Herbert Busemann
Encyclopedia
Herbert Busemann was a German-American mathematician
specializing in convex
and differential geometry. He is the author of Busemann's theorem
in Euclidean geometry
and geometric tomography
. He was a member of the Royal Danish Academy
and a winner of the Lobachevsky Medal
(1985), the first American mathematician to receive it. He was also a Fulbright scholar in New Zealand
in 1952.
to a well-to-do family. His father was one of the directors of Krupp
, where Busemann also worked for several years. He studied at University of Munich, Paris
, and Rome. He defended his dissertation in University of Göttingen in 1931, where his advisor was Richard Courant
. He remained in Göttingen
as an assistant until 1933, when he escaped Nazi Germany
to Copenhagen
(he had a Jewish grandfather
). He worked at the University of Copenhagen
until 1936, when he left to the United States
. There, he got married in 1939 and naturalized in 1943. He had temporary positions at the Institute of Advanced Studies, Johns Hopkins University
, Illinois Institute of Technology
, Smith College
, and eventually became a professor in 1947 at University of Southern California
. He advanced to a distinguished professor in 1964, and continued working at USC until his retirement in 1970. Over the course of his work at USC, he supervised over 10 Ph.D. students.
He is the author of six monographs, two of which were translated into Russian. According to the Los Angeles Times
, the Lobachevsky Medal
he received in 1985, was honored with 2,000 roubles for his "innovative book" titled The geometry of geodesics (Academic Press, 1959).
Busemann was also an active mathematical citizen. At different times, he was the president of the California
chapter of Mathematical Association of America
, and a member of the council of the American Mathematical Society
.
Busemann was also an accomplished linguist; he was able to read and speak in French
, German
, Spanish
, Italian
, Russian
, and Danish
. He could also read Arabic
, Latin
, Greek
and Swedish
. He translated a number of papers and monograph, most notably from Russian
, a rare language at the time. He also painted and had several public exhibitions. He died in Santa Ynez, California
on February 3, 1994, at the age of 88.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
specializing in convex
Convex geometry
Convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming,...
and differential geometry. He is the author of Busemann's theorem
Busemann's theorem
In mathematics, Busemann's theorem is a theorem in Euclidean geometry and geometric tomography. It was first proved by Herbert Busemann in 1949 and was motivated by his theory of area in Finsler spaces.-Statement of the theorem:...
in Euclidean geometry
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
and geometric tomography
Tomography
Tomography refers to imaging by sections or sectioning, through the use of any kind of penetrating wave. A device used in tomography is called a tomograph, while the image produced is a tomogram. The method is used in radiology, archaeology, biology, geophysics, oceanography, materials science,...
. He was a member of the Royal Danish Academy
Royal Danish Academy of Sciences and Letters
Royal Danish Academy of Sciences and Letters is a Danish non-governmental science Academy, founded 13 November 1742 by permission of the King Christian VI, as a historical Collegium Antiquitatum...
and a winner of the Lobachevsky Medal
Lobachevsky Medal
The Lobachevsky Prize, awarded by the Russian Academy of Sciences, and the Lobachevsky Medal, awarded by the Kazan State University, are mathematical awards in honor of Nikolai Ivanovich Lobachevsky.-History:...
(1985), the first American mathematician to receive it. He was also a Fulbright scholar in New Zealand
New Zealand
New Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...
in 1952.
Biography
Herbert Busemann was born in BerlinBerlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
to a well-to-do family. His father was one of the directors of Krupp
Krupp
The Krupp family , a prominent 400-year-old German dynasty from Essen, have become famous for their steel production and for their manufacture of ammunition and armaments. The family business, known as Friedrich Krupp AG Hoesch-Krupp, was the largest company in Europe at the beginning of the 20th...
, where Busemann also worked for several years. He studied at University of Munich, Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
, and Rome. He defended his dissertation in University of Göttingen in 1931, where his advisor was Richard Courant
Richard Courant
Richard Courant was a German American mathematician.- Life :Courant was born in Lublinitz in the German Empire's Prussian Province of Silesia. During his youth, his parents had to move quite often, to Glatz, Breslau, and in 1905 to Berlin. He stayed in Breslau and entered the university there...
. He remained in Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
as an assistant until 1933, when he escaped Nazi Germany
Nazi Germany
Nazi Germany , also known as the Third Reich , but officially called German Reich from 1933 to 1943 and Greater German Reich from 26 June 1943 onward, is the name commonly used to refer to the state of Germany from 1933 to 1945, when it was a totalitarian dictatorship ruled by...
to Copenhagen
Copenhagen
Copenhagen is the capital and largest city of Denmark, with an urban population of 1,199,224 and a metropolitan population of 1,930,260 . With the completion of the transnational Øresund Bridge in 2000, Copenhagen has become the centre of the increasingly integrating Øresund Region...
(he had a Jewish grandfather
Nuremberg Laws
The Nuremberg Laws of 1935 were antisemitic laws in Nazi Germany introduced at the annual Nuremberg Rally of the Nazi Party. After the takeover of power in 1933 by Hitler, Nazism became an official ideology incorporating scientific racism and antisemitism...
). He worked at the University of Copenhagen
University of Copenhagen
The University of Copenhagen is the oldest and largest university and research institution in Denmark. Founded in 1479, it has more than 37,000 students, the majority of whom are female , and more than 7,000 employees. The university has several campuses located in and around Copenhagen, with the...
until 1936, when he left to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
. There, he got married in 1939 and naturalized in 1943. He had temporary positions at the Institute of Advanced Studies, Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
, Illinois Institute of Technology
Illinois Institute of Technology
Illinois Institute of Technology, commonly called Illinois Tech or IIT, is a private Ph.D.-granting university located in Chicago, Illinois, with programs in engineering, science, psychology, architecture, business, communications, industrial technology, information technology, design, and law...
, Smith College
Smith College
Smith College is a private, independent women's liberal arts college located in Northampton, Massachusetts. It is the largest member of the Seven Sisters...
, and eventually became a professor in 1947 at University of Southern California
University of Southern California
The University of Southern California is a private, not-for-profit, nonsectarian, research university located in Los Angeles, California, United States. USC was founded in 1880, making it California's oldest private research university...
. He advanced to a distinguished professor in 1964, and continued working at USC until his retirement in 1970. Over the course of his work at USC, he supervised over 10 Ph.D. students.
He is the author of six monographs, two of which were translated into Russian. According to the Los Angeles Times
Los Angeles Times
The Los Angeles Times is a daily newspaper published in Los Angeles, California, since 1881. It was the second-largest metropolitan newspaper in circulation in the United States in 2008 and the fourth most widely distributed newspaper in the country....
, the Lobachevsky Medal
Lobachevsky Medal
The Lobachevsky Prize, awarded by the Russian Academy of Sciences, and the Lobachevsky Medal, awarded by the Kazan State University, are mathematical awards in honor of Nikolai Ivanovich Lobachevsky.-History:...
he received in 1985, was honored with 2,000 roubles for his "innovative book" titled The geometry of geodesics (Academic Press, 1959).
Busemann was also an active mathematical citizen. At different times, he was the president of the California
California
California is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...
chapter of Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America 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 and applied mathematicians; computer scientists;...
, and a member of the council of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
.
Busemann was also an accomplished linguist; he was able to read and speak in French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
, German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
, Spanish
Spanish language
Spanish , also known as Castilian , is a Romance language in the Ibero-Romance group that evolved from several languages and dialects in central-northern Iberia around the 9th century and gradually spread with the expansion of the Kingdom of Castile into central and southern Iberia during the...
, Italian
Italian language
Italian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
, Russian
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
, and Danish
Danish language
Danish is a North Germanic language spoken by around six million people, principally in the country of Denmark. It is also spoken by 50,000 Germans of Danish ethnicity in the northern parts of Schleswig-Holstein, Germany, where it holds the status of minority language...
. He could also read Arabic
Arabic language
Arabic is a name applied to the descendants of the Classical Arabic language of the 6th century AD, used most prominently in the Quran, the Islamic Holy Book...
, Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
, Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
and Swedish
Swedish language
Swedish is a North Germanic language, spoken by approximately 10 million people, predominantly in Sweden and parts of Finland, especially along its coast and on the Åland islands. It is largely mutually intelligible with Norwegian and Danish...
. He translated a number of papers and monograph, most notably from Russian
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
, a rare language at the time. He also painted and had several public exhibitions. He died in Santa Ynez, California
Santa Ynez, California
Santa Ynez is a census-designated place in Santa Barbara County, California, United States. The town of Santa Ynez is one of the communities that make up the Santa Ynez Valley, and features the Santa Ynez Airport for general aviation with a paved 2804 x 75 foot runway. The population was 4,418...
on February 3, 1994, at the age of 88.
See also
- Busemann function
- Busemann–Petty problemBusemann–Petty problemIn the mathematical field of convex geometry, the Busemann–Petty problem, introduced by , asks whether it is true that a symmetric convex body with larger central hyperplane sections has larger volume...
Books
- Introduction to algebraic manifolds, Princeton University Press, 1939.
- with Paul J. Kelly: Projective geometry and projective metrics, Academic Press, 1953, Dover 2006.
- Convex Surfaces, Interscience 1958, Dover, 2008.
- Geometry of Geodesics, Academic Press 1955, Dover, 2005.
- Metric methods in Finsler spaces and in the foundations of geometry, Princeton University Press, Oxford University Press, 1942.
- with Bhalchandra Phadke: Spaces with distinguished geodesics, Dekker, 1987.
- Recent synthetic differential geometry, Springer 1970.
External links
- Herbert Busemann's biography (in SpanishSpanish languageSpanish , also known as Castilian , is a Romance language in the Ibero-Romance group that evolved from several languages and dialects in central-northern Iberia around the 9th century and gradually spread with the expansion of the Kingdom of Castile into central and southern Iberia during the...
).