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George Spencer-Brown (born April 2, 1923, Grimsby, Lincolnshire, England) is a polymath best known as the author of Laws of Form. He describes himself as a "mathematician, consulting engineer, psychologist, educational consultant and practitioner, consulting psychotherapist, author, and poet."[1].

Spencer-Brown obtained an M.B. in 1940 from London Hospital Medical College (now part of Queen Mary, University of London). After serving in the Royal Navy (1943-47), he studied at Trinity College Cambridge, earning Honours in Philosophy (1950) and Psychology (1951), and where he met Bertrand Russell. From 1952 to 1958, he taught philosophy at Christ Church College, Oxford, earning M.A. degrees in 1954 from both Oxford and Cambridge, and writing his 1957 book Probability and Scientific Inference. During the 1960s, he became a disciple of the innovative Scottish psychiatrist R. D. Laing, frequently cited in Laws of Form.

In 1964, on Bertrand Russell's recommendation, he became a lecturer in formal mathematics at the University of London. From 1969 onward, he was affiliated with the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. In the 1970s and 1980s he was visiting professor at the University of Western Australia, Stanford University, and at the University of Maryland, College Park.

Laws of Form, at once a work of mathematics and of philosophy, emerged out of work in electronic engineering Spencer-Brown did around 1960, and from lectures on mathematical logic he later gave under the auspices of the University of London's extension program. First published in 1969, it has never since gone out of print. Spencer-Brown referred to the mathematical system of Laws of Form as the "primary algebra" and the "calculus of indications"; others have termed it "boundary algebra." The primary algebra is essentially an elegant minimalist notation for the two-element Boolean algebra, very similar to formal systems Charles Peirce devised in work written in the 1880s and 90s (see entitative graph), but in some cases not published until after the first edition of Laws of Form. Laws of Form has influenced, among others, Heinz von Foerster, Louis Kauffman, Niklas Luhmann, Humberto Maturana, Francisco Varela and William Bricken. Some of these authors devised "enhanced" or modified versions of Spencer-Brown's Laws of Form, with interesting consequences.

In a 1976 letter to the Editor of Nature, Spencer-Brown claimed a noncomputational proof of the four-color theorem. While this claim of proof has yet to be verified, Kauffman has incorporated parts of Spencer-Brown's reasoning into his own work. Spencer-Brown has also written on number theory, especially the determination of primality.

The preface of the 1979 edition of Laws of Form repeats the four-color theorem claim, together with a claim that the accepted proof by Appel, Haken, and Koch has 'failed' (page xii). Given the general acceptance of this proof by the mathematical community and the lack, as of 2007, of any acceptance of Spencer-Brown's proof, his various claims must be taken with some skepticism.

Spencer-Brown claimed in 1998 to have a proof of Goldbach's conjecture, and in 2006 to have a proof of the Riemann hypothesis.

Spencer-Brown has also written some novels and poems, sometimes employing the pen name James Keys.

Quote: "...to teach pride in knowledge is to put up an effective barrier against any advance upon what is already known, since it makes one ashamed to look beyond the bounds imposed by one's own ignorance." Laws of Form, Appendix 1.

Recent extensions by "disciples": Since 2003, a new web site (multiforms.netfirms. c o m "Multiple Form Logic") claims to have "generalised Spencer-Brown's system into Multiple Truth Values" and to be "more consistent with Experience"; it uses the XOR operator and three "alternative axioms". The author is a member of the "Laws of Form Forum", where this theory (among others) was presented and discussed in recent years.

• Laws of Form
• Charles Peirce
• Entitative graph

• 1957. Probability and Scientific Inference.
• Selected editions of Laws of Form:
  • 1969. London: Allen & Unwin.
  • 1972. Crown Publishers, hardcover. ISBN 0-517-52776-6
  • 1994. Cognizer Company, paperback. ISBN 0-9639899-0-1
  • 1997. German translation titled Gesetze der Form. Lübeck: Bohmeier Verlag. ISBN 3-89094-321-7
• "Claim of Proof to Four Colour Theorem." Letter to the Editor of Nature. 17 December 1976.

• G Spencer-Brown: Laws of Form, website with Tutorial, Flash animations, downloads.
• Richard Shoup's website devoted to Spencer-Brown, his work, and related ideas. Includes an extensive bibliography of the secondary literature on Laws of Form.
• Brief bio of G. Spencer-Brown.
• "A short proof of the Rieman hypothesis" by G. Spencer-Brown (Juli 2006).
• Draw a distinction... The space of imagination based on Spencer-Brown.
• Kauffman, Louis H., "Reformulating the Map Color Theorem".
• Transcript of Spencer-Brown's talks at Esalen, 1973.