Leopold Löwenheim
{{Short description|German mathematician}}
{{Infobox scientist
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| name = Leopold Löwenheim
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| image = Lowenheim Portrait.jpg
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| birth_date = {{birth date |1878|06|26}}
| birth_place = Krefeld, Germany
| death_date = {{death date and age |1957|05|05 |1878|06|26}}
| death_place = Berlin, Germany
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| fields = Mathematical logic
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| alma_mater = University of Berlin, Technische Universität Berlin
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| known_for = Löwenheim–Skolem theorem
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| spouse = Johanna Rassmussen
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Leopold Löwenheim [ˈle:o:pɔl̩d ˈlø:vɛnhaɪm] (26 June 1878 in Krefeld – 5 May 1957 in Berlin) was a German mathematician doing work in mathematical logic. The Nazi regime forced him to retire because under the Nuremberg Laws he was considered only three quarters Aryan. In 1943 much of his work was destroyed during a bombing raid on Berlin. Nevertheless, he survived the Second World War, after which he resumed teaching mathematics.{{MacTutor Biography|id=Lowenheim}}
Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem, often considered the starting point for model theory.
Leopold was the son of Ludwig Löwenheim, a mathematics teacher at the polytechnic in Krefeld and Elizabeth Röhn, a writer. In 1881 the three of them left Krefeld first for Naples and then Berlin where Ludwig was a private scholar working on a comprehensive account of the influence of Democritus on modern science. Although he hoped this would gain him a teaching job at Humboldt University Ludwig died in 1894.{{cite journal |last1=Thiel |first1=Christopher |editor1-last=Beklemishev |editor1-first=Lev D. |title=Leopold löwenheim, Life, Work and Early Influence |journal=Provability, Computability and Reflection |date=2009 |url=https://books.google.com/books?id=AViIv0zlsKEC&q=E.+Stamm+%22Monatshefte+f%C3%BCr+Mathematik+und+Physik%22&pg=PA250 |publisher=Elsevier |isbn=9780080954967 |language=en}}
Publications
- {{cite journal |last=Löwenheim |first=Leopold |author-link=Leopold Löwenheim |year=1908 |title=Über das Auflösungsproblem im logischen Klassenkalkül |language=de |journal=Sitzungsberichte der Berliner Mathematischen Gesellschaft |volume=7 |pages=89–94 |url=http://www.math.berlin/publikationen/sitzungsberichte.html}}
- {{cite journal |last=Löwenheim |first=Leopold |author-link=Leopold Löwenheim |year=1910 |title=Über die Auflösung von Gleichungen im logischen Gebietekalkül |language=de |journal=Mathematische Annalen |volume=68 |issue=2 |pages=169–207 |doi= 10.1007/bf01474159 |s2cid=122434845 |url=http://gdz.sub.uni-goettingen.de/download/PPN235181684_0068/PPN235181684_0068___LOG_0021.pdf}}
- {{cite journal |last=Löwenheim |first=Leopold |author-link=Leopold Löwenheim |year=1913 |title=Über Transformationen im Gebietekalkül |language=de |journal=Mathematische Annalen |volume=73 |issue=2 |pages=245–272 |doi= 10.1007/bf01456715 |s2cid=120979593 |url=http://gdz.sub.uni-goettingen.de/download/PPN235181684_0073/PPN235181684_0073___LOG_0024.pdf}}
- {{cite journal |last=Löwenheim |first=Leopold |author-link=Leopold Löwenheim |year=1915 |title=Über Möglichkeiten im Relativkalkül |language=de |journal=Mathematische Annalen |pages=447–470 |volume=76 |issue=4 |doi=10.1007/bf01458217 |s2cid=116581304 |url=http://gdz.sub.uni-goettingen.de/download/PPN235181684_0076/PPN235181684_0076___LOG_0039.pdf}} Translated as "On possibilities in the calculus of relatives" in Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press: 228–251.
- {{cite journal |last=Löwenheim |first=Leopold |author-link=Leopold Löwenheim |year=1915 |title=Über eine Erweiterung des Gebietekalküls, welche auch die gewöhnliche Algebra umfaßt |language=de |journal=Archiv für Systematische Philosophie |volume=21 |pages=137–148 |url=http://www.digizeitschriften.de/dms/img/?PID=PPN827940653_0021}}
- {{cite journal |last=Löwenheim |first=Leopold |author-link=Leopold Löwenheim |year=1940 |title=Einkleidung der Mathematik in Schröderschen Relativkalkül |language=de |journal=Journal of Symbolic Logic |volume=5 |issue=1 |pages=1–15 |jstor=2269177 |doi=10.2307/2269177|s2cid=250344187 }}
- {{cite journal |last=Löwenheim |first=Leopold |author-link=Leopold Löwenheim |others=Translated by Willard Van Orman Quine |year=1946 |title=On Making Indirect Proofs Direct |journal=Scripta Mathematica |volume=12 |number=2 |pages=125–147}}
References
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Further reading
- Brady, Geraldine, 2000. From Peirce to Skolem. North Holland. Contains a detailed exegesis of the proof in Löwenheim (1915), and discusses how Thoralf Skolem simplified that proof and extended the scope and generality of the theorem.
External links
- [http://www.encyclopedia.com/doc/1G2-2830905231.html Löwenheim, Leopold] at encyclopedia.com
- {{cite journal |last=Thiel |first=Christian |date=November 2007 |title=A Short Introduction to Löwenheim's Life and Work and to a Hitherto Unknown Paper |journal=History and Philosophy of Logic |doi=10.1080/01445340701708852|volume=28 |issue=4 |pages=289–302|s2cid=170174740 |doi-access=free }}
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Category:20th-century German mathematicians
Category:19th-century German philosophers
Category:20th-century German philosophers
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