David Eugene Muller (November 2, 1924 – April 27, 2008) was an American
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, structure, space, models, and change.
History
On ...
and
computer scientist. He was a professor of mathematics and computer science at the
University of Illinois
The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univer ...
(1953–92), after which he became an emeritus professor, and was an adjunct professor of mathematics at the
New Mexico State University
New Mexico State University (NMSU or NM State) is a public land-grant research university based primarily in Las Cruces, New Mexico. Founded in 1888, it is the oldest public institution of higher education in New Mexico and one of the state's ...
(1995–2008). Muller received his BS in 1947 and his PhD in 1951 in physics from
Caltech
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 ...
; an honorary PhD was conferred by the
University of Paris
, image_name = Coat of arms of the University of Paris.svg
, image_size = 150px
, caption = Coat of Arms
, latin_name = Universitas magistrorum et scholarium Parisiensis
, motto = ''Hic et ubique terrarum'' (Latin)
, mottoeng = Here and a ...
in 1989. He was the inventor of the
Muller C-element (or Muller C-gate), a device used to implement
asynchronous circuit
Asynchronous circuit (clockless or self-timed circuit) is a sequential digital logic circuit that does not use a global clock circuit or signal generator to synchronize its components. Instead, the components are driven by a handshaking circui ...
ry in electronic computers. He also co-invented the
Reed–Muller codes. He discovered the codes, and
Irving S. Reed proposed the majority logic decoding for the first time. Furthermore, he invented
Muller automata, an automaton model for
infinite words. In
geometric group theory
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such group (mathematics), groups and topology, topological and geometry, geometric pro ...
Muller is known for the
Muller–Schupp theorem, joint with
Paul Schupp, characterizing
finitely generated virtually
In mathematics, especially in the area of abstract algebra that studies infinite groups, the adverb virtually is used to modify a property so that it need only hold for a subgroup of finite index. Given a property P, the group ''G'' is said to b ...
free group
In mathematics, the free group ''F'S'' over a given set ''S'' consists of all words that can be built from members of ''S'', considering two words to be different unless their equality follows from the group axioms (e.g. ''st'' = ''suu''−1' ...
s as finitely generated groups with
context-free word problem.
[David E. Muller, and Paul E. Schupp]
''Groups, the theory of ends, and context-free languages''.
Journal of Computer and System Sciences 26 (1983), no. 3, 295--310
Family
David E. Muller was the son of
Hermann Joseph Muller and
Jessie Jacobs Muller Offermann (formerly Jesse Marie Jacobs). He was born in
Austin,
Texas
Texas (, ; Spanish: ''Texas'', ''Tejas'') is a state in the South Central region of the United States. At 268,596 square miles (695,662 km2), and with more than 29.1 million residents in 2020, it is the second-largest U.S. state by ...
, when his parents taught at
The University of Texas
The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...
. His mother was one of the first women to receive a Ph.D. in mathematics in the United States, and he credited her with inspiring his early interest in mathematics.
[ See p.260–262. Biography on p.470-472 of th]
Supplementary Material
a
AMS
/ref> She lost her position as an instructor in pure mathematics at Texas because she became pregnant, and according to Hermann Joseph Muller's biographer, "her colleagues felt that a mother could not give full attention to classroom duties and remain a good mother."[Elof Carlson, ''Genes, Radiation, and Society'', Cornell University Press, 1982, 133.] As a child he was with his parents in Berlin
Berlin ( , ) is the capital and List of cities in Germany by population, largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's List of cities in the European Union by population within ci ...
and Leningrad
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...
in 1933–34. His family was dissolved in the Soviet Union
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
. He returned to Austin with his mother in July 1934. His mother obtained a divorce in Texas in the summer of 1935. Sometime between October 1935 and January 1936, Jessie Muller married Carlos Alberto Offermann, who had been working in Muller's laboratory and was on a visit to Austin from the Soviet Union at that time. Hermann Joseph Muller left the Soviet Union in 1937 after the start of Stalin's political persecutions. After a brief stay in Madrid
Madrid ( , ) is the capital and most populous city of Spain. The city has almost 3.4 million inhabitants and a Madrid metropolitan area, metropolitan area population of approximately 6.7 million. It is the Largest cities of the Europ ...
and Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...
, in September 1937, Hermann moved to Edinburgh
Edinburgh ( ; gd, Dùn Èideann ) is the capital city of Scotland and one of its 32 council areas. Historically part of the county of Midlothian (interchangeably Edinburghshire before 1921), it is located in Lothian on the southern shore of t ...
, where he married Dorothea Kantorowicz in May 1939. They had a daughter, Helen Juliette. Hermann Joseph Muller received the Nobel Prize in Physiology or Medicine
The Nobel Prize in Physiology or Medicine is awarded yearly by the Nobel Assembly at the Karolinska Institute for outstanding discoveries in physiology or medicine. The Nobel Prize is not a single prize, but five separate prizes that, accord ...
in 1946.
David E. Muller died in 2008 in Las Cruces, New Mexico
)
, population_demonym = New Mexican ( es, Neomexicano, Neomejicano, Nuevo Mexicano)
, seat = Santa Fe
, LargestCity = Albuquerque
, LargestMetro = Tiguex
, OfficialLang = None
, Languages = English, Spanish ( New Mexican), Navajo, Ke ...
. He is survived by his children, Chandra L. Muller and Kenneth J. Muller. His half-sister
Helen J. Muller
is a professor emerita at the University of New Mexico
The University of New Mexico (UNM; es, Universidad de Nuevo México) is a public research university in Albuquerque, New Mexico. Founded in 1889, it is the state's flagship academic institution and the largest by enrollment, with over 25,400 ...
. He was predeceased by his wife Alice Mimi Muller, who died in Urbana, Illinois, in 1989, and divorced (posthumously) in 2009 from his second wife, Denise Impens Muller, in Las Cruces, New Mexico.
See also
* Muller C-element
*Reed–Muller code
Reed–Muller codes are error-correcting codes that are used in wireless communications applications, particularly in deep-space communication. Moreover, the proposed 5G standard relies on the closely related polar codes for error correction in ...
*Reed–Muller expansion
In Boolean logic, a Reed–Muller expansion (or Davio expansion) is a decomposition of a Boolean function.
For a Boolean function f(x_1,\ldots,x_n) : \mathbb^n \to \mathbb we call
:
\begin
f_(x) & = f(x_1,\ldots,x_,1,x_,\ldots,x_n) \\
f_(x)& = ...
*Muller's method
Muller's method is a root-finding algorithm, a numerical method for solving equations of the form ''f''(''x'') = 0. It was first presented by David E. Muller in 1956.
Muller's method is based on the secant method, which constructs at every itera ...
(an established root finding method in numerical analysis)
*Muller automaton In automata theory, a Muller automaton is a type of an ω-automaton.
The acceptance condition separates a Muller automaton from other ω-automata.
The Muller automaton is defined using a Muller acceptance condition, i.e. the set of all states visi ...
References
{{DEFAULTSORT:Muller, David E.
1924 births
2008 deaths
20th-century American engineers
20th-century American mathematicians
21st-century American mathematicians
American people of British-Jewish descent
Coding theorists
Logic gates
New Mexico State University faculty
University of Illinois faculty