Alfred Washington Hales (born November 30, 1938) is an American mathematician, a professor emeritus of mathematics at the

University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

, and one of the namesakes of the

Hales–Jewett theorem In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory named after Alfred W. Hales and Robert I. Jewett, concerning the degree to which high-dimensional objects must necessarily exhibit some combinatorial ...

. He was born in

Pasadena, California Pasadena ( ) is a city in Los Angeles County, California, northeast of downtown Los Angeles. It is the most populous city and the primary cultural center of the San Gabriel Valley. Old Pasadena is the city's original commercial district. I ...

, and is the older brother of R. Stanton Hales.

Professional career

As an undergraduate, Hales was a two-time

Putnam Fellow The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regard ...

for the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

, in 1958 and 1959. Hales stayed at Caltech for his graduate studies, earning his Ph.D. in 1962 under the supervision of

Robert P. Dilworth Robert Palmer Dilworth (December 2, 1914 – October 29, 1993) was an American mathematician. His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say ...

. He is the former chair of the mathematics department at UCLA, and in 2010 became chair of the board of trustees of the Institute for Pure and Applied Mathematics at UCLA.Al Hales Chairs IPAM Board of Trustees
IPAM News & Announcements
, July 15, 2010, retrieved 2013-01-21.

Contributions

In 1963, Hales and Jewett published the

, which is a standard part of

Ramsey theory Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a ...

now. They motivated their theorem as a form of

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 ...

: it shows that certain high-dimensional generalizations of

tic tac toe Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. T ...

cannot have any tied positions. Hales also contributed to Solomon W. Golomb's highly cited work on

shift register A shift register is a type of digital circuit using a cascade of flip-flops where the output of one flip-flop is connected to the input of the next. They share a single clock signal, which causes the data stored in the system to shift from one loc ...

s, and he has been noted for his work using Ulm invariants to characterize infinite

abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commut ...

Awards and honors

In 1971, Hales shared the

George Pólya Prize The Society for Industrial and Applied Mathematics (SIAM) has three prizes named after George Pólya: the George Pólya Prize for Mathematical Exposition, established in 2013; the George Pólya Prize in Applied Combinatorics, established in 1969 ...

with

Ronald Graham Ronald Lewis Graham (October 31, 1935July 6, 2020) was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He ...

, Klaus Leeb,

Bruce Lee Rothschild Bruce Lee Rothschild (born August 26, 1941) is an American mathematician and educator, specializing in combinatorial mathematics. He is a professor emeritus of mathematics at the University of California, Los Angeles. Early life and education Roth ...

, and R. I. Jewett, for their work in Ramsey theory. In 2009, Hales was elected a

Fellow of the AAAS Fellowship of the American Association for the Advancement of Science (FAAAS) is an honor accorded by the American Association for the Advancement of Science (AAAS) to distinguished persons who are members of the Association. Fellows are elected ...

,6 UCLA professors named fellows by American Association for the Advancement of Science
, Stuart Wolpert, UCLA, December 17, 2009, retrieved 2013-01-21. and in 2012 he became a 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, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-01-21.

Selected publications

References

{{DEFAULTSORT:Hales, Alfred W. Living people 20th-century American mathematicians 21st-century American mathematicians California Institute of Technology alumni University of California, Los Angeles faculty Putnam Fellows Fellows of the American Association for the Advancement of Science Fellows of the American Mathematical Society 1938 births People from Pasadena, California Mathematicians from California