James Gary Propp is a professor of

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 ...

at the

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

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 Compet ...

(USAMO), and an alumnus of the

Hampshire College Summer Studies in Mathematics Hampshire (, ; abbreviated to Hants) is a ceremonial and non-metropolitan county in western South East England on the coast of the English Channel. Home to two major English cities on its south coast, Southampton and Portsmouth, Hampshire is ...

. Propp obtained his AB in mathematics in 1982 at

Harvard 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 ...

. After advanced study at

Cambridge Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...

, 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. Established in 1868 as the University of California, it is the state's first land-grant univ ...

. He has held professorships at seven universities, including

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the mo ...

, the

University of Wisconsin A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...

, 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 among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

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

and

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

, 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, college, and high school teachers; graduate and undergraduate students; pure a ...

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

Boston Boston (), officially the City of Boston, is the state capital and most populous city of the Commonwealth of Massachusetts, as well as the cultural and financial center of the New England region of the United States. It is the 24th- mo ...

and later in

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

. In 1996, Propp and David Wilson invented

coupling from the past Among Markov chain Monte Carlo (MCMC) algorithms, coupling from the past is a method for sampling from the stationary distribution of a Markov chain. Contrary to many MCMC algorithms, coupling from the past gives in principle a perfect sample from ...

, a method for sampling from the

stationary distribution Stationary distribution may refer to: * 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. Assum ...

of a

Markov chain A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...

among

Markov chain Monte Carlo In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain ...

(MCMC)

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

. 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 number In mathematics, the surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals s ...

s in

; the solution to the counting of alternating sign matrices; and

occurrences of Grandi's series This article lists occurrences of the paradoxical infinite "sum" +1 -1 +1 -1 ... , sometimes called Grandi's series. Parables Guido Grandi illustrated the series with a parable involving two brothers who share a gem. Thomson's lamp is a supert ...

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 ...

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 disti ...

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

Other contributions

Propp was a member of the

National Puzzlers' League The National Puzzlers' League (NPL) is a nonprofit organization focused on puzzle, puzzling, primarily in the realm of word play and word games. Founded in 1883, it is the oldest puzzlers' organization in the world. It originally hosted semiannual c ...

under the

nom NOM may refer to: * National Organization for Marriage * Natural organic matter * New Order Mormons * Nickelodeon Original Movies * ''Nintendo Official Magazine'', official British Nintendo magazine; now discontinued, superseded by ''Official Ni ...

Aesop. He was recruited for the organisation by colleague Henri Picciotto,

cruciverbalist A crossword is a word puzzle that usually takes the form of a square or a rectangular grid of white- and black-shaded squares. The goal is to fill the white squares with letters, forming words or phrases, by solving clues which lead to the ans ...

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 occurs in natural or formal languages when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding. In philoso ...

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 concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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 faculty Alumni of the University of Cambridge Recreational mathematicians Probability theorists 20th-century American mathematicians 21st-century American mathematicians Fellows of the American Mathematical Society