James Gary Propp is a professor of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

at the

University of Massachusetts Lowell The University of Massachusetts Lowell (UMass Lowell and UML) is a Public university, public research university in Lowell, Massachusetts, with a satellite campus in Haverhill, Massachusetts. It is the northernmost member of the University of M ...

Education and career

In high school, Propp was one of the national winners of the

United States of America Mathematical Olympiad The United States of America Mathematical Olympiad (USAMO) is a highly selective high school mathematics competition held annually in the United States. Since its debut in 1972, it has served as the final round of the American Mathematics Compe ...

(USAMO), and an alumnus of the Hampshire College Summer Studies in Mathematics. Propp obtained his AB in mathematics in 1982 at

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

. After advanced study at

Cambridge Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 Unit ...

, he obtained his PhD from the

University of California at Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a public land-grant research university in Berkeley, California, United States. Founded in 1868 and named after the Anglo-Irish philosopher George Berkele ...

. He has held professorships at seven universities, including

MIT The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

, the

University of Wisconsin A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Uni ...

, and the

Mathematical research

Propp is the co-editor of the book ''Microsurveys in Discrete Probability'' (1998) and has written more than fifty journal articles on

game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

and

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

, and

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

. He lectures extensively and has served on the Mathematical Olympiad Committee of the

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...

, which sponsors the USAMO. In the early 90s Propp lived in

Boston Boston is the capital and most populous city in the Commonwealth (U.S. state), Commonwealth of Massachusetts in the United States. The city serves as the cultural and Financial centre, financial center of New England, a region of the Northeas ...

and later in

Arlington, Massachusetts Arlington is a town in Middlesex County, Massachusetts, United States. The town is six miles (10 km) northwest of Boston, Massachusetts, Boston, and its population was 46,308 at the 2020 United States census, 2020 census. History Europe ...

. In 1996, Propp and David Wilson invented coupling from the past, a method for sampling from the

stationary distribution Stationary distribution may refer to: * and , a special distribution for a Markov chain such that if the chain starts with its stationary distribution, the marginal distribution of all states at any time will always be the stationary distribution. ...

of a

Markov chain In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally ...

among

Markov chain Monte Carlo In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that ...

(MCMC)

algorithms In mathematics and computer science, an algorithm () is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for per ...

. Contrary to many MCMC algorithms, coupling from the past gives in principle a perfect sample from the stationary distribution. His papers have discussed the use of surcomplex numbers in

; the solution to the counting of alternating sign matrices; and occurrences of Grandi's series as an

Euler characteristic In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's ...

infinite-dimensional In mathematics, the dimension of a vector space ''V'' is the cardinality (i.e., the number of vectors) of a basis of ''V'' over its base field. p. 44, §2.36 It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to d ...

real projective space In mathematics, real projective space, denoted or is the topological space of lines passing through the origin 0 in the real space It is a compact, smooth manifold of dimension , and is a special case of a Grassmannian space. Basic properti ...

Other contributions

Propp was a member of the National Puzzlers' League under the

pseudonym A pseudonym (; ) or alias () is a fictitious name that a person assumes for a particular purpose, which differs from their original or true meaning ( orthonym). This also differs from a new name that entirely or legally replaces an individual's o ...

Aesop. He was recruited for the organisation by colleague Henri Picciotto, cruciverbalist and co-author of the league's first cryptic crossword collection. Propp is the creator of the "Self-Referential Aptitude Test", a humorous multiple-choice test in which all questions except the last make

self-reference Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields. In natural or formal languages, self-reference ...

s to their own answers. It was created in the early 1990s for a puzzlers' party. Propp is the author of ''Tuscanini'', a 1992 children's book about a musical elephant, illustrated by Ellen Weiss.

Awards and honours

In 2015 he was elected as a

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

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, ...

"for contributions to combinatorics and probability, and for mentoring and exposition."

Personal

He is married to research psychologist Alexandra (Sandi) Gubin. They have a son Adam and a daughter Eliana.Propp's page at UMass Lowell
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Notes

External links

Propp's website
* {{DEFAULTSORT:Propp, Jim Year of birth missing (living people) Living people Harvard University alumni University of California, Berkeley alumni University of Wisconsin–Madison faculty Massachusetts Institute of Technology faculty Harvard University Department of Mathematics faculty Alumni of the University of Cambridge Recreational mathematicians American probability theorists 20th-century American mathematicians 21st-century American mathematicians Fellows of the American Mathematical Society University of Massachusetts Lowell faculty