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{{short description|German mathematician}}
{{short description|German mathematician}}
{{Infobox scientist
{{Infobox scientist
| name = Eberhard Hopf
| name = Eberhard Hopf
| image = Eberhard Hopf.jpg
| image = Eberhard Hopf.jpg
| image_size =
| image_size =
| caption =
| caption =
| birth_date = {{birth date|1902|4|17|df=y}}
| birth_date = {{birth date|1902|4|4|df=y}}
| birth_place = [[Salzburg]], [[Austria-Hungary]]
| birth_place = [[Salzburg]], [[Austria-Hungary]]
| death_date = {{death date and age|1983|7|24|1902|4|14|df=y}}
| death_date = {{death date and age|1983|7|24|1902|4|14|df=y}}
| death_place = [[Bloomington, Indiana]], United States
| death_place = [[Bloomington, Indiana]], United States
| nationality = [[Germany|German]]
| residence = Germany, United States
| nationality = [[Germany|German]]
| field = [[Mathematician]]
⚫
| work_institution = [[Massachusetts Institute of Technology|MIT]] (1931-36)<br>[[University of Leipzig]] (1936-42)<br/>[[University of Munich]] (1944-47)<br>[[Indiana University Bloomington|Indiana Univ. Bloomington]] (1949-83)
| field = [[Mathematician]]
⚫
| alma_mater = [[Technical University of Berlin|University of Berlin]]
⚫
| work_institution = [[Massachusetts Institute of Technology|MIT]] (1931-36)<br>[[University of Leipzig]] (1936-42)<br/>[[University of Munich]] (1944-47)<br>[[Indiana University Bloomington|Indiana Univ. Bloomington]] (1949-83)
⚫
| doctoral_advisor = [[Erhard Schmidt]]<br>[[Issai Schur]]
⚫
| alma_mater = [[Technical University of Berlin|University of Berlin]]
⚫
| doctoral_advisor = [[Erhard Schmidt]]<br>[[Issai Schur]]
| doctoral_students = [[Albert Schaeffer]]
| doctoral_students = [[Albert Schaeffer]]
| known_for = [[Ergodic theory]]<br>[[Partial differential equation]]<br>[[Differential geometry]]
| known_for = [[Bifurcation theory]]<br>[[Differential geometry]]<br>[[Ergodic theory]]<br>[[Partial differential equation]]<br>[[Hopf bifurcation]]<br>[[Hopf decomposition]]<br>[[Hopf lemma]]<br>[[Hopf maximum principle]]<br>[[Cole–Hopf transformation]]<br>{{no wrap|[[Landau–Hopf theory of turbulence]]}}<br>[[Wiener–Hopf method]]
| prizes = [[Leroy P. Steele Prize]] (1981)<br>[[Josiah Willard Gibbs Lectureship|Gibbs Lecture]] (1971)<br>[[List of International Congresses of Mathematicians Plenary and Invited Speakers|ICM speaker]] (1950)
| prizes =
}}
}}
'''Eberhard Frederich Ferdinand Hopf''' (April 17, 1902 in [[Salzburg]], [[Austria-Hungary]] – July 24, 1983 in [[Bloomington, Indiana]]) was a [[mathematician]] and [[astronomer]], one of the founding fathers of [[ergodic theory]] and a pioneer of [[bifurcation theory]] who also made significant contributions to the subjects of [[partial differential equation]]s and [[integral equation]]s, [[fluid dynamics]], and [[differential geometry]]. The [[Hopf maximum principle]] is an early result of his (1927) that is one of the most important techniques in the theory of [[elliptic partial differential equation]]s.
'''Eberhard Frederich Ferdinand Hopf''' (April 4, 1902 in [[Salzburg]], [[Austria-Hungary]] – July 24, 1983 in [[Bloomington, Indiana]], USA) was a German [[mathematician]] and [[astronomer]], one of the founding fathers of [[ergodic theory]] and a pioneer of [[bifurcation theory]] who also made significant contributions to the subjects of [[partial differential equation]]s and [[integral equation]]s, [[fluid dynamics]], and [[differential geometry]]. The [[Hopf maximum principle]] is an early result of his (1927) that is one of the most important techniques in the theory of [[elliptic partial differential equation]]s.


==Biography==
==Biography==
⚫
Hopf was born in Salzburg, Austria-Hungary, but his scientific career was divided between Germany and the United States. He received his Ph.D. in mathematics in 1926 and his ''[[Habilitation]]'' in mathematical astronomy from the [[Technical University of Berlin|University of Berlin]] in 1929.


⚫
In 1971, Hopf was the [[American Mathematical Society]] [[Josiah Willard Gibbs|Gibbs]] Lecturer.<ref>[https://www.ams.org/meetings/lectures/meet-gibbs-lect Josiah Willard Gibbs Lectures #42], AMS</ref> In 1981, he received the [[Leroy P. Steele Prize]] from the American Mathematical Society for seminal contributions to research.
⚫
Eberhard Hopf was born in [[Salzburg]], [[Austria-Hungary]], but his scientific career was divided between Germany and the United States. He received his Ph.D. in Mathematics in 1926 and his [[Habilitation]] in Mathematical Astronomy from the [[Technical University of Berlin|University of Berlin]] in 1929.


== Major publications ==
In 1930 he received a fellowship from the [[Rockefeller Foundation]] to study [[classical mechanics]] with [[George David Birkhoff|George Birkhoff]] at [[Harvard]], but his appointment was at the Harvard College Observatory. In late 1931, with the help of [[Norbert Wiener]], Hopf joined the Department of Mathematics of the [[Massachusetts Institute of Technology]], accepting the position of Assistant Professor. While at MIT, Hopf did much of his work on [[ergodic theory]].
{{refbegin}}
*{{cite journal|title=Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus|year=1927|jfm=53.0454.02|pages=147–152|language=de|journal=Sitzungsberichte der Preußischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse|last1=Hopf|first1=E.}}
*{{cite journal|title=Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen zweiter Ordnung|language=de|journal=[[Mathematische Zeitschrift]]|year=1932|volume=34|pages=194–233|zbl=0002.34003|doi=10.1007/BF01180586|url=https://eudml.org/doc/168309|jfm=57.0556.01|last1=Hopf|first1=Eberhard|s2cid=120040877 }}
*{{cite journal|mr=0001464|last1=Hopf|first1=Eberhard|title=Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung|language=de|journal=Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Physische Klasse|volume=91|year=1939|pages=261–304|jfm=65.1413.02|zbl=0024.08003}}
*{{cite journal|mr=0039141|last1=Hopf|first1=Eberhard|title=Abzweigung einer periodischen Lösung von einer stationären eines Differentialsystems|language=de|journal=Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Physische Klasse|volume=95|year=1943|issue=1|pages=3–22|zbl=0063.02065}}
*{{cite journal|mr=0030113|last1=Hopf|first1=Eberhard|zbl=0031.32901|title=A mathematical example displaying features of turbulence|journal=[[Communications on Pure and Applied Mathematics]]|volume=1|year=1948a|pages=303–322|issue=4|doi=10.1002/cpa.3160010401}}
*{{cite journal|mr=0023591|last1=Hopf|first1=Eberhard|zbl=0030.07901|title=Closed surfaces without conjugate points|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|volume=34|year=1948b|pages=47–51|issue=2|doi=10.1073/pnas.34.2.47|pmid=16588785 |pmc=1062913 |bibcode=1948PNAS...34...47H |doi-access=free}}
*{{cite journal|mr=0047234|last1=Hopf|first1=Eberhard|title=The partial differential equation {{math|''u''<sub>''t''</sub> + ''uu''<sub>''x''</sub> {{=}} μ''u''<sub>''xx''</sub>}}|zbl=0039.10403|journal=[[Communications on Pure and Applied Mathematics]]|volume=3|year=1950|pages=201–230|issue=3|doi=10.1002/cpa.3160030302}}
*{{cite journal|mr=0050423|last1=Hopf|first1=Eberhard|zbl=0042.10604|title=Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen|language=de|journal=[[Mathematische Nachrichten]]|volume=4|year=1951|pages=213–231|doi=10.1002/mana.3210040121|issue=1–6}}
*{{cite journal|mr=0050126|last1=Hopf|first1=Eberhard|title=A remark on linear elliptic differential equations of second order|zbl=0048.07802|journal=[[Proceedings of the American Mathematical Society]]|volume=3|year=1952a|pages=791–793|issue=5|doi=10.1090/S0002-9939-1952-0050126-X|doi-access=free}}
*{{cite journal|mr=0059119|last1=Hopf|first1=Eberhard|title=Statistical hydromechanics and functional calculus|journal=[[Indiana University Mathematics Journal|Journal of Rational Mechanics and Analysis]]|volume=1|year=1952b|pages=87–123|issue=1|doi=10.1512/iumj.1952.1.51004|zbl=0049.41704|doi-access=free}}
*{{cite journal|mr=0182790|last1=Hopf|first1=Eberhard|title=Generalized solutions of non-linear equations of first order|journal=[[Indiana University Mathematics Journal|Journal of Mathematics and Mechanics]]|volume=14|year=1965|pages=951–973|issue=6|jstor=24901315|zbl=0168.35101}}
A non-comprehensive selection of his work was published in 2002:
⚫
*{{Cite encyclopedia | editor1-last=Morawetz | editor1-first=Cathleen S. | editor2-last=Serrin | editor2-first=James B. | editor3-last=Sinai | editor3-first=Yakov G. | title=Selected works of Eberhard Hopf with commentaries | url=https://books.google.com/books?id=8TOqgRLbpaQC | publisher=[[American Mathematical Society]] | location=Providence, RI | isbn=978-0-8218-2077-3 | mr=1985954 | year=2002|zbl=1011.01017|editor-link1=Cathleen Morawetz|editor-link2=James Serrin|editor-link3=Yakov Sinai|series=Collected Works|volume=17|s2cid=117548743}}
{{refend}}


⚫
==Notes==
In Cambridge Hopf worked on many mathematical and astronomical subjects. His paper ''On the Time Average Theorem in Dynamics'',<ref>{{cite web|last1=Hopf|first1=Eberhard|title=On the Time Average Theorem in Dynamics|url=http://www.pnas.org/content/18/1/93.full.pdf}}</ref> which appeared in the [[Proceedings of the National Academy of Sciences]], is considered by many to be the first readable paper in modern ergodic theory. His book ''Mathematical problems of radiative equilibrium'' first appeared in 1934 and was reprinted in 1964. Another important contribution from this period is the theory of [[Wiener-Hopf equation]]s, which he developed in collaboration with Norbert Wiener. By 1960, a discrete version of these equations was being extensively used in electrical engineering and geophysics, their use continuing until the present day. During this time, Hopf gained a reputation for his ability of illuminating the most complex subjects for his colleagues and even for non-specialists. Because of this talent, many discoveries and proofs of other mathematicians became easier to understand after they had been described by Hopf.
⚫
{{reflist}}
In 1936 Hopf received and accepted an offer of a full professorship from the [[University of Leipzig]]. Hopf, with his wife Ilse and their infant daughter Barbara, returned to Germany, which by this time was under the control of the [[Nazi Party]].

The book ''Ergodentheorie'', most of which was written when Hopf was still at the Massachusetts Institute of Technology, was published in 1937. In that book, containing only 81 pages, Hopf presented a precise and elegant summary of ergodic theory. In 1939 Hopf established ergodicity of the [[geodesic flow]] on [[compact space|compact]] [[hyperbolic manifold|manifolds of constant negative curvature]]. In 1940 Hopf was on the list of the invited lecturers to the [[International Congress of Mathematicians]] to be held in [[Cambridge, Massachusetts]]. Because of the start of [[World War II]], however, the Congress was cancelled.

In 1942 Hopf was drafted to work in the German Aeronautical Institute. In 1944, one year before the end of World War II, Hopf was appointed to a professorship at the [[University of Munich]].
On 22 February 1949 Hopf became a US citizen and joined [[Indiana University (Bloomington)|Indiana University at Bloomington]] as a Professor of Mathematics. In 1962 he was made Research Professor of Mathematics, staying in that position until his death.

Hopf was never forgiven by many people for his moving to Germany in 1936, where the Nazi party was in power. As a result, most of his work in ergodic theory and topology was neglected or even attributed to others in the years following the end of World War II.{{Citation needed|date=August 2018}} An example of this was the expulsion of Hopf's name from the discrete version of the [[Wiener–Hopf equations]], which were frequently referred to as "[[Wiener filter]]".

==Awards and honors==
⚫
In 1971 Hopf was the [[American Mathematical Society]] [[Josiah Willard Gibbs|Gibbs]] Lecturer.<ref>[http://www.ams.org/meetings/lectures/meet-gibbs-lect AMS Website. Josiah Willard Gibbs Lectures #42]</ref> In 1981 he received the [[Leroy P. Steele Prize]] from the American Mathematical Society for seminal contributions to research.

==See also==

* [[Hopf alternative]]
* [[Hopf bifurcation]]
* [[Hopf–Cole transformation]] (see [[Burgers' equation]])
* [[Hopf decomposition]]
* [[Wiener–Hopf method]]

== Bibliography ==

⚫
*{{Citation | last1=Hopf | first1=Eberhard | editor1-last=Morawetz | editor1-first=Cathleen S. | editor2-last=Serrin | editor2-first=James B. | editor3-last=Sinai | editor3-first=Yakov G. | title=Selected works of Eberhard Hopf with commentaries | url=https://books.google.com/books?id=8TOqgRLbpaQC | publisher=[[American Mathematical Society]] | location=Providence, R.I. | isbn=978-0-8218-2077-3 | mr=1985954 | year=2002}}


==External links==
==External links==
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*{{MathGenealogy|id=12959}}
*{{MathGenealogy|id=12959}}
* [http://gdz.sub.uni-goettingen.de/dms/suche/?tx_goobit3_search%5Border%5D=0&tx_goobit3_search%5Blink%5D=1&tx_goobit3_search%5Bformquery%5D=Hopf%20Eberhard Online list of E. Hopf's works from Göttinger Digitalisierungszentrum]
* [http://gdz.sub.uni-goettingen.de/dms/suche/?tx_goobit3_search%5Border%5D=0&tx_goobit3_search%5Blink%5D=1&tx_goobit3_search%5Bformquery%5D=Hopf%20Eberhard Online list of E. Hopf's works from Göttinger Digitalisierungszentrum]

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==Notes==
⚫
{{reflist}}


{{Authority control}}
{{Authority control}}
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[[Category:1902 births]]
[[Category:1902 births]]
[[Category:1983 deaths]]
[[Category:1983 deaths]]
[[Category:People from Salzburg]]
[[Category:Scientists from Salzburg]]
[[Category:20th-century German mathematicians]]
[[Category:20th-century German mathematicians]]
[[Category:Topologists]]
[[Category:German topologists]]
[[Category:People from Austria-Hungary]]
[[Category:Immigrants to Germany]]
[[Category:Immigrants to the United States]]

Latest revision as of 11:19, 18 July 2024

Eberhard Hopf
Born(1902-04-04)4 April 1902
Salzburg, Austria-Hungary
Died24 July 1983(1983-07-24) (aged 81)
Bloomington, Indiana, United States
NationalityGerman
Alma materUniversity of Berlin
Known forBifurcation theory
Differential geometry
Ergodic theory
Partial differential equation
Hopf bifurcation
Hopf decomposition
Hopf lemma
Hopf maximum principle
Cole–Hopf transformation
Landau–Hopf theory of turbulence
Wiener–Hopf method
AwardsLeroy P. Steele Prize (1981)
Gibbs Lecture (1971)
ICM speaker (1950)
Scientific career
FieldsMathematician
InstitutionsMIT (1931-36)
University of Leipzig (1936-42)
University of Munich (1944-47)
Indiana Univ. Bloomington (1949-83)
Doctoral advisorErhard Schmidt
Issai Schur
Doctoral studentsAlbert Schaeffer

Eberhard Frederich Ferdinand Hopf (April 4, 1902 in Salzburg, Austria-Hungary – July 24, 1983 in Bloomington, Indiana, USA) was a German mathematician and astronomer, one of the founding fathers of ergodic theory and a pioneer of bifurcation theory who also made significant contributions to the subjects of partial differential equations and integral equations, fluid dynamics, and differential geometry. The Hopf maximum principle is an early result of his (1927) that is one of the most important techniques in the theory of elliptic partial differential equations.

Biography

[edit]

Hopf was born in Salzburg, Austria-Hungary, but his scientific career was divided between Germany and the United States. He received his Ph.D. in mathematics in 1926 and his Habilitation in mathematical astronomy from the University of Berlin in 1929.

In 1971, Hopf was the American Mathematical Society Gibbs Lecturer.[1] In 1981, he received the Leroy P. Steele Prize from the American Mathematical Society for seminal contributions to research.

Major publications

[edit]

A non-comprehensive selection of his work was published in 2002:

Notes

[edit]
  1. ^ Josiah Willard Gibbs Lectures #42, AMS
[edit]
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