Felix Bernstein (mathematician): Difference between revisions

Felix Bernstein
Felix Bernstein
Born	24 February 1878; Halle
Died	3 December 1956 (aged 78); Zürich, Switzerland
Alma mater	University of Göttingen
Known for	Schröder–Bernstein theorem
Children	Marianne Bernstein-Wiener
	Scientific career
Theses	Untersuchungen aus der Mengenlehre (1901); Über den Klassenkörper eines algebraischen Zahlkörpers (1903);
Doctoral advisor	David Hilbert

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Felix Bernstein (24 February 1878 – 3 December 1956), was a German mathematician known for proving in 1896 the Schröder–Bernstein theorem, a central result in set theory,^[1]^: 5–6^[2]^[3]^{[note 1]} and less well known for demonstrating in 1924 the correct blood group inheritance pattern of multiple alleles at one locus through statistical analysis.

Life

Felix Bernstein was born in Halle on 24 February 1878 to a Jewish family of academics.^[4] His father Julius held the Chair of Physiology at the Martin Luther University of Halle-Wittenberg, and was the Director of the Physiological Institute at the University of Halle.

While still in gymnasium in Halle, Bernstein heard the university seminar of Georg Cantor, who was a friend of Bernstein's father.^[1]^: 5r From 1896 to 1900, Bernstein studied in Munich, Halle, Berlin and Göttingen.^[5]^: 166 In the early Weimar Republic, Bernstein temporarily was Göttingen vice-chairman of the local chapter of German Democratic Party .^[6]^: 7^[7]^: 118^[8] In 1933,^{[note 2]} after Hitler's rise to power, Bernstein was removed from his chair, per §6 of the Nazi Law for the Restoration of the Professional Civil Service, often used against politically unpopular persons. He received the message of his dismissal during a research/lecturing journey (started on Dec. 1st, 1932) to the United States, and he stayed there.^[5]^: 166^[6]^: 7–8^[8] He was a visiting professor of mathematics at Columbia University from 1933 to 1936 and a professor of biometry at New York University from 1936 to 1943.^[9] In 1942 he was elected a fellow of the American Association for the Advancement of Science.^[10] In 1948, Bernstein retired from teaching in the US, and returned to Europe.^[2] He mainly lived in Rome and Freiburg, occasionally visiting Göttingen,^[5]^: 166 where he became professor emeritus.^[2] He died in Zürich on 3 December 1956.^[1]^: 6r^[2]

Publications

Felix Bernstein (1903). Über den Klassenkörper eines algebraischen Zahlkörpers (Habilitation thesis). Univ. Göttingen.
Felix Bernstein (1905). "Untersuchungen aus der Mengenlehre". Mathematische Annalen. 61: 117–155. doi:10.1007/bf01457734. S2CID 119658724. Archived from the original on 2014-02-02. Retrieved 2014-02-01. (Dissertation, 1901); reprint Jan 2010, ISBN 1141370263
Felix Bernstein (1905). "Über die isoperimetrische Eigenschaft des Kreises auf der Kugeloberfläche und in der Ebene" (PDF). Mathematische Annalen. 60: 117–136. doi:10.1007/bf01447496. S2CID 121773961.
Felix Bernstein (1905). "Über die Reihe der transfiniten Ordnungszahlen" (PDF). Mathematische Annalen. 60 (2): 187–193. doi:10.1007/bf01677265. S2CID 119726638.
Felix Bernstein (1905). "Die Theorie der reellen Zahlen" (PDF). Jahresbericht der Deutschen Mathematiker-Vereinigung. 14: 447–449.
Felix Bernstein (1905). "Zum Kontinuumproblem" (PDF). Mathematische Annalen. 60 (3): 463–464. doi:10.1007/bf01457626. S2CID 179177776.
Felix Bernstein (1907). "Über das Gaußsche Fehlergesetz" (PDF). Mathematische Annalen. 64 (3): 417–448. doi:10.1007/bf01476025. S2CID 125418501.
Felix Bernstein (1907). "Zur Theorie der trigonometrischen Reihe" (PDF). Journal für die reine und angewandte Mathematik. 132: 270–278.
Felix Bernstein (1919). "Die Mengenlehre Georg Cantors und der Finitismus" (PDF). Jahresbericht der Deutschen Mathematiker-Vereinigung. 28: 63–78.
Felix Bernstein (1919). "Die Übereinstimmung derjenigen beiden Summationsverfahren einer divergenten Reihe, welche von T.E. Stieltjes und E. Borel herrühren" (PDF). Jahresbericht der Deutschen Mathematiker-Vereinigung. 28: 50–63. — Corrections in Vol.29 (1920), p. 94
Felix Bernstein (1923). "Zur Statistik der sekundären Geschlechtsmerkmale beim Menschen" (PDF). Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. 1923: 89–95.

Notes

^ In 1897 (aged 19), according to Oliver Deiser (2010). "Zeittafel zur frühen Mengenlehre" (PDF). Einführung in die Mengenlehre — Die Mengenlehre Georg Cantors und ihre Axiomatisierung durch Ernst Zermelo (3rd ed.). Heidelberg: Springer. ISBN 978-3-540-20401-5.
^ In 1934, according to O'Connor, Robertson (MacTutor).

References

^ ^a ^b ^c ^d Crow, J. F. (1993). "Felix Bernstein and the first human marker locus". Genetics. 133 (1): 4–7. doi:10.1093/genetics/133.1.4. PMC 1205297. PMID 8417988.
^ ^a ^b ^c ^d O'Connor, John J.; Robertson, Edmund F., "Felix Bernstein (mathematician)", MacTutor History of Mathematics Archive, University of St Andrews
^ Nathan, Henry (1970–1980). "Bernstein, Felix". Dictionary of Scientific Biography. Vol. 2. New York: Charles Scribner's Sons. pp. 58–59. ISBN 978-0-684-10114-9.
^ "Felix Bernstein". International Statistical Review (2005), 73: 1. 3-7.
^ ^a ^b ^c Max Pinl (1970). "Kollegen in einer dunklen Zeit (2)" (PDF). Jahresbericht der Deutschen Mathematiker-Vereinigung. 72: 165–189.
^ ^a ^b Norbert Schappacher (1987). "Das Mathematische Institut der Universität Göttingen 1929—1950" (PDF). In Becker; Dahms; Wegeler (eds.). Die Universität Göttingen unter dem Nationalsozialismus. München: K.G.Saur. pp. 345–373. — Schappacher gives a lot of details from the Göttingen University archive.
^ Barbara Marshall (1972). The Political Development of German University Towns in the Weimar Republic: Göttingen and Münster 1918—1930 (Ph.D. thesis). Univ. of London.
^ ^a ^b Steffi Laemmle; Willy Tiabou; Christoph Bichlmeier (May 2003). "Verfolgte Mathematiker (Persecuted Mathematicians)". Seminar für überfachliche Grundlagen: Mathematiker in der NS-Zeit (Term Paper). TU Munich.
^ Cattell, Jaques, ed. (1949). American Men of Science: A Biographical Dictionary. Lancaster, Pennsylvania: The Science Press. p. 192.
^ "Historic Fellows". American Association for the Advancement of Science.

External links

Biography at the Felix-Bernstein-Institute for Mathematical Statistics in the Biosciences at the Göttingen University
Felix Bernstein at the Mathematics Genealogy Project

[4] In 1897 (aged 19), according to Oliver Deiser (2010). "Zeittafel zur frühen Mengenlehre" (PDF). Einführung in die Mengenlehre — Die Mengenlehre Georg Cantors und ihre Axiomatisierung durch Ernst Zermelo (3rd ed.). Heidelberg: Springer. ISBN 978-3-540-20401-5.

[10] In 1934, according to O'Connor, Robertson (MacTutor).

[Crow.1993-1] Crow, J. F. (1993). "Felix Bernstein and the first human marker locus". Genetics. 133 (1): 4–7. doi:10.1093/genetics/133.1.4. PMC 1205297. PMID 8417988.

[OConnor.Robertson-2] O'Connor, John J.; Robertson, Edmund F., "Felix Bernstein (mathematician)", MacTutor History of Mathematics Archive, University of St Andrews

[3] Nathan, Henry (1970–1980). "Bernstein, Felix". Dictionary of Scientific Biography. Vol. 2. New York: Charles Scribner's Sons. pp. 58–59. ISBN 978-0-684-10114-9.

[5] "Felix Bernstein". International Statistical Review (2005), 73: 1. 3-7.

[Pinl.1970-6] Max Pinl (1970). "Kollegen in einer dunklen Zeit (2)" (PDF). Jahresbericht der Deutschen Mathematiker-Vereinigung. 72: 165–189.

[Schappacher.1987-7] Norbert Schappacher (1987). "Das Mathematische Institut der Universität Göttingen 1929—1950" (PDF). In Becker; Dahms; Wegeler (eds.). Die Universität Göttingen unter dem Nationalsozialismus. München: K.G.Saur. pp. 345–373. — Schappacher gives a lot of details from the Göttingen University archive.

[8] Barbara Marshall (1972). The Political Development of German University Towns in the Weimar Republic: Göttingen and Münster 1918—1930 (Ph.D. thesis). Univ. of London.

[Bichlmeier.Laemmle.Tiabou.2003-9] Steffi Laemmle; Willy Tiabou; Christoph Bichlmeier (May 2003). "Verfolgte Mathematiker (Persecuted Mathematicians)". Seminar für überfachliche Grundlagen: Mathematiker in der NS-Zeit (Term Paper). TU Munich.

[11] Cattell, Jaques, ed. (1949). American Men of Science: A Biographical Dictionary. Lancaster, Pennsylvania: The Science Press. p. 192.

[12] "Historic Fellows". American Association for the Advancement of Science.

[1]

[2]

[3]

[note 1]

[4]

[5]

[6]

[7]

[8]

[note 2]

[9]

[10]

@@ Line 1: / Line 1: @@
+{{short description|German Jewish mathematician}}
-:''Not to be confused with [[Felix Bernstein]].''
 {{Infobox scientist
 | name = Felix Bernstein
@@ Line 7: / Line 6: @@
 | birth_place = [[Halle, Saxony-Anhalt|Halle]]
 | death_date = {{Death date and age|1956|12|3|1878|2|24|df=y}}
-| death_place = [[Zurich]]
+| death_place = [[Zürich]], Switzerland
 | image_size  =
-| alt         =
 | caption     =
 | death_cause =
@@ Line 22: / Line 20: @@
 | patrons     =
 | education   =
-| alma_mater  = [[G&ouml;ttingen University]]
+| alma_mater  = [[University of Göttingen]]
-| thesis_title = Untersuchungen aus der Mengenlehre
+| thesis1_title = Untersuchungen aus der Mengenlehre
+| thesis1_url  = http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0061&DMDID=DMDLOG_0015&L=1
-| thesis_url  =
-| thesis_year = 1901
+| thesis1_year = 1901
+| thesis2_title = Über den Klassenkörper eines algebraischen Zahlkörpers
+| thesis2_year = 1903
 | doctoral_advisor = [[David Hilbert]]
 | academic_advisors =
 | doctoral_students =
 | notable_students =
-| known_for   =
+| known_for   = [[Schröder–Bernstein theorem]]
 | influences  =
 | influenced  =
@@ Line 38: / Line 38: @@
 | spouse      =         <!--(or | spouses = )-->
 | partner     =         <!--(or | partners = )-->
-| children    =
+| children    = Marianne Bernstein-Wiener<ref name="Crow.1993"/>{{rp|7r}}
 | signature   =         <!--(filename only)-->
 | signature_alt =
@@ Line 44: / Line 44: @@
 | footnotes   =
 }}
+'''Felix Bernstein''' (24 February 1878 – 3 December 1956), was a German [[mathematician]] known for proving in 1896 the [[Schröder–Bernstein theorem]], a central result in [[set theory]],<ref name="Crow.1993"/>{{rp|5–6}}<ref name="OConnor.Robertson"/><ref>{{DSB|first=Henry|last=Nathan|title=Bernstein, Felix|volume=2|pages=58–59}}</ref><ref group="note">In 1897 (aged 19), according to {{cite book | author=Oliver Deiser | contribution=Zeittafel zur frühen Mengenlehre | title=Einführung in die Mengenlehre &mdash; Die Mengenlehre Georg Cantors und ihre Axiomatisierung durch Ernst Zermelo | location=Heidelberg | publisher=Springer | edition=3rd | contribution-url=https://link.springer.com/content/pdf/bbm%3A978-3-642-01445-1%2F1.pdf | isbn=978-3-540-20401-5 | year=2010}}
-'''Felix Bernstein''' (24 February 1878, [[Halle, Saxony-Anhalt|Halle]], [[German Empire|Germany]] – 3 December 1956, [[Zurich]], [[Switzerland]]) was a [[Germany|German]] [[Jewish]] [[mathematician]] known for developing [[Cantor–Bernstein–Schroeder theorem|a theorem of the equivalence of sets]] in 1897, and less well known for demonstrating the correct [[Blood type|blood group]] inheritance pattern of multiple [[allele]]s at one [[Locus (genetics)|locus]] in 1924 through [[statistical analysis]]. He studied under [[Georg Cantor]].
+</ref> and less well known for demonstrating in 1924 the correct [[Blood type|blood group]] inheritance pattern of multiple [[allele]]s at one [[Locus (genetics)|locus]]  through [[statistical analysis]].
+==Life==
-In 1934, after [[Hitler]]'s rise to power, Bernstein was deprived from his chair. Bernstein then emigrated to the [[USA]]. After the war, Bernstein returned to [[Europe]] and died of [[cancer]] in [[Zurich]] on 3 December 1956.
+Felix Bernstein was born in [[Halle, Saxony-Anhalt|Halle]] on 24 February 1878 to a Jewish family of academics.<ref>"Felix Bernstein". International Statistical Review (2005), 73: 1. 3-7.</ref> His father [[Julius Bernstein|Julius]] held the Chair of Physiology at the [[Martin Luther University of Halle-Wittenberg]], and was the Director of the Physiological Institute at the University of Halle.
+While still in [[gymnasium (Germany)|gymnasium]] in Halle, Bernstein heard the university seminar of [[Georg Cantor]], who was a friend of Bernstein's father.<ref name="Crow.1993"/>{{rp|5r}}
+From 1896 to 1900, Bernstein studied in [[Munich]], Halle, [[Berlin]] and [[Göttingen]].<ref name="Pinl.1970">{{cite journal | author=Max Pinl | title=Kollegen in einer dunklen Zeit (2) | journal=Jahresbericht der Deutschen Mathematiker-Vereinigung | volume=72 | pages=165–189 | url=http://www.digizeitschriften.de/download/PPN37721857X_0072/log14.pdf | year=1970 }}</ref>{{rp|166}}
+In the early [[Weimar Republic]], Bernstein temporarily was Göttingen vice-chairman of the local chapter of [[German Democratic Party]] .<ref name="Schappacher.1987">{{cite book | author=Norbert Schappacher | contribution=Das Mathematische Institut der Universität Göttingen 1929&mdash;1950 | pages=345–373 | contribution-url=http://www-irma.u-strasbg.fr/~schappa/NSch/Publications_files/GoeNS.pdf |editor=Becker |editor2=Dahms |editor3=Wegeler | title=Die Universität Göttingen unter dem Nationalsozialismus | location=München | publisher=K.G.Saur | year=1987 }} &mdash; Schappacher gives a lot of details from the Göttingen University archive.</ref>{{rp|7}}<ref>{{cite thesis | type=Ph.D. thesis | author=Barbara Marshall | title=The Political Development of German University Towns in the Weimar Republic: Göttingen and Münster 1918&mdash;1930 | institution=Univ. of London | year=1972 }}</ref>{{rp|118}}<ref name="Bichlmeier.Laemmle.Tiabou.2003">{{cite report |author1=Steffi Laemmle |author2=Willy Tiabou |author3=Christoph Bichlmeier | title=Seminar für überfachliche Grundlagen: Mathematiker in der NS-Zeit | contribution=Verfolgte Mathematiker (Persecuted Mathematicians) | institution=TU Munich | type=Term Paper | contribution-url=http://www5.in.tum.de/lehre/seminare/math_nszeit/SS03/vortraege/verfolgt | date=May 2003 }}</ref>
+In 1933,<ref group="note">In 1934, according to O'Connor, Robertson (MacTutor).</ref>
+after [[Hitler]]'s rise to power, Bernstein was removed from his chair, per §6 of the Nazi [[Law for the Restoration of the Professional Civil Service]], often used against politically unpopular persons.
+He received the message of his dismissal during a research/lecturing journey (started on Dec. 1st, 1932) to the United States, and he stayed there.<ref name="Pinl.1970"/>{{rp|166}}<ref name="Schappacher.1987"/>{{rp|7–8}}<ref name="Bichlmeier.Laemmle.Tiabou.2003"/> He was a visiting professor of mathematics at [[Columbia University]] from 1933 to 1936 and a professor of biometry at [[New York University]] from 1936 to 1943.<ref>{{cite book|editor=Cattell, Jaques|title=American Men of Science: A Biographical Dictionary|page=192|year=1949|publisher=The Science Press|location=Lancaster, Pennsylvania|url=https://books.google.com/books?id=Ea9CC4lCicQC&pg=PA192}}</ref> In 1942 he was elected a fellow of the [[American Association for the Advancement of Science]].<ref>{{cite web|title=Historic Fellows|website=American Association for the Advancement of Science|url=https://www.aaas.org/fellows/historic}}</ref> In 1948, Bernstein retired from teaching in the US, and returned to Europe.<ref name="OConnor.Robertson">{{MacTutor Biography|id=Bernstein_Felix}}</ref>
+He mainly lived in [[Rome]] and [[Freiburg]], occasionally visiting Göttingen,<ref name="Pinl.1970"/>{{rp|166}} where he became [[professor emeritus]].<ref name="OConnor.Robertson"/>
+He died in [[Zürich]] on 3 December 1956.<ref name="Crow.1993">{{Cite journal |last1 = Crow | first1 = J. F. |title = Felix Bernstein and the first human marker locus |journal = Genetics |volume = 133 |issue = 1 |pages = 4–7 |year = 1993 |doi = 10.1093/genetics/133.1.4 |pmid = 8417988 |pmc = 1205297}}</ref>{{rp|6r}}<ref name="OConnor.Robertson"/>
 ==Publications==
+* {{cite thesis | type=Habilitation thesis | author=Felix Bernstein | title=Über den Klassenkörper eines algebraischen Zahlkörpers | institution=Univ. Göttingen | year=1903 }}
-* {{cite journal |title=Untersuchungen aus der Mengenlehre |author=Felix Bernstein |journal=Mathematische Annalen |volume=61 |year=1905 |pages=117–155| url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0061&DMDID=DMDLOG_0015&L=1 |publisher=Springer |location= Berlin |doi=10.1007/bf01457734}} (Dissertation); reprint Jan 2010, ISBN 1141370263
+* {{cite journal |title=Untersuchungen aus der Mengenlehre |author=Felix Bernstein |journal=[[Mathematische Annalen]] |volume=61 |year=1905 |pages=117–155 |url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0061&DMDID=DMDLOG_0015&L=1 |doi=10.1007/bf01457734 |s2cid=119658724 |access-date=2014-02-01 |archive-url=https://web.archive.org/web/20140202210121/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0061&DMDID=DMDLOG_0015&L=1 |archive-date=2014-02-02 |url-status=dead }} (Dissertation, 1901); reprint Jan 2010, {{ISBN|1141370263}}
+* {{cite journal | author=Felix Bernstein | title=Über die isoperimetrische Eigenschaft des Kreises auf der Kugeloberfläche und in der Ebene | journal=[[Mathematische Annalen]] | volume=60 | pages=117–136 | url=http://www.digizeitschriften.de/download/PPN235181684_0060/log9.pdf | year=1905 | doi=10.1007/bf01447496| s2cid=121773961 }}
+* {{cite journal | author=Felix Bernstein | title=Über die Reihe der transfiniten Ordnungszahlen | journal=Mathematische Annalen | volume=60 | issue=2 | pages=187–193 | url=http://www.digizeitschriften.de/download/PPN235181684_0060/log23.pdf | year=1905 | doi=10.1007/bf01677265| s2cid=119726638 }}
+* {{cite journal | author=Felix Bernstein | title=Die Theorie der reellen Zahlen | journal=[[Jahresbericht der Deutschen Mathematiker-Vereinigung]] | volume=14 | pages=447–449 | url=http://www.digizeitschriften.de/download/PPN37721857X_0014/log113.pdf | year=1905 }}
+* {{cite journal | author=Felix Bernstein | title=Zum Kontinuumproblem | journal=[[Mathematische Annalen]] | volume=60 | issue=3 | pages=463–464 | url=http://www.digizeitschriften.de/download/PPN235181684_0060/log49.pdf | year=1905 | doi=10.1007/bf01457626| s2cid=179177776 }}
+* {{cite journal | author=Felix Bernstein | title=Über das Gaußsche Fehlergesetz | journal=Mathematische Annalen | volume=64 | issue=3 | pages=417–448 | url=http://www.digizeitschriften.de/download/PPN235181684_0064/log43.pdf | year=1907 | doi=10.1007/bf01476025| s2cid=125418501 }}
+* {{cite journal | author=Felix Bernstein | title=Zur Theorie der trigonometrischen Reihe | journal=[[Journal für die reine und angewandte Mathematik]] | volume=132 | pages=270–278 | url=http://www.digizeitschriften.de/download/PPN243919689_0132/log21.pdf | year=1907 }}
+* {{cite journal | author=Felix Bernstein | title=Die Mengenlehre Georg Cantors und der Finitismus | journal=Jahresbericht der Deutschen Mathematiker-Vereinigung | volume=28 | pages=63–78 | url=http://www.digizeitschriften.de/download/PPN37721857X_0028/log10.pdf | year=1919 }}
+* {{cite journal | author=Felix Bernstein | title=Die Übereinstimmung derjenigen beiden Summationsverfahren einer divergenten Reihe, welche von T.E. Stieltjes und E. Borel herrühren | journal=Jahresbericht der Deutschen Mathematiker-Vereinigung | volume=28 | pages=50–63 | url=http://www.digizeitschriften.de/download/PPN37721857X_0028/log9.pdf | year=1919 }} &mdash; [http://www.digizeitschriften.de/download/PPN37721857X_0029/log8.pdf Corrections] in Vol.29 (1920), p.&nbsp;94
+* {{cite journal | author=Felix Bernstein | title=Zur Statistik der sekundären Geschlechtsmerkmale beim Menschen | journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse | volume=1923 | pages=89–95 | url=http://www.digizeitschriften.de/download/PPN252457811_1923/log15.pdf | year=1923 }}
-==Further reading==
+==Notes==
+{{Reflist|group="note"}}
-{{DSB
-|first=Henry
+==See also==
-|last=Nathan
+*[[Cantor–Bernstein theorem]]
-|title=Bernstein, Felix
+*[[Schröder–Bernstein property]]
-|volume=2
-|pages=58–59
+==References==
-}}
+{{Reflist}}
 == External links ==
+* [https://web.archive.org/web/20150822200445/http://www.fbms.math.uni-goettingen.de/index.php?id=62 Biography] at the [http://fbms.math.uni-goettingen.de Felix-Bernstein-Institute for Mathematical Statistics in the Biosciences] at the [[Göttingen University]]
-* {{MacTutor Biography|id=Bernstein_Felix}}
-* {{Cite pmid|8417988|noedit}}
-* http://www-history.mcs.st-and.ac.uk/history/Biographies/Bernstein_Felix.html
 * {{MathGenealogy|id=7346}}
-{{Authority control|VIAF=3214308}}
+{{Authority control}}
-{{Persondata
-| NAME              = Bernstein, Felix
-| ALTERNATIVE NAMES =
-| SHORT DESCRIPTION = [[Germany|German]] [[Jewish]] [[mathematician]]
-| DATE OF BIRTH     = 24 February 1878
-| PLACE OF BIRTH    =[[Halle, Saxony-Anhalt|Halle]]
-| DATE OF DEATH     = 3 December 1956
-| PLACE OF DEATH    =[[Zurich]]
-}}
 {{DEFAULTSORT:Bernstein, Felix}}
 [[Category:1878 births]]
 [[Category:1956 deaths]]
-[[Category:19th-century mathematicians]]
+[[Category:20th-century German mathematicians]]
-[[Category:20th-century mathematicians]]
-[[Category:German mathematicians]]
 [[Category:People from Halle (Saale)]]
 [[Category:People from the Province of Saxony]]
-[[Category:Bernstein family]]
+[[Category:20th-century German Jews]]
-[[Category:German Jews]]
+[[Category:Set theorists]]
-[[Category:ICM 1908 Plenary and Invited Speakers]]
+[[Category:University of Göttingen alumni]]
+[[Category:Fellows of the American Association for the Advancement of Science]]
+[[Category:Emigrants from Nazi Germany to the United States]]
+[[Category:Mathematicians from the German Empire]]
-{{Germany-mathematician-stub}}

Authority control databases
International	ISNI VIAF FAST WorldCat
National	Germany United States Netherlands Poland
Academics	Mathematics Genealogy Project zbMATH MathSciNet
People	Deutsche Biographie DDB
Other	IdRef SNAC