Raymond Merrill Smullyan (born 1919) is a mathematician, logician, philosopher, and magician. 1919 (MCMXIX) was a common year starting on Wednesday (see link for calendar). ... This article is in need of attention from an expert on the subject. ... A logician is a philosopher, mathematician, or other whose topic of scholarly study is logic. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... Magic, including the arts of prestidigitation and conjuring, is the art of entertaining an audience by performing illusions that baffle and amaze, often by giving the impression that something impossible has been achieved, almost as if the performer had magic or supernatural powers. ...

Born in Far Rockaway, New York, his first career (like Persi Diaconis a generation later) was stage magic. He then obtained a BSc from Chicago in 1955 and a Ph.D. from Princeton in 1959. He is one of many outstanding logicians to have studied under Alonzo Church. Far Rockaway is one of the four neighborhoods on the Rockaway Peninsula in the New York City borough of Queens in the United States. ... Official language(s) None, English de facto Capital Albany Largest city New York City Area  - Total  - Width  - Length  - % water  - Latitude  - Longitude Ranked 27th 141,205 km² 455 km 530 km 13. ... Persi W. Diaconis (born January 31, 1945) is an American mathematician and former professional magician. ... Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science. ...

While a Ph.D. student, Smullyan published a paper in the 1957 Journal of Symbolic Logic showing that Gödelian incompleteness held for formal systems a good deal more elementary than that of Gödel's 1931 landmark paper. The contemporary understanding of Gödel's theorem dates from this paper. Smullyan later made a compelling case that much of the fascination with Gödel's theorem should be directed at Tarski's theorem, which is much easier to prove and equally disturbing philosophically. The culmination of Smullyan's lifelong reflection on the classic limitative theorems of mathematical logic is his quite readable: In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ... Several results obtained by the noted logician Alfred Tarski are commonly referred to as Tarskis theorem: Tarskis theorem on real closed fields established the decidability of the first order theory of real numbers. ...

Smullyan, R M (2001) "Gödel's Incompleteness Theorems " in Goble, Lou, ed., The Blackwell Guide to Philosophical Logic. Blackwell (ISBN 0-63120693-0).

Smullyan is the author of many books on recreational mathematics, recreational logic, etc. Most notably, one is titled What is the name of this book?. Recreational mathematics includes many mathematical games, and can be extended to cover such areas as logic and other puzzles of deductive reasoning. ...

Many of his logic problems are extensions of classic puzzles. Those involving knights (who always tell the truth) and knaves (who always lie) are based on the story of the two doors & two guards, one who lies and one who doesn't. One door leads to heaven and one to hell, and the puzzle is to find out which door leads to heaven by asking one of the guards a question. One way to do this is to ask "Which door would the other guard say leads to hell?".

In more complex puzzles, he introduces characters who may lie or tell the truth (referred to as "normals"), and furthermore instead of answering "yes" or "no", use words which mean "yes" or "no", but the reader does not know which word means which. In his Transylvania puzzles, half of the inhabitants are insane, and believe only false things, whereas the other half are sane and believe only true things. In addition, humans always tell the truth, and vampires always lie. For example, an insane vampire will believe a false thing (2 + 2 is not 4) but will then lie about it, and say that it is. A sane vampire knows 2 + 2 is 4, but will lie and say it isn't. And mutatis mutandis for humans. Thus everything said by a sane human or an insane vampire is true, while everything said by an insane human or a sane vampire is false. This article deals with vampires in folklore and legends. ... In Latin, mutatis mutandis means upon changing what needs to be changed, where what needs to be changed is usually implied by a prior statement assumed to be understood by the reader. ...

His book Forever Undecided popularises Gödel's incompleteness theorems by phrasing them in terms of reasoners and their beliefs, rather than formal systems and what can be proved in them. For example, if a native of a knight/knave island says to a sufficiently self-aware reasoner "You will never believe that I am a knight", the reasoner cannot believe either that the native is a knight or that he is a knave without becoming inconsistent (i.e. holding two contradictory beliefs). The equivalent theorem is that for any formal system S, there exists a mathematical statement which can be interpreted as "This statement is not provable in formal system S". If the system S is consistent, neither the statement nor its opposite will be provable in it. Kurt Gödel Kurt Gödel [kurt gøːdl], (April 28, 1906 Brno, Czech Republic –January 14, 1978 Princeton, New Jersey) was a logician, mathematician, and philosopher of mathematics. ... In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proved by Kurt Gödel in 1931. ...

His book To Mock a Mocking Bird is a splendid recreational introduction to an arcane subject: combinatory logic. Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. ...

Apart from writing about and teaching logic, Smullyan has recently released a recording of his favourite classical piano pieces by composers such as Bach, Scarlatti and Schubert. He has also written an autobiography titled Some Interesting Memories: A Paradoxical Life (ISBN 1-88871010-1). Johann Sebastian Bach (21 March 1685 O.S. – 28 July 1750 N.S.) was a prolific German composer and organist whose sacred and secular works for choir, orchestra and solo instruments drew together almost all of the strands of the baroque style and brought it to its ultimate maturity. ... Domenico Scarlatti (October 26, 1685 – July 23, 1757) was an Italian composer of the Baroque era. ... Franz Schubert Franz Peter Schubert (January 31, 1797 – November 19, 1828), was an Austrian composer, considered the last master of the Viennese Classical school and one of the earliest proponents of musical Romanticism. ... An autobiography (from the Greek auton, self, bios, life and graphein, write) is a biography written by the subject or composed conjointly with a collaborative writer (styled as told to or with). The term dates from the late eighteenth century, but the form is much older. ...

Selected publications

Popular

• The Tao is Silent
• The Chess Mysteries of Sherlock Holmes
• The Chess Mysteries of the Arabian Knights
• The Lady or the Tiger?
• The Riddle of Scheherazade
• This Book Needs No Title
• Alice in Puzzle-land - Shopping ...
• What Is the Name of This Book?
• Forever Undecided
• To Mock a Mockingbird
• Satan, Cantor and Infinity
• Some Interesting Memories: A Paradoxical Life
• Who Knows?

Academic

• First-order Logic
• Theory of Formal Systems
• Gödel's Incompleteness Theorems

Quotations

Quotations About Smullyan

I now introduce Professor Smullyan, who will prove to you that either he doesn't exist or you don't exist, but you won't know which. Melvin Fitting

External links

• Raymond Smullyan's website at Indiana University. [1]
• At The MacTutor History of Mathematics archive. [2]
• At The Mathematics Genealogy Project. [3]

External references

• Is God a Taoist? by Raymond Smullyan, 1977. [4]
• Planet Without Laughter by Raymond Smullyan, 1980. [5]
• An Epistemological Nightmare by Raymond Smullyan, 1982. [6]