Helmut Ulm (born 21 June 1908 in

Gelsenkirchen Gelsenkirchen (, , ; ) is the List of cities in Germany by population, 25th-most populous city of Germany and the 11th-most populous in the state of North Rhine-Westphalia with 262,528 (2016) inhabitants. On the Emscher, Emscher River (a tribu ...

; died 13 June 1975) was a

German German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who established the classification of

countable In mathematics, a Set (mathematics), set is countable if either it is finite set, finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function fro ...

periodic Periodicity or periodic may refer to: Mathematics * Bott periodicity theorem, addresses Bott periodicity: a modulo-8 recurrence relation in the homotopy groups of classical groups * Periodic function, a function whose output contains values tha ...

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 commu ...

s by means of their Ulm invariants.

Career

Helmut Ulm's father was an elementary school teacher in

Elberfeld Elberfeld is a municipal subdivision of the Germany, German city of Wuppertal; it was an independent town until 1929. History The first official mentioning of the geographic area on the banks of today's Wupper River as "''elverfelde''" was ...

. After finishing high school in

Wuppertal Wuppertal (; ) is a city in North Rhine-Westphalia, in western Germany, with a population of 355,000. Wuppertal is the seventh-largest city in North Rhine-Westphalia and List of cities in Germany by population, 17th-largest in Germany. It ...

in 1926, he attended the universities of

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

(1926–1927),

Jena Jena (; ) is a List of cities and towns in Germany, city in Germany and the second largest city in Thuringia. Together with the nearby cities of Erfurt and Weimar, it forms the central metropolitan area of Thuringia with approximately 500,000 in ...

(1927) and

Bonn Bonn () is a federal city in the German state of North Rhine-Westphalia, located on the banks of the Rhine. With a population exceeding 300,000, it lies about south-southeast of Cologne, in the southernmost part of the Rhine-Ruhr region. This ...

(1927–1930), where he studied mathematics and physics, attending the lectures of

Richard Courant Richard Courant (January 8, 1888 – January 27, 1972) was a German-American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real ...

Erich Bessel-Hagen Erich Bessel-Hagen (12 September 1898 in Charlottenburg – 29 March 1946 in Bonn) was a German mathematician and a historian of mathematics. Erich Paul Werner Bessel-Hagen was born in 1898 in Charlottenburg, a suburb, later a district in Berlin. ...

Felix Hausdorff Felix Hausdorff ( , ; November 8, 1868 – January 26, 1942) was a German mathematician, pseudonym Paul Mongré (''à mogré' (Fr.) = "according to my taste"), who is considered to be one of the founders of modern topology and who contributed sig ...

, and the joint Hausdorff–

Otto Toeplitz Otto Toeplitz (1 August 1881 – 15 February 1940) was a German mathematician working in functional analysis., reprinted in Life and work Toeplitz was born to a Jewish family of mathematicians. Both his father and grandfather were ''Gymnasiu ...

seminar. He graduated

summa cum laude Latin honors are a system of Latin phrases used in some colleges and universities to indicate the level of distinction with which an academic degree has been earned. The system is primarily used in the United States. It is also used in some Sout ...

in 1930 with a thesis about countable periodic abelian groups (1933). In 1933–1935 he was an assistant in Göttingen and worked with

Wilhelm Magnus Hans Heinrich Wilhelm Magnus, known as Wilhelm Magnus (5 February 1907 in Berlin, Germany – 15 October 1990 in New Rochelle, New York), was a German-American mathematician. He made important contributions in combinatorial group theory, Lie algeb ...

and

Olga Taussky-Todd Olga Taussky-Todd (August 30, 1906 – October 7, 1995) was an Austrian and later Czech Americans, Czech-American mathematician. She published more than 300 research papers on algebraic number theory, integral matrices, and Matrix (mathematics), ...

editing

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

's ''Collected Works''. His

Habilitationsschrift Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

developed a generalization of the elementary divisor theory to infinite matrices, continuing ideas of Ulm's teacher Toeplitz. It was submitted in Münster in 1936 and refereed by Heinrich Behnke, Gottfried Köthe, F. K. Schmidt, and

B. L. van der Waerden Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amster ...

. Ulm's promotion was delayed, apparently, due to his anti-

Nazi Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During H ...

views. From 1935 until his retirement in 1974 Ulm worked at the

University of Münster The University of Münster (, until 2023 , WWU) is a public research university located in the city of Münster, North Rhine-Westphalia in Germany. With more than 43,000 students and over 120 fields of study in 15 departments, it is Germany's ...

, as an assistant, docent, and eventually professor (1968). Besides his three important papers on the classification of infinite abelian groups, Ulm published only a few notes in the proceedings of the Münster mathematical seminar, one of which dealt with solution of systems of linear equations by a computer. He suffered from poor health. During the

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

, Ulm worked as a

cryptographer Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More gen ...

Pers Z S The Pers Z S was the signals intelligence agency of the German Foreign Office () before and during World War II. It consisted of two cryptologic sections. Pers Z S was the cryptanalytic section which was called ''Special Service of Z Branch of th ...

starting in August 1941 on a part-time basis from Thursday through to Saturday and on Monday through Wednesday at Münster. After the war he mostly taught courses in applied mathematics and supervised several Ph.D. theses; those of G. Tillmann (1952) and G. Roth (1961) were close to his old work on infinite-dimensional linear algebra and infinite groups.

Bibliography

* Helmut Ulm, ''Zur Theorie der abzählbar-unendlichen Abelschen Gruppen''. Math. Ann. 107, 774–803 (1933) * Helmut Ulm, ''Zur Theorie der nicht-abzählbaren primären abelschen Gruppen''. Math. Z. 40, 205–207 (1935) * Helmut Ulm, ''Elementarteilertheorie unendlicher Matrizen''. Math. Ann. 114, 493–505 (1937)

References

* Göbel, R., ''Helmut Ulm: his work and its impact on recent mathematics''. Abelian group theory (Perth, 1987), 1–10, Contemp. Math., 87, Amer. Math. Soc., Providence, RI, 1989 * Sanford Segal, ''Mathematicians under the Nazis''. Princeton University Press, 2003

External links

* 20th-century German mathematicians Group theorists 1975 deaths 1908 births {{Germany-mathematician-stub