Elias Menachem Stein (January 13, 1931 – December 23, 2018) was an American mathematician who was a leading figure in the field of

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...

. He was the

Albert Baldwin Dod Albert Baldwin Dod (March 24, 1805 – November 20, 1845) was an American Presbyterian theologian and professor of mathematics. Early life Dod was born on March 24, 1805 in Mendham, New Jersey. He was the son of Daniel Dod (1778–1823) and Nanc ...

Professor of Mathematics, Emeritus, at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

, where he was a faculty member from 1963 until his death in 2018.

Biography

Stein was born in Antwerp Belgium, to Elkan Stein and Chana Goldman,

Ashkenazi Jews Ashkenazi Jews ( ; he, יְהוּדֵי אַשְׁכְּנַז, translit=Yehudei Ashkenaz, ; yi, אַשכּנזישע ייִדן, Ashkenazishe Yidn), also known as Ashkenazic Jews or ''Ashkenazim'',, Ashkenazi Hebrew pronunciation: , singu ...

from Belgium.University of St Andrews, Scotland - School of Mathematics and Statistics: "Elias Menachem Stein" by J.J. O'Connor and E F Robertson
February 2010 After the German invasion in 1940, the Stein family fled to the United States, first arriving in New York City. He graduated from

Stuyvesant High School Stuyvesant High School (pronounced ), commonly referred to among its students as Stuy (pronounced ), is a State school, public university-preparatory school, college-preparatory, Specialized high schools in New York City, specialized high school ...

in 1949, where he was classmates with future

Fields Medalist The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

Paul Cohen Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician. He is best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was award ...

, before moving on to 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 ...

for college. In 1955, Stein earned a Ph.D. from the

under the direction of

Antoni Zygmund Antoni Zygmund (December 25, 1900 – May 30, 1992) was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. ...

. He began teaching at

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 m ...

in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton. Stein worked primarily in the field of

, and made contributions in both extending and clarifying Calderón–Zygmund theory. These include ''Stein interpolation'' (a variable-parameter version of complex interpolation), the ''Stein maximal principle'' (showing that under many circumstances,

almost everywhere convergence In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared. Definition Suppose that X is a set and ...

is equivalent to the boundedness of a

maximal function Maximal functions appear in many forms in harmonic analysis (an area of mathematics). One of the most important of these is the Hardy–Littlewood maximal function. They play an important role in understanding, for example, the differentiability p ...

), '' Stein complementary series representations'', ''Nikishin–Pisier–Stein factorization'' in operator theory, the ''Tomas–Stein restriction theorem'' in

Fourier analysis In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Josep ...

, the ''Kunze–Stein phenomenon'' in

convolution In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is ...

semisimple group In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group ''G'' over a perfect field is reductive if it has a representation with finite kernel which is a direct ...

s, the

Cotlar–Stein lemma In mathematics, in the field of functional analysis, the Cotlar–Stein almost orthogonality lemma is named after mathematicians Mischa Cotlar and Elias Stein. It may be used to obtain information on the operator norm on an operator, acting from o ...

concerning the sum of almost orthogonal operators, and the Fefferman–Stein theory of the

Hardy space In complex analysis, the Hardy spaces (or Hardy classes) ''Hp'' are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . ...

H^1

and the space

BMO

of functions of bounded mean oscillation. He wrote numerous books on harmonic analysis (see e.g. ,3,5, which are often cited as the standard references on the subject. His ''

Princeton Lectures in Analysis The ''Princeton Lectures in Analysis'' is a series of four mathematics textbooks, each covering a different area of mathematical analysis. They were written by Elias M. Stein and Rami Shakarchi and published by Princeton University Press between ...

'' series ,7,8,9were penned for his sequence of undergraduate courses on analysis at Princeton. Stein was also noted as having trained a high number of graduate students (he has had at least 52 students, according to the

Mathematics Genealogy Project The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. By 31 December 2021, it contained information on 274,575 mathematical scientists who contributed to research-level mathematics. For a ty ...

), so shaping modern Fourier analysis. They include two

Fields medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

ists,

Charles Fefferman Charles Louis Fefferman (born April 18, 1949) is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. He was awarded the Fields Medal in 1978 for his contrib ...

and

Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes ...

. His honors included the

Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have ...

(1984 and 2002), the

Schock Prize The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm, Sweden, in 1993 and, since 2005, are awarded every three years. Each recipient current ...

in Mathematics (1993), the

Wolf Prize in Mathematics The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. ...

(1999), and the

National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...

(2001). In addition, he had fellowships to

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National I ...

Sloan Foundation The Alfred P. Sloan Foundation is an American philanthropic nonprofit organization. It was established in 1934 by Alfred P. Sloan Jr., then-president and chief executive officer of General Motors. The Sloan Foundation makes grants to support or ...

, Guggenheim Foundation, and

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 ...

. Stein was elected as a member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

in 1982. In 2005, Stein was awarded the Stefan Bergman prize in recognition of his contributions in real, complex, and harmonic analysis. 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, ...

Personal life

In 1959, he married Elly Intrator, a former

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

refugee during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

. They had two children, Karen Stein and

Jeremy C. Stein Jeremy Chaim Stein (born October 17, 1960) is an American macroeconomist and the Moise Y. Safra Professor of Economics at Harvard University; he also chaired Harvard's economics department. He served as a member of the Federal Reserve Board of Go ...

, and grandchildren named Alison, Jason, and Carolyn. His son Jeremy is a professor of financial economics at Harvard, former adviser to

Tim Geithner Timothy Franz Geithner (; born August 18, 1961) is a former American central banker who served as the 75th United States Secretary of the Treasury under President Barack Obama from 2009 to 2013. He was the President of the Federal Reserve Bank o ...

and

Lawrence Summers Lawrence Henry Summers (born November 30, 1954) is an American economist who served as the 71st United States secretary of the treasury from 1999 to 2001 and as director of the National Economic Council from 2009 to 2010. He also served as pre ...

, and served on the

Federal Reserve Board of Governors The Board of Governors of the Federal Reserve System, commonly known as the Federal Reserve Board, is the main governing body of the Federal Reserve System. It is charged with overseeing the Federal Reserve Banks and with helping implement the mon ...

from 2012 to 2014. Elias Stein died of complications of

lymphoma Lymphoma is a group of blood and lymph tumors that develop from lymphocytes (a type of white blood cell). In current usage the name usually refers to just the cancerous versions rather than all such tumours. Signs and symptoms may include enlar ...

in 2018, aged 87.

Bibliography

* * * * * *
2011 reprint

2010 reprint

2009 reprint
*

Notes

References

External links

*
Citation for Elias Stein for the 2002 Steele prize for lifetime achievement

Elias Stein Curriculum Vitae
* * – Extended video interview. {{DEFAULTSORT:Stein, Elias M. 1931 births 2018 deaths 20th-century American mathematicians 21st-century American mathematicians American people of Belgian-Jewish descent Belgian emigrants to the United States Belgian Jews Fellows of the American Mathematical Society Harmonic analysis Jewish American scientists Mathematicians from New York (state) Mathematical analysts Members of the United States National Academy of Sciences National Medal of Science laureates Princeton University faculty Rolf Schock Prize laureates Stuyvesant High School alumni University of Chicago alumni Wolf Prize in Mathematics laureates