View source for Solomon Lefschetz

{{Short description|Russian-born American mathematician (1884–1972)}}
{{Infobox scientist
| name              = Solomon Lefschetz
| image             = Solomon Lefschetz.jpg
| image_size        = 180
| caption           =
| birth_date        = {{birth date|1884|09|03|df=y}}
| birth_place       = [[Moscow]], [[Russian Empire]]
| death_date        = {{death date and age|1972|10|05|1884|09|03|df=y}}
| death_place       = [[Princeton, New Jersey]], US
| citizenship       = US
| fields            = [[Algebraic topology]]
| workplaces        = {{unbulleted list|[[University of Nebraska–Lincoln|University of Nebraska]]|[[University of Kansas]]|[[Princeton University]]|[[National Autonomous University of Mexico]]<ref name=mexico>{{cite journal|url=https://www.mathunion.org/fileadmin/IMU/Publications/CircularLetters/2014/IMU_AO_CL_3_2014-PB03-14_MATHEMATICS_IN_MEXICO.PDF|title=Mathematics in Mexico|journal=Sociedad Matematica Mexicana|archive-date=2023-03-08|access-date=2018-07-11|archive-url=https://web.archive.org/web/20230308185538/https://www.mathunion.org/fileadmin/IMU/Publications/CircularLetters/2014/IMU_AO_CL_3_2014-PB03-14_MATHEMATICS_IN_MEXICO.PDF|url-status=live}}</ref>|[[Brown University]]}}
| alma_mater        = [[École Centrale Paris]]<br />[[Clark University]]
| doctoral_advisor  = [[William Edward Story]]<ref name="mathgene">{{MathGenealogy|id=7461}}</ref>
| thesis_title      = On the Existence of Loci with Given Singularities
| thesis_url        = https://www.proquest.com/docview/301745812/
| thesis_year       = 1911
| doctoral_students = [[Edward Begle]]<br /> [[Richard Bellman]]<br /> [[Felix Browder]]<br />[[Clifford Dowker]]<br />[[George F. D. Duff]]<br />[[Ralph Fox]]<br />[[Ralph Gomory]]<br />[[John McCarthy (computer scientist)|John McCarthy]]<br /> [[Robert Prim]]<br /> [[Paul A. Smith]]<br />[[Norman Steenrod]]<br />[[Arthur Harold Stone]] <br />[[Clifford Truesdell]]<br /> [[Albert W. Tucker]]<br /> [[John Tukey]]<br />[[Henry Wallman]]<br />[[Shaun Wylie]]<ref name="mathgene"/>
| notable_students  = [[Sylvia de Neymet]]
| known_for         = [[Lefschetz fixed-point theorem]]<br>[[Picard–Lefschetz theory]]<br>[[Hairy ball theorem#Lefschetz connection|Lefschetz connection]]<br>[[Lefschetz hyperplane theorem]]<br>[[Lefschetz duality]]<br>[[Lefschetz manifold]]<br>[[Lefschetz number]]<br>[[Algebraic geometry and analytic geometry#The Lefschetz principle|Lefschetz principle]]<br>[[Lefschetz zeta function]]<br>[[Lefschetz pencil]]<br>[[Lefschetz theorem on (1,1)-classes]]
| author_abbrev_bot =
| author_abbrev_zoo =
| influences        =
| influenced        =
| awards            = [[Bôcher Memorial Prize]] <small>(1924)</small><br>[[National Medal of Science]] <small>(1964)</small><br>[[Leroy P. Steele Prize]] <small>(1970)</small><br>[[Fellow of the Royal Society]]<ref name="frs">{{Cite journal | last1 = Hodge | first1 = W. V. D.|authorlink = W. V. D. Hodge| doi = 10.1098/rsbm.1973.0016 | title = Solomon Lefschetz 1884–1972 | journal = [[Biographical Memoirs of Fellows of the Royal Society]] | volume = 19 | pages = 433–453 | year = 1973 | s2cid = 122747688 }}</ref>
| signature         =
| footnotes         =
| honorific_suffix  = [[Foreign Member of the Royal Society|ForMemRS]]
}}
'''Solomon Lefschetz''' {{Post-nominals|country=||list=[[Foreign Member of the Royal Society|ForMemRS]]}} ({{langx|ru|Соломо́н Ле́фшец}}; 3 September 1884 – 5 October 1972) was a Russian-born American [[mathematician]] who did fundamental work on [[algebraic topology]], its applications to [[algebraic geometry]], and the theory of non-linear [[ordinary differential equation]]s.<ref name="mathgene"/><ref name="frs"/><ref>{{cite journal|author=Markus, L.|title=Solomon Lefschetz: An appreciation in memoriam|journal=Bull. Amer. Math. Soc.|year=1973|volume=79|issue=4|pages=663–680|url=http://projecteuclid.org/euclid.bams/1183534736|doi=10.1090/s0002-9904-1973-13256-2|doi-access=free|archive-date=2020-06-26|access-date=2012-07-16|archive-url=https://web.archive.org/web/20200626043411/https://projecteuclid.org/euclid.bams/1183534736|url-status=live}}</ref><ref name="mactutor">{{MacTutor Biography|id=Lefschetz}}</ref>

==Life==
He was born in [[Moscow]], the son of Alexander Lefschetz and his wife Sarah or Vera Lifschitz, Jewish traders who used to travel around Europe and the Middle East (they held [[Ottoman Empire|Ottoman]] passports).<ref name="mactutor"/> Shortly thereafter, the family moved to [[Paris]]. He was educated there in [[engineering]] at the [[École Centrale Paris]], but emigrated to the US in 1905.

He was badly injured in an industrial accident in 1907, losing both hands.<ref>{{Google books |id=dZh2SnbSxAcC |title=Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical |page=148 }}</ref> He moved towards mathematics, receiving a [[Doctor of Philosophy|Ph.D.]] in algebraic geometry from [[Clark University]] in Worcester, Massachusetts in 1911.<ref name="thesis-lefschetz-1911">{{cite thesis |url=https://www.proquest.com/docview/301745812 |title=On the existence of LocI with given singularities |date=1911 |publisher=[[Clark University]] |type=Ph.D. |last=Lefschetz |first=Solomon |id={{ProQuest|301745812}} |url-access=subscription |oclc=245921866 |archive-date=2023-03-17 |access-date=2022-05-24 |archive-url=https://web.archive.org/web/20230317113654/https://www.proquest.com/docview/301745812/ |url-status=live }}</ref> He then took positions at the [[University of Nebraska–Lincoln|University of Nebraska]] and [[University of Kansas]], moving to [[Princeton University]] in 1924, where he was soon given a permanent position. He remained there until 1953.

In the application of topology to algebraic geometry, he followed the work of [[Charles Émile Picard]], whom he had heard lecture in Paris at the [[École Centrale Paris]]. He proved theorems on the topology of [[hyperplane]] sections of [[algebraic varieties]], which provide a basic inductive tool (these are now seen as allied to [[Morse theory]], though a [[Lefschetz pencil]] of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other). The [[Picard–Lefschetz theory|Picard–Lefschetz formula]] in the theory of [[vanishing cycle]]s is a basic tool relating the [[degeneracy (mathematics)|degeneration]] of families of varieties with 'loss' of topology, to [[monodromy]]. He was an Invited Speaker of the [[International Congress of Mathematicians|ICM]] in 1920 in Strasbourg.<ref>{{cite book|chapter-url=http://www.mathunion.org/ICM/ICM1920/Main/icm1920.0300.0307.ocr.pdf|pages=300–307|year=1921|title=Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920|chapter=''Quelques remarques sur la multiplication complexe'' by S. Lefschetz|url-status=dead|archive-url=https://web.archive.org/web/20171029065313/http://www.mathunion.org/ICM/ICM1920/Main/icm1920.0300.0307.ocr.pdf|archive-date=2017-10-29}}</ref> His book ''L'analysis situs et la géométrie algébrique'' from 1924, though opaque foundationally given the current technical state of [[homology theory]], was in the long term very influential (one could say that it was one of the sources for the eventual proof of the [[Weil conjectures]], through [[Séminaire de Géométrie Algébrique du Bois Marie#SGA 7|SGA 7]]  also for the study of [[Picard group]]s of [[Zariski surface]]). In 1924 he was awarded the [[Bôcher Memorial Prize]] for his work in [[mathematical analysis]]. He was elected to the United States [[National Academy of Sciences]] in 1925 and the [[American Philosophical Society]] in 1929.<ref>{{Cite web |title=Solomon Lefschetz |url=http://www.nasonline.org/member-directory/deceased-members/20001615.html |access-date=2023-07-20 |website=www.nasonline.org}}</ref><ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=Solomon+Lefschetz&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2023-07-20 |website=search.amphilsoc.org |archive-date=2023-07-20 |archive-url=https://web.archive.org/web/20230720152257/https://search.amphilsoc.org/memhist/search?creator=Solomon+Lefschetz&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |url-status=live }}</ref>

The [[Lefschetz fixed-point theorem]], now a basic result of topology, was developed by him in papers from 1923 to 1927, initially for [[manifold]]s. Later, with the rise of [[cohomology theory]] in the 1930s, he contributed to the [[intersection number]] approach (that is, in cohomological terms, the ring structure) via the [[cup product]] and duality on manifolds. His work on topology was summed up in his monograph ''[http://www.ams.org/online_bks/coll27/ Algebraic Topology]'' (1942). From 1944 he worked on [[differential equation]]s.

He was editor of the ''[[Annals of Mathematics]]'' from 1928 to 1958. During this time, the ''Annals'' became an increasingly well-known and respected journal, and Lefschetz played an important role in this.<ref name=NAS>{{Cite web |url = https://www.ma.utexas.edu/users/dafr/M382C/Readings/slefschetz.pdf |title = Solomon Lefschetz 1884–1972 |first1=Phillip |last1=Griffiths|author-link1=Phillip Griffiths|first2= Donald|last2= Spencer|author-link2=Donald Spence|first3=George|last3=Whitehead| author-link3=George W. Whitehead |date = 1992 |publisher = National Academy of Sciences |url-status = dead |archive-url = https://web.archive.org/web/20141222053811/https://www.ma.utexas.edu/users/dafr/M382C/Readings/slefschetz.pdf |archive-date = 2014-12-22 }}</ref>

In 1945 he travelled to Mexico for the first time, where he joined the Institute of Mathematics at the [[National University of Mexico]] as a visiting professor. He visited frequently for long periods, and during 1953–1966 he spent most of his winters in Mexico City.<ref name=NAS /> He played an important role in the foundation of mathematics in Mexico, and sent several students back to Princeton. His students included Emilio Lluis, [[José Adem]], [[Samuel Gitler Hammer|Samuel Gitler]], [[Santiago López de Medrano]], [[Francisco Javier González-Acuña]] and Alberto Verjovsky.<ref name=mexico/>

Lefschetz came out of retirement in 1958, because of the launch of [[Sputnik]], to augment the mathematical component of [[Glenn L. Martin Company]]'s [[Research Institute for Advanced Studies]] (RIAS) in Baltimore, Maryland. His team became the world's largest group of mathematicians devoted to research in [[nonlinear differential equation]]s.<ref>Allen, K. N. (1988, January). Undaunted genius. ''Clark News'', '''11'''(1), p. 9.</ref>  The RIAS mathematics group stimulated the growth of nonlinear differential equations through conferences and publications. He left RIAS in 1964 to form the Lefschetz Center for Dynamical Systems at [[Brown University]], Providence, Rhode Island.<ref>{{Cite web|url=https://sites.brown.edu/dynamical-systems/|title=Lefschetz Center for Dynamical Systems|website=sites.brown.edu}}</ref>

==Selected works==
* ''L´Analysis situs et la géométrie algébrique'', Paris, Gauthier-Villars 1924<ref>{{cite journal|last=Alexander|first=James W.|author-link=James Waddell Alexander II|title=Review: S. Lefschetz, ''L'Analysis Situs et la Géométrie Algébrique''|journal=Bull. Amer. Math. Soc.|year=1925|volume=31|issue=9|pages=558–559|url=http://www.ams.org/journals/bull/1925-31-09/S0002-9904-1925-04116-6/|doi=10.1090/s0002-9904-1925-04116-6|doi-access=free|archive-date=2023-03-17|access-date=2012-09-02|archive-url=https://web.archive.org/web/20230317113659/https://www.ams.org/journals/bull/1925-31-09/S0002-9904-1925-04116-6/|url-status=live}}</ref>
* ''Intersections and transformations of complexes and manifolds'', [[Transactions of the American Mathematical Society]] vol. 28, 1926, pp.&nbsp;1–49, [http://www.ams.org/journals/tran/1926-028-01/S0002-9947-1926-1501331-3/S0002-9947-1926-1501331-3.pdf online]; fixed-point theorem, published in vol. 29, 1927, pp.&nbsp;429–462, [http://www.ams.org/journals/tran/1927-029-02/S0002-9947-1927-1501397-1/S0002-9947-1927-1501397-1.pdf online].
* ''Géométrie sur les surfaces et les variétés algébriques'', Paris, Gauthier Villars 1929<ref>{{cite journal|last=Zariski|first=Oscar|author-link=Oscar Zariski|title=Review: S. Lefschetz, ''Géométrie sur les Surfaces et les Variétés Algébriques''|journal=[[Bulletin of the American Mathematical Society]]|year=1930|volume=36|issue=9|pages=617–618|url=http://projecteuclid.org/euclid.bams/1183494223|doi=10.1090/s0002-9904-1930-05017-x|doi-access=free|archive-date=2020-06-27|access-date=2012-08-11|archive-url=https://web.archive.org/web/20200627075350/https://projecteuclid.org/euclid.bams/1183494223|url-status=live}}</ref>
* ''Topology'', AMS 1930<ref>{{cite journal|last=Smith|first=Paul A.|author-link=Paul A. Smith|title=Letschetz on Topology|journal=[[Bulletin of the American Mathematical Society]]|year=1931|volume=37|issue=9, Part 1|pages=645–648|url=http://projecteuclid.org/euclid.bams/1183494969|doi=10.1090/S0002-9904-1931-05201-0|doi-access=free|archive-date=2020-06-12|access-date=2012-08-22|archive-url=https://web.archive.org/web/20200612144153/https://projecteuclid.org/euclid.bams/1183494969|url-status=live}}</ref>
* ''Algebraic Topology'', New York, American Mathematical Society 1942
* ''Introduction to topology'', Princeton 1949
* with [[Joseph P. LaSalle]], ''Stability by Liapunov's direct method with applications'', New York, Academic Press 1961<ref>{{cite journal|author=Antosiewicz, H. A.|title=Review: Joseph LaSalle and Solomon Lefschetz, ''Stability by Liapunov's direct method with applications''|journal=[[Bulletin of the American Mathematical Society]]|year=1963|volume=69|issue=2|pages=209–210|url=http://projecteuclid.org/euclid.bams/1183525110|doi=10.1090/s0002-9904-1963-10915-5|doi-access=free|archive-date=2020-06-10|access-date=2012-08-11|archive-url=https://web.archive.org/web/20200610220318/https://projecteuclid.org/euclid.bams/1183525110|url-status=live}}</ref>
* ''Algebraic geometry'', Princeton 1953, 2nd edn., 1964
* ''Differential equations: geometric theory'', Interscience, 1957,<ref>{{cite journal|author=Haas, Felix|title=Review: S. Lefschetz, ''Differential equations: Geometric theory''|journal=[[Bulletin of the American Mathematical Society]]|year=1958|volume=64|issue=4|pages=203–206|url=http://projecteuclid.org/euclid.bams/1183522569|doi=10.1090/s0002-9904-1958-10212-8|doi-access=free|archive-date=2020-06-15|access-date=2012-08-11|archive-url=https://web.archive.org/web/20200615173131/https://projecteuclid.org/euclid.bams/1183522569|url-status=live}}</ref> 2nd edn., 1963
* ''Stability of nonlinear control systems'', 1965
* [http://www.ams.org/samplings/math-history/hmath1-lefschetz14.pdf ''Reminiscences of a mathematical immigrant in the United States''], [[American Mathematical Monthly]], vol.77, 1970, pp.&nbsp;344–350.

==References==
{{Reflist}}

==External links==
{{Wikiquote}}
* {{Internet Archive author |sname=Solomon Lefschetz}}
* {{Librivox author |id=3303}}
* [https://web.archive.org/web/20150310024937/http://www.princeton.edu/~mudd/finding_aids/mathoral/pmcxrota.htm "Fine Hall in its golden age: Remembrances of Princeton in the early fifties"] by [[Gian-Carlo Rota]]. Contains a lengthy section on Lefschetz at Princeton.
* Gompf: [http://www.ams.org/notices/200508/200508-toc.html ''What is a Lefschetz Pencil?'', Notices AMS 2005]
* [http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/lefschetz-solomon.pdf National Academy of Sciences Biographical Memoir]

{{Winners of the National Medal of Science|math-stat-comp}}
{{John von Neumann Lecturers}}
{{AMS Presidents|state=collapsed}}
{{Authority control}}

{{DEFAULTSORT:Lefschetz, Solomon}}
[[Category:1884 births]]
[[Category:1972 deaths]]
[[Category:American topologists]]
[[Category:École Centrale Paris alumni]]
[[Category:Jewish American scientists]]
[[Category:Russian Jews]]
[[Category:Emigrants from the Russian Empire to the United States]]
[[Category:20th-century American mathematicians]]
[[Category:Princeton University faculty]]
[[Category:Clark University alumni]]
[[Category:National Medal of Science laureates]]
[[Category:Foreign members of the Royal Society]]
[[Category:University of Nebraska–Lincoln faculty]]
[[Category:University of Kansas faculty]]
[[Category:Presidents of the American Mathematical Society]]
[[Category:Brown University faculty]]
[[Category:Members of the American Philosophical Society]]