oldest living active mathematician? It was hard to find out on the web so I ask you.


  1. Certainly best known for his logic work, but because he was such a strict empiricist I think his take on spirituality/religion is also very interesting and worth mentioning. I'm familiar with his 3 works: "The Tao Is Silent," "A Spiritual Journey," and "Who Knows," and I believe he may have authored 1-2 other spiritual-related volumes.
    In any event, thanks for writing this; it's a shame there aren't more tributes of length appearing for such a multi-talented polymath/musician/magician.

  2. I was thrilled to meet Smullyan when I was a graduate student. I had enjoyed "What is the Name of this Book?" He talked about trying to get the rights to the name "Sherlock Holmes" for his upcoming book "The Chess Mysteries of Sherlock Holmes." He must have obtained them since it was published soon after, although he said that the name was going to be public domain within a few years anyway.

    I recall thinking that he was an old man, maybe because of his long white hair. It is sobering to realize (as Tom Lehrer might say), that I am now older than he was. Of course, I will never, ever be old, and, I guess, he was never old either.

    -Clyde Kruskal

  3. It should be mentioned that Smullyan also published two books on chess composition, in particular retro chess problems: “The Chess Mysteries of Sherlock Holmes (1979)” and “The Chess Mysteries of the Arabian Knights (1981).” Though he was not the inventor of retrograde analysis in chess (you find it already since the beginning of the 20th century) these books did (and still do) much to popularize the genre.
    A good introduction to his work by many prominent contributors is the recent book “Four Lives: A Celebration of Raymond Smullyan (2014)” by Jason Rosenhouse. (In it Kostas Prentos examines his work on retro chess.)

    1. To follow up on your comment, which I should have mentioned above ... “The Chess Mysteries of Sherlock Holmes” and “The Chess Mysteries of the Arabian Knights" are fantastic books, full of interesting, creative problems. I greatly enjoyed both, although I finished neither.

      -Clyde Kruskal

  4. Recreational...
    I strongly dislike that kind of shit and I think it's a shame for mathematicians to indulge in it.
    OF COURSE you "can" mix up things with multiple levels of references and quotation, moving inconspicuously from a statement to a QUOTE of this same statement, this is the basic ingredient of all such games starting with Godel incompleteness and piling up more and more levels of logic operators to befuddle the innocent onlooker and relish in your "smartness" (Smullyan as a magician) but how good is this for the advancement of human understanding?
    Any nearer to the famous question P=NP?
    Any simple, understandable, proof of Fermat theorem?
    Any hint at some approach to the remaining Clay prizes?

    1. First off, its an inappropriate place to trash someone's work in a comment on their obit. Second off, its obvious to us NOW that you can mix up levels, partly BECAUSE of the work of Godel, Smullyan, and many others. Thirdly, bringing up P vs NP or FLT or Clay prize problems as things he should have worked on? Really? Note that many problems get solved by people NOT working on them. For all we know self-reference may be the KEY to solving P vs NP (less likely for FLT). Maybe you just dislike Rec math in general-- I going to write a post on the benefits of working on Rec math later and I hope you will leave an intelligent counterargument there. Not here.

  5. The previous anonymous comment made me very sad. I suggest the administrators remove it (together with my comment, if they so wish). Call this a call for censorship if you will, but I think someone's death is definitely not the occasion to belittle their accomplishments (especially in such an unfair and baseless way). I am not even going to debunk the statement that the comment is making (it would be very easy to do so), this is simply not the time and place to do this. He (or she) is welcome to go on making contributions to any of the Clay problems or whatever they consider worthwhile. If this even needs to be argued, imagine if family members of the deceased stumble upon this thread, is this the image we (as the professional peers of Smullyan) want to create about him? Is this what their loved ones (who perhaps didn't follow his professional activity) should remember about him?

    1. A very interesting reply, political correctness is about to infect mathematics as it did of more "social" fields.
      You will reap exactly what you deserve.
      (I am the same "Anonymous" as above)

    2. What I was suggesting has nothing to do with political correctness -- you know very well that you wouldn't be making the above comment in real life, say at the funeral of a person. It would be partly because of basic decency, partly for fear of being punched in the face. However, online, behind the mask of anonymity, you can make any comment without any personal risk. It's like throwing your garbage in the park during the night. And then if someone tells you that this makes the park a worse place for everyone, claim that they are being PC and limit your freedom. (I am also the same Laszlo as above)

    3. Terry Tao's gentle-yet-factual rejoinder (here) to a comparably mean-spirited "anonymous" is commended to readers of Computational Complexity.

      It is notable, too, that Prof. Tao did not hesitate to remove subsequent comments by "anonymous" for the stated reason "[Unsubstantiated anonymous allegation deleted. -T.]"

      Summary  Allowing mean-spirited comments pass without response seems ill-advised (to me).