Persi Warren Diaconis (; born January 31, 1945) is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

descent and former professional magician. He is the Mary V. Sunseri Professor of

Statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

and

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

. He is particularly known for tackling mathematical problems involving

randomness In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual rand ...

and

randomization Randomization is the process of making something random. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution d ...

, such as

coin flipping Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking obverse and reverse, which side is showing when it lands, in order to choose between two alternatives, heads or tails, sometimes used to res ...

and

shuffling playing cards Shuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to help ensure that the shuffler has not manipulated the outcome. __TOC__ Techniques Over ...

Biography

Diaconis left home at 14 to travel with

sleight-of-hand Sleight of hand (also known as prestidigitation or ''legerdemain'' ()) refers to fine motor skills when used by performing artists in different art forms to entertain or manipulate. It is closely associated with close-up magic, card magic, car ...

legend

Dai Vernon Dai Vernon (pronounced alternatively as "DIE" or as "DAY" as in David; June 11, 1894 – August 21, 1992), a.k.a. The Professor, was a Canadian magician. His sleight of hand technique and knowledge, particularly with card tricks and close ...

, and dropped out of high school, returning to school at age 24 to learn math, motivated to read

William Feller William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian-American mathematician specializing in probability theory. Early life and education Feller was born in Zagreb to Ida Oemichen-Perc, a Croa ...

's famous two-volume treatise on probability theory, ''An Introduction to Probability Theory and Its Applications''. He attended the

City College of New York The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a public university within the City University of New York (CUNY) system in New York City. Founded in 1847, Cit ...

for his undergraduate work, graduating in 1971, and then obtained a Ph.D. in Mathematical Statistics from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

in 1974), learned to read Feller, and became a mathematical probabilist.Jeffrey R. Young, "The Magical Mind of Persi Diaconis" ''Chronicle of Higher Education'' October 16, 201

/ref> According to

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis ...

, at school, Diaconis supported himself by playing

poker Poker is a family of comparing card games in which players wager over which hand is best according to that specific game's rules. It is played worldwide, however in some places the rules may vary. While the earliest known form of the game w ...

on ships between New York and

South America South America is a continent entirely in the Western Hemisphere and mostly in the Southern Hemisphere, with a relatively small portion in the Northern Hemisphere at the northern tip of the continent. It can also be described as the southe ...

. Gardner recalls that Diaconis had "fantastic second deal and bottom deal". Diaconis is married to Stanford statistics professor Susan Holmes.

Career

Diaconis received a

MacArthur Fellowship The MacArthur Fellows Program, also known as the MacArthur Fellowship and commonly but unofficially known as the "Genius Grant", is a prize awarded annually by the MacArthur Foundation, John D. and Catherine T. MacArthur Foundation typically to ...

in 1982. In 1990, he published (with

Dave Bayer David Allen Bayer (born November 29, 1955) is an American mathematician known for his contributions in algebra and symbolic computation and for his consulting work in the movie industry. He is a professor of mathematics at Barnard College, Columbi ...

) a paper entitled "Trailing the Dovetail Shuffle to Its Lair" (a term coined by magician Charles Jordan in the early 1900s) which established rigorous results on how many times a deck of playing cards must be riffle shuffled before it can be considered random according to the mathematical measure

total variation distance In probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric, and is sometimes called the statistical distance, statistical difference or variational dista ...

. Diaconis is often cited for the simplified proposition that it takes seven shuffles to randomize a deck. More precisely, Diaconis showed that, in the

Gilbert–Shannon–Reeds model In the mathematics of shuffling playing cards, the Gilbert–Shannon–Reeds model is a probability distribution on riffle shuffle permutations that has been reported to be a good match for experimentally observed outcomes of human shuffling, and th ...

of how likely it is that a riffle results in a particular

riffle shuffle permutation In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of n items that can be obtained by a single riffle shuffle, in which a sorted deck of n cards is cut into ...

, it takes 5 riffles before the total variation distance of a 52-card deck begins to drop significantly from the maximum value of 1.0, and 7 riffles before it drops below 0.5 very quickly (a threshold phenomenon), after which it is reduced by a factor of 2 every shuffle. When

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

is viewed as the probabilistic distance, riffle

shuffling Shuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to help ensure that the shuffler has not manipulated the outcome. __TOC__ Techniques Overha ...

seems to take less time to mix, and the threshold phenomenon goes away (because the entropy function is subadditive). Diaconis has coauthored several more recent papers expanding on his 1992 results and relating the problem of shuffling cards to other problems in mathematics. Among other things, they showed that the separation distance of an ordered

blackjack Blackjack (formerly Black Jack and Vingt-Un) is a casino banking game. The most widely played casino banking game in the world, it uses decks of 52 cards and descends from a global family of casino banking games known as Twenty-One. This fami ...

deck (that is, aces on top, followed by 2's, followed by 3's, etc.) drops below .5 after 7 shuffles. Separation distance is an upper bound for variation distance. Diaconis has been hired by casino executives to search for subtle flaws in their automatic card shuffling machines. Diaconis soon found some and the horrified executives responded, "We are not pleased with your conclusions but we believe them and that's what we hired you for." He served on the Mathematical Sciences jury of the

Infosys Prize The Infosys Prize is an annual award given to scientists, researchers, engineers and social scientists of Indian origin (not necessarily born in India) by the Infosys Science Foundation and ranks among the highest monetary awards in India to re ...

in 2011 and 2012.

Recognition

*1982 – Awarded a

*1982 – Awarded the

Rollo Davidson Prize The Rollo Davidson Prize is a prize awarded annually to early-career probabilists by the Rollo Davidson trustees. It is named after English mathematician Rollo Davidson (1944–1970). Rollo Davidson Trust In 1970, Rollo Davidson, a Fellow-el ...

*1990 – Invited Speaker of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

(ICM) *1995 – Elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

*1997 – Gibbs Lecturer, American Mathematical Society *1998 – Plenary Speaker of the ICM *2003 – Received an honorary D. Sci. degree from the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

. *2005 – Elected to the

American Philosophical Society The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...

*2006 – Awarded the Van Wijngaarden Award *2012 – Awarded the

Levi L. Conant Prize The Levi L. Conant Prize is a mathematics prize of the American Mathematical Society, which has been awarded since 2000 for outstanding expository papers published in the ''Bulletin of the American Mathematical Society'' or the ''Notices of the Amer ...

*2012 – Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

*2013 – Received an Honorary Degree from the

University of St Andrews (Aien aristeuein) , motto_lang = grc , mottoeng = Ever to ExcelorEver to be the Best , established = , type = Public research university Ancient university , endowment ...

. *2014 – Recipient of Cahit Arf Lecture by Middle East Technical University, Ankara, Turkey

Works

The books written or coauthored by Diaconis include: * ''Group Representations In Probability And Statistics'' (Institute of Mathematical Statistics, 1988) * ''Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks'' (with Ronald L. Graham, Princeton University Press, 2012), winner of the 2013

Euler Book Prize The Euler Book Prize is an award named after Swiss mathematician and physicist Leonhard Euler (1707-1783) and given annually at the Joint Mathematics Meetings by the Mathematical Association of America to an outstanding book in mathematics that is ...

* ''Ten Great Ideas about Chance'' (with

Brian Skyrms Brian Skyrms (born 1938) is an American philosopher, Distinguished Professor of Logic and Philosophy of Science and Economics at the University of California, Irvine, and a professor of philosophy at Stanford University. He has worked on problem ...

, Princeton University Press, 2018)Reviews of ''Ten Great Ideas about Chance'': * * * * * * * * * * * * * His other publications include: *"Theories of data analysis: from magical thinking through classical statistics", in *

References

External links