Norman Laurence Gilbreath

Norman Laurence Gilbreath (born 1936) is an American magician and author known for originating the Gilbreath shuffle.[1] He is also known for Gilbreath's conjecture concerning prime numbers.[2]

Life and career

Gilbreath got a BS in mathematics at University of California, Los Angeles (UCLA). Following graduate work in applied mathematics, which saw him work under C. C. Chang, he spent his entire career at the Rand Corporation as an expert on compilers and optimization tasks.[1] His book Magic for an Audience was published in 1989 as a series of three articles in Genii Magazine.[3] He lives in Los Angeles and performed regularly in the 2000s at Hollywood's Magic Castle.

The Gilbreath shuffle is a method of shuffling a deck of cards, by riffling two packs of cards after reversing one of them. Unlike a standard riffle, it preserves certain properties of the sequence of cards, leading to its use in magic tricks. Gilbreath introduced the Gilbreath principle – the basis of card tricks using the Gilbreath shuffle – in 1958 in an article in Genii magazine. In 1966 he published a generalization that is now called the Second Gilbreath principle.[4] But the principal only became well known after Martin Gardner wrote about it in his July 1972 "Mathematical Games column" in Scientific American.[5]

In number theory, he is known for Gilbreath's conjecture, an unproven pattern in the difference sequences of prime numbers. Gilbreath found this as a student in 1958 at UCLA. Two other students, R. B. Killgrove and K. E. Ralston, took advantage of the state-of-the-art SWAC computer installed at UCLA and confirmed it for the first 63419 primes.[6] Unknown to them, the same pattern had been observed many years earlier by François Proth, but it is by Gilbreath's name that the conjecture is now known.

Books
  • Magic for an Audience, Genii Magazine, Vol. 52, No. 09-10-11, Spring 1989.
  • Beyond Imagination, Publisher: H&R Magic Books (2014).

References
  1. The Mathematical Ideas That Animate Great Magic Tricks by Persi Diaconis & Ron Graham, Chapter 5: From the Gilbreath Principle to the Mandelbrot Set, Princeton University Press (2011), ISBN 978-1-4008-3938-4
  2. The Second Norman Invasion Mathematical Association of America, August 2006
  3. Norman Gilbreath in Magicpedia.
  4. The Gilbreath shuffle, The Linking Ring, Volume 38, No. 5, July 1958.
  5. A Quarter-Century of Recreational Mathematics by Martin Gardner, Scientific American. August 1998.
  6. R. B. Killgrove and K. E. Ralston, On a conjecture concerning the primes. Math. Comp. 13 (1959), 121–122.
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