{{Short description|German-born American mathematician}} {{distinguish|Heinrich August Rothe}} {{Infobox scientist | name = Erich Hans Rothe | image = | caption = | birth_date = {{birth date|1895|7|21}} | birth_place = Berlin, German Empire | death_date = {{death date and age|1988|2|19|1895|7|21}} | death_place = Ann Arbor, Michigan, United States | field = Mathematical analysis, differential equations, integral equations, mathematical physics | known_for = Rothe method, Rothe's fixed point theorem, results in degree theory | education = Technical University of Berlin (PhD, 1927) | doctoral_advisor = Erhard Schmidt, Richard von Mises | spouse = Hildegard Ille (m. 1928) | children = Erhard W. Rothe | doctoral_students = Jane Cronin Scanlon, George J. Minty }} '''Erich Hans Rothe''' (July 21, 1895, Berlin – February 19, 1988, Ann Arbor, Michigan) was a German-born American mathematician, who did research in mathematical analysis, differential equations, integral equations, and mathematical physics.<ref name=macbio>{{MacTutor Biography|title=Erich Hans Rothe|id=Rothe_Erich}}</ref><ref>{{cite book|title=Displaced German Scholars: A Guide to Academics in Peril in Nazi Germany During the 1930s|url=https://books.google.com/books?id=47XdGC6Ch-wC&pg=PA53|date=1 January 1993|publisher=Wildside Press LLC|page=53|isbn=978-0-89370-474-2}}</ref> He is known for the Rothe method (also known as the method of lines or the method of semidiscretization) used for solving evolution equations.<ref name="Rothe1930">{{cite journal|last1=Rothe|first1=Erich|title=Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben|journal=Mathematische Annalen|volume=102|issue=1|year=1930|pages=650–670|issn=0025-5831|doi=10.1007/BF01782368|s2cid=123325520 }}</ref><ref name="Kačur1986">{{cite book|chapter=''Method of Rothe in evolution equations'' by J. Kačur|volume=1192|year=1986|pages=23–34|issn=0075-8434|title=Equadiff 6: Proceedings of the International Conference on Differential Equations and their Applications, held in Brno, Czechoslovakia August 21–30, 1985|doi=10.1007/BFb0076049|hdl=10338.dmlcz/700142 }}</ref>
==Biography== Rothe, whose father was a lawyer, attended Berlin's Royal Wilhelm Gymnasium and passed his ''Abitur'' in October 1913. After completing two semesters at the University of Munich, he volunteered to join the German Army in a field artillery regiment. He was wounded in the Battle of Verdun and was discharged from the German Army in December 1918. In 1919 he continued his mathematical studies for one semester at Technische Hochschule Berlin (now TU Berlin) and then transferred to Berlin's ''Friedrich-Wilhelms-Universität'' (Friedrich Wilhelm University, now called the Humboldt University of Berlin). There he studied mathematics, physics, and philosophy and in 1923 passed the ''Lehramtsexamen'' qualifying him to become a ''Gymnasium'' teacher. From 1923 to 1926 he taught at Berlin's ''Mommsen-Gymnasium''.<ref name=macbio/> In 1927 he received his ''Promotion'' from TU Berlin. His dissertation ''Über einige Analogien zwischen linearen partiellen und linearen gewöhnlichen Differentialgleichungen'' (About some analogies between linear partial and linear ordinary differential equations) was supervised by Erhard Schmidt and Richard von Mises.<ref>{{MathGenealogy|name=Erich Hans Rothe|id=7784}}</ref> Rothe worked from 1926 to 1927 at the Institute of Applied Mathematics of the Friedrich Wilhelm University. In 1928 he married the mathematician Hildegard Ille (1899–1942).<ref name=macbio/> From 1928 to 1931 he was a ''Privatdozent'' and ''Assistent'' under Fritz Noether at the ''Technische Hochschule Breslau''. There he received his ''Habilitation'' in 1928. From 1931 to 1935 he was a ''Privatdozent'' at the University of Breslau. There he received his ''Umhabilitation'' in 1931).<ref>{{cite book|editor=Scharlau, Winfried|editor-link=Winfried Scharlau|title=Mathematische Institute in Deutschland, 1800–1945|publisher=Vieweg|year=1990|pages=64 & 70|doi=10.1007/978-3-663-14036-8 |isbn=978-3-528-08992-4 |url=https://link.springer.com/book/10.1007%2F978-3-663-14036-8}}</ref><ref>The term ''Umhabilitation'' refers to the academic procedure in which professors or ''Privatdozenten'' acquire the license to teach (''venia legendi'') at another university by means of a shortened procedure.</ref> During the time he held positions in Breslau, he took study leave for a year at the University of Göttingen. In Breslau in April 1931 Hildegard Rothe gave birth to Erhard W. Rothe.<ref name=macbio/>
After being dismissed in 1935 from the German civil service because he was a Jew, Rothe with his wife and son escaped to Zurich and in emigrated in 1937 to the USA. From 1937 to 1943 he taught mathematics (with a very small salary) at William Penn College (now William Penn University) in Oskaloosa, Iowa.<ref name=macbio/><ref name="Siegmund-Schultze2009">{{cite book|author=Siegmund-Schultze, Reinhard|title=Mathematicians Fleeing from Nazi Germany: Individual Fates and Global Impact|url=https://books.google.com/books?id=jBoEmGB3B3MC&pg=194|page=194|year=2009|publisher=Princeton University Press|isbn=978-0-691-12593-0}}</ref> His wife died of cancer in December 1942. At the University of Michigan, Rothe was an assistant professor from 1944 to 1949, an associate professor from 1949 to 1955, and a full professor from 1955 to 1964, when he retired as professor emeritus.<ref name=macbio/> In retirement, he taught at the University of Michigan–Dearborn<ref name=FHP>{{cite web|title=Erich Hans Rothe|website=Faculty History Project, University of Michigan|url=http://faculty-history.dc.umich.edu/faculty/erich-hans-rothe|access-date=2025-02-25|archive-date=2021-05-15|archive-url=https://web.archive.org/web/20210515204859/http://faculty-history.dc.umich.edu/faculty/erich-hans-rothe|url-status=dead}}</ref> and in the academic year 1967–1968 at Western Michigan University (WMU).<ref name=macbio/> During his year at WMU, Rothe helped to develop the PhD program for WMU's mathematics department, which awarded its first PhD in December 1969.<ref>{{cite journal|title=A Brief History of Mathematics at WMU|journal=Mathematical Association of America Michigan Section Newsletter|date=December 2003|volume=30|issue=1|page=16|url=http://sections.maa.org/michigan/newsletters/30_1%20Fall%202003%20Newsletter.pdf}}</ref>
Rothe published more than 50 mathematical papers.<ref name=FHP/> He was a co-author, with Hans Rademacher, of chapter 19 of the 7th edition of ''Die Differential- und Integralgleichungen der Mechanik und Physik''.<ref>{{cite book|editor=von Mises, Richard|editor2=Frank, Philipp|title=Die Differential- und Integralgleichungen der Mechanik und Physik: als 7. Auflage von Riemann-Webers Partiellen Differentialgleichungen der mathematischen Physik|url=https://books.google.com/books?id=wjvvAAAAMAAJ&q=rothe|year=1925|publisher=F. Vieweg}}</ref> In 1986 at the age of 91, Rothe published the 242-page book ''Introduction to Various Aspects of Degree Theory in Banach Spaces''.<ref name=macbio/>
In addition to the Rothe Method, he is also known for his theorem, proven in 1937, that a functional in a Hilbert space is weakly continuous if and only if its Fréchet derivative is a completely continuous operator<ref>{{cite journal|author=Cesari, Lamberto|title=Introductory remarks to a lecture of Erich H. Rothe|journal=Journal of Mathematical Analysis and Applications|volume=12|year=1965|issue=3 |pages=382–383|doi=10.1016/0022-247X(65)90003-X |url=https://core.ac.uk/download/pdf/82624044.pdf}}</ref><ref>Maximilian Pinl: ''Kollegen in einer dunklen Zeit'', Jahresbericht der DMV '''71''', 208/209, 1969</ref><ref>{{cite journal|author=Rothe, E. H.|title=Über Abbildungsklassen von Kugeln des Hilbertschen Raumes|journal=Compositio Math.|volume=4|year=1937|pages=294–307}}</ref><ref>{{cite journal|author=Rothe, E. H.|title=Über den Abbildungsgrad bei Abbildungen von Kugeln des Hilbertschen Raumes|journal=Compositio Math.|volume=5|year=1937|pages=166–176}}</ref> and for Rothe's fixed point theorem, proven in 1937.<ref name="Smart1980">{{cite book|author=Smart, D. R.|title=Fixed Point Theorems|url=https://books.google.com/books?id=y5g4AAAAIAAJ&pg=PA26|pages=26–27|date=14 February 1980|publisher=CUP Archive|isbn=978-0-521-29833-9}}</ref><ref>{{cite journal|author=Rothe, E. H.|title=Zur Theorie der topologischen Ordnung und der Vektorfelder in Benachschen Raumen|journal=Compositio Math.|volume=5|year=1937|pages=177–197}}</ref> In 1978 a collection of papers was published in his honor.<ref name="Rothe1978">{{cite book|editor=Cesari, L.|editor2=Kannan, R.|editor3=Weinberger, H. F.|title=Nonlinear Analysis: A Collection of Papers in Honor of Erich H. Rothe|url=https://books.google.com/books?id=OC7vAAAAMAAJ|year=1978|publisher=Academic Press|isbn=978-0-12-165550-1}} (This book contains a list of Rothe's publications.)</ref> His doctoral students include Jane Cronin Scanlon and George J. Minty.<ref name=Kaplan>{{cite journal|author=Kaplan, Wilfred|title=A tribute to Erich H. Rothe|journal=Journal of Mathematical Analysis and Applications|volume=12|issue=3|year=1965|pages=381–382|doi=10.1016/0022-247X(65)90002-8 |url=https://core.ac.uk/download/pdf/81151477.pdf}}</ref>
Upon his death, Erich Rothe was survived by his son and two granddaughters.<ref name=FHP/>
==Selected publications== * {{cite journal|doi=10.2307/1969094|jstor=1969094|last1=Rothe|first1=E. H.|title=Gradient Mappings in Hilbert Space|journal=Annals of Mathematics|year=1946|volume=47|issue=3|pages=580–592}} * {{cite journal|doi=10.2307/1969277|jstor=1969277|last1=Rothe|first1=E. H.|author-mask=2|title=Completely Continuous Scalars and Variational Methods|journal=Annals of Mathematics|year=1948|volume=49|issue=2|pages=265–278}} * {{cite journal|last1=Rothe|first1=E. H.|author-mask=2|title=Gradient mappings and extrema in Banach spaces|journal=Duke Mathematical Journal|volume=15|issue=2|pages=421–431|year=1948|issn=0012-7094|doi=10.1215/S0012-7094-48-01540-3}} * {{cite journal|doi=10.2307/1990549|jstor=1990549|title=Weak Topology and Nonlinear Integral Equations|last1=Rothe|first1=E. H.|author-mask=2|journal=Transactions of the American Mathematical Society|year=1949|volume=66|issue=1|pages=75–92|doi-access=free}} * {{cite journal|doi=10.1002/mana.3210040103|title=A relation between the type numbers of a critical point and the index of the corresponding field of gradient vectors. Erhard Schmidt zum 75. Geburtstag gewidmet|year=1950|last1=Rothe|first1=Erich H.|author-mask=2|journal=Mathematische Nachrichten|volume=4|issue=1–6|pages=12–27}} * {{cite journal|doi=10.1007/BF02395742|title=Critical points and gradient fields of scalars in Hilbert space|year=1951|last1=Rothe|first1=E. H.|author-mask=2|journal=Acta Mathematica|volume=85|pages=73–98|doi-access=free}} * {{cite journal|doi=10.2307/1969643|jstor=1969643|last1=Rothe|first1=E. H.|author-mask=2|title=Leray-Schauder Index and Morse Type Numbers in Hilbert Space|journal=Annals of Mathematics|year=1952|volume=55|issue=3|pages=433–467}} * {{cite journal|doi=10.2307/2372083|jstor=2372083|title=A Remark on Isolated Critical Points|last1=Rothe|first1=Erich H.|author-mask=2|journal=American Journal of Mathematics|year=1952|volume=74|issue=1|pages=253–263}} * {{cite journal|author=Rothe, E. H.|author-mask=2|title=A note on the Banach spaces of Calkin and Morrey|journal=Pacific J. Math.|volume=3|issue=2|year=1953|pages=493–499|doi=10.2140/pjm.1953.3.493|url=https://msp.org/pjm/1953/3-2/pjm-v3-n2-p.pdf#page=239}} * {{cite journal|doi=10.1090/S0002-9904-1953-09649-5|title=Gradient mappings|year=1953|last1=Rothe|first1=E. H.|author-mask=2|journal=Bulletin of the American Mathematical Society|volume=59|pages=5–20|doi-access=free}} * {{cite journal|doi=10.1002/cpa.3160090325|title=Remarks on the application of gradient mappings to the calculus of variations and the connected boundary value problems in partial differential equations|year=1956|last1=Rothe|first1=E. H.|author-mask=2|journal=Communications on Pure and Applied Mathematics|volume=9|issue=3|pages=551–568}} * {{cite journal|doi=10.2307/2033624|jstor=2033624|last1=Rothe|first1=E. H.|author-mask=2|title=A Note on Gradient Mappings|journal=Proceedings of the American Mathematical Society|year=1959|volume=10|issue=6|pages=931–935|doi-access=free}} * {{cite journal|author=Rothe, Erich H.|author-mask=2|title=Critical point theory in Hilbert space under general boundary conditions|journal=Journal of Mathematical Analysis and Applications|year=1965|volume=11|pages=357–409|doi=10.1016/0022-247X(65)90092-2|hdl=2027.42/32071|url=https://deepblue.lib.umich.edu/bitstream/handle/2027.42/32071/0000115.pdf?sequence=1}} * {{cite journal|author=Rothe, Erich H.|author-mask=2|title=An existence theorem in the calculus of variations based on Sobolev's imbedding theorems|journal=Arch. Rational Mech. Analysis|year=1966|volume=21|issue=2|pages=151–162|doi=10.1007/BF00266572|hdl=2027.42/46175|s2cid=30858816|url=https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46175/205_2004_Article_BF00266572.pdf;sequence=1|hdl-access=free}} * {{cite journal|author=Rothe, Erich H.|author-mask=2|title=Critical point theory in Hilbert space under regular boundary conditions|journal=Journal of Mathematical Analysis and Applications|year=1971|volume=36|issue=2|pages=377–431|doi=10.1016/0022-247X(71)90010-2|url=https://deepblue.lib.umich.edu/bitstream/handle/2027.42/33542/0000041.pdf?sequence=1}} * {{cite journal|jstor=44236313|title=Morse Theory in Hilbert Space|last1=Rothe|first1=E. H.|author-mask=2|journal=The Rocky Mountain Journal of Mathematics|year=1973|volume=3|issue=2|pages=251–274|doi=10.1216/RMJ-1973-3-2-251|doi-access=free}} * {{cite journal|author=Rothe, Erich H.|author-mask=2|title=A generalization of the Seifert-Threlfall proof for the Lusternik-Schnirelman category inequality|year=1975|journal=Journal of Mathematical Analysis and Applications|volume=50|issue=2|pages=243–267|doi=10.1016/0022-247X(75)90020-7|url=https://deepblue.lib.umich.edu/bitstream/handle/2027.42/22173/0000604.pdf?sequence=1}} * {{cite book|title=Introduction to Various Aspects of Degree Theory in Banach Spaces|series=Mathematical Surveys and Monographs|volume=23|publisher=American Mathematical Society|location=Providence, Rhode Island|year=1986|isbn=9780821827703 |url=https://books.google.com/books?id=XM2FAwAAQBAJ}}<ref>{{cite journal|title=Review of ''Introduction to various aspects of degree theory in Banach spaces'' by E. H. Rothe|author=Deimling, Klaus|journal=Bull. Amer. Math. Soc. (N.S.)|volume=17|issue=2|pages=340–343|date=October 1987|doi=10.1090/S0273-0979-1987-15585-6 |url=http://www.projecteuclid.org/euclid.bams/1183554191|doi-access=free}}</ref>
==References== <references/>
==External links== * {{cite journal|title=Faculty Bibliography of Erich H. Rothe|journal=Journal of Mathematical Analysis and Applications|volume=12|year=1965|issue=3 |pages=384–386|doi=10.1016/0022-247X(65)90004-1 |url=https://core.ac.uk/reader/82707960|doi-access=}}
{{authority control}}
{{DEFAULTSORT:Rothe, Erich}} Category:20th-century German mathematicians Category:20th-century American mathematicians Category:American people of German-Jewish descent Category:Humboldt University of Berlin alumni Category:William Penn University faculty Category:University of Michigan faculty Category:1895 births Category:1988 deaths Category:Emigrants from Nazi Germany to the United States