1. Ruth Moufang Ruth Moufang. January 10, 1905 November 26, 1977. Moufang studied mathematics at the University of Frankfurt, passing the teacher's examination in 1929. She received her Ph.D. in 1931 on projective http://www.agnesscott.edu/lriddle/women/moufang.htm

Ruth Moufang January 10, 1905 - November 26, 1977 Moufang studied mathematics at the University of Frankfurt, passing the teacher's examination in 1929. She received her Ph.D. in 1931 on projective geometry, then spent a fellowship year in Rome. She returned to Germany to lecture at the University of Konigsberg, then at the University of Frankfurt. She went on to complete her habilitation thesis, which entitled her to teach at the university level in Germany, but because she was a woman, Hitler's minister of education would not allowed her to teach the mostly male student population. Moufang therefore became the first German woman with a doctorate to be employed as an industrial mathematician when she went to work for the Krupps Research Institute in the fall of 1937. In 1946 she was finally able to accept a teaching position at the University of Frankfurt where, in 1957, she became the first woman in Germany to be appointed as a full professor. Moufang helped to create a new mathematical specialty in the algebraic analysis of projective planes that drew upon a mixture of geometry and algebra. She studied what are known today as the Moufang plane and Moufang loops. Moufang also published several papers in theoretical physics. References Srinivasan, Bhama. "Ruth Moufang, 1905-1977," The Mathematical Intelligencer, Vol 6, No. 2 (1984), 51-55.

2. Moufang Ruth Moufang. Born 10 Jan Ruth Moufang was supervised by Dehn andobtained a Ph.D. in 1931 on projective geometry. From 1931 to http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Moufang.html

Ruth Moufang Born: 10 Jan 1905 in Darmstadt, Germany Died: 26 Nov 1977 in Frankfurt, Germany Click the picture above to see four larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Ruth Moufang was supervised by Dehn and obtained a Ph.D. in 1931 on projective geometry . From 1931 to 1937 she studied projective planes introducing Moufang planes and non-associative systems called Moufang loops. In [2] Chandler and Magnus describe her contributions to geometry, putting them into context as follows:- A large part of her work is dedicated to the foundations of geometry. Her most outstanding contribution to this field is a result which adds a third important discovery to two others made previously by Hilbert and . Reversing a development going from Euclid to Descartes in which geometry is replaced by algebra as a fundamental discipline of mathematics, Hilbert had shown that a subset of his axioms for plane geometry essentially the incidence axioms together with the incidence theorem of Desargues permits the introduction of coordinates on a straight line which are elements of a skew field. If

3. Poster Of Moufang Ruth Moufang. lived from 1905 to 1977. Moufang studied projective planes, introducingMoufang planes and nonassociative systems called Moufang loops. http://www-gap.dcs.st-and.ac.uk/~history/Posters2/Moufang.html

Ruth Moufang lived from 1905 to 1977 Moufang studied projective planes, introducing Moufang planes and non-associative systems called Moufang loops. Find out more at http://www-history.mcs.st-andrews.ac.uk/history/ Mathematicians/Moufang.html

4. Search Results lehmer emma lovelace augusta ada macintyre sheila scott malonemayes vivienne mcduffdusa merrill winifred morawetz cathleen moufang ruth nelson evelyn roden http://www.webcactus.com/psearch/results.asp?q=ladd koresh

5. The Science Bookstore - Chronology 1905 AD. moufang , ruth. Born 1/10/1905 http://www.thesciencebookstore.com/chron.asp?pg=27

6. Moufang Biography of ruth moufang (19051977) ruth moufang. Born 10 Jan 1905 in Darmstadt, Germany ruth moufang was supervised by Dehn and obtained a Ph.D http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Moufang.html

Ruth Moufang Born: 10 Jan 1905 in Darmstadt, Germany Died: 26 Nov 1977 in Frankfurt, Germany Click the picture above to see four larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Ruth Moufang was supervised by Dehn and obtained a Ph.D. in 1931 on projective geometry . From 1931 to 1937 she studied projective planes introducing Moufang planes and non-associative systems called Moufang loops. In [2] Chandler and Magnus describe her contributions to geometry, putting them into context as follows:- A large part of her work is dedicated to the foundations of geometry. Her most outstanding contribution to this field is a result which adds a third important discovery to two others made previously by Hilbert and . Reversing a development going from Euclid to Descartes in which geometry is replaced by algebra as a fundamental discipline of mathematics, Hilbert had shown that a subset of his axioms for plane geometry essentially the incidence axioms together with the incidence theorem of Desargues permits the introduction of coordinates on a straight line which are elements of a skew field. If

7. Ruth Moufang [was Re: In Memoriam...] By Julio Gonzalez Cabillon ruth moufang was Re In Memoriam by Julio Gonzalez Cabillon. reply to this message. post a message on a new topic. Back to mathhistory-list. Subject ruth moufang was Re In Memoriam http://mathforum.com/epigone/math-history-list/nimflefoi

Ruth Moufang [was Re: In Memoriam...] by Julio Gonzalez Cabillon reply to this message post a message on a new topic Back to math-history-list Subject: Ruth Moufang [was Re: In Memoriam...] Author: jgc@adinet.com.uy Date: http://www-groups.dcs.st-and.ac.uk./~history/Mathematicians/Moufang.html The Math Forum

8. Women Mathematicians-Chronological Index 19021997) Irmgard Flugge-Lotz (1903-1974) Dorothy McCoy (1903-2001) Sophie Piccard(1904- ) Rózsa Péter (1905-1977) ruth moufang (1905-1977) Kate Fenchel http://www.agnesscott.edu/lriddle/women/chronol.htm

Biographies of Women Mathematicians , Agnes Scott College] Search Chronological Index of Women Mathematicians The choice of what century to use is a bit subjective. For the sake of this index I have listed each woman by the century of her birth. Eighteenth Century and Before Theano (5th Century B.C.) Hypatia (370?-415) Elena Lucrezia Cornaro Piscopia (1646-1684) Emilie du Chatelet (1706-1749 ... Mary Fairfax Somerville (1780-1872) Nineteenth Century Ada Byron King, Countess of Lovelace (1815-1852) Florence Nightingale (1820-1910) Mary Everest Boole (1832-1916) Susan Jane Cunningham (1842-1921) ... Pelageya Yakovlevna Polubarinova-Kochina (1899- ) Twenthieth Century Gertrude Mary Cox (1900-1978) Mary Lucy Cartwright (1900-1998) Nina Karlovna Bari (1901-1961) Edna Kramer Lassar (1902-1984) ... Karen E. Smith (1965- ) Need Help on these with date of birth (and death if appropriate)! Gloria Gilmer Goldie Prentis Horton Home Names ... LRiddle@AgnesScott.edu Last modified May 18, 2004 Agnes Scott College , Decatur, GA

9. Ruth Moufang By Walter Felscher ruth moufang by Walter Felscher. reply to this message. post a message on a new topic. Back to mathhistory-list Subject ruth moufang Author Walter Felscher walter.felscher@uni-tuebingen.de http://mathforum.com/epigone/math-history-list/tysmolclerm

Ruth Moufang by Walter Felscher reply to this message post a message on a new topic Back to math-history-list Subject: Ruth Moufang Author: walter.felscher@uni-tuebingen.de Date: Sat, 15 Feb 1997 12:34:11 -0500 Ruth Moufang (1905-1977) was a student of Max Dehn and wrote a series of articles on projective planes, most of them between 1931 and 1937 and considered as ground breaking for this particular field of geometry. In 1936 , she obtained her Habilitation for mathematics at the Universitaet Frankfurt. While this was an academic promotion in the hands of the university, appointment to a salaried position was a matter of the state, and as in those years it was the state's policy not to appoint women [ a policy which changed 1940 after the outbreak of the war ], Miss Moufang had to look for other employment. She found it in Essen at the research institute of Krupp, the steel and arms manufacturer, where she worked from 1938 onwards. In 1946, she resumed her position at the Universitaet Frankfurt where, in 1955 and by an in-house appointment, she obtained a full professorship. W.F. The Math Forum

10. AIM Reprint Library: Y Z. Listing for moufang, ruth. Viewing Page 1. Max Dehn zum Gedachtnis.Magnus, Wilhelm moufang, ruth. Viewing Page http://www.aimath.org/library/library.cgi?database=reprints;mode=display;BrowseT

11. AIM Reprint Library: Motzkin, Theodore S. Mouche, PHMv moufang, ruth Moullin, RA Moulton, V. Moulton,Vincent Mourant, WJ Moussong, G. Mower, L. Moy, Allen Moyal, JE Moyls BN http://www.aimath.org/library/library.cgi?database=reprints;mode=display;BrowseL

12. Biography-center - Letter M art/collections/bio/a6261.html. moufang, ruth. www-history.mcs.st-and.ac.uk/~history/ Mathematicians/moufang.html. moufang, ruth. www.agnesscott.edu/lriddle/women/moufang. htm http://www.biography-center.com/m.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish M 791 biographies www-history.mcs.st-and.ac.uk/~history/Mathematicians/Meray.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Mobius.html MacArthur, Douglas www.pbs.org/wgbh/pages/amex/macarthur/peopleevents/pandeAMEX106.html Macarthur, Elizabeth www.abc.net.au/btn/australians/macarthu.htm MacArthur, Mary P.H. www.pbs.org/wgbh/pages/amex/macarthur/peopleevents/pandeAMEX109.html Macaulay, Eunice www.nfb.ca/e/highlights/eunice_macaulay.html Macaulay, Francis www-history.mcs.st-and.ac.uk/~history/Mathematicians/Macaulay.html MacBride, Seán www.nobel.se/peace/laureates/1974/macbride-cv.html Macció, Rómulo www.proa.org.ar/exhibicion/maccio/exhibi-fr.html MacCullagh, James www-history.mcs.st-and.ac.uk/~history/Mathematicians/MacCullagh.html MacCurtain, Margaret

13. Mathematikerinnen In Deutschland - Ruth Moufang moufang, ruth, in Dictionary of Scientific Biography,Volumes XVII - XVIII, Supplement II, herausgegeben von Frederic L. Holmes. http://www.mathematikerin.de/moufang.htm

Ruth Moufang geb.: 10.01.1905 in Darmstadt gest.: 26.11.1977 in Frankfurt Schule und Beruf Mathematische Leistungen Schule und Beruf Studium der Mathematik mit der Berechtigung zu lehren 1929. Promotion zum Thema projektive Geometrie 1931. Ein Jahr Stipendium in Rom. Mathematische Leistungen Srinivasan, Bhama Ruth Moufang, 1905 - 1977 , The mathematical intelligencer Vol 6, No. 2(1984), 51 - 55 Mehrtens, H. Moufang, Ruth , in Dictionary of Scientific Biography, Volumes XVII - XVIII, Supplement II, herausgegeben von Frederic L. Holmes. Charles Scribner's Sons, 1990, S.659 Chandler, B. und Magnus, W. The History of Combinatorial Group Theory: A Case Study in the History of Ideas , (New York - Heidelberg - Berlin, 1982), 123, 136 - 137

14. Tamara Werner's CU Princeton University Press, 1968. Eagle, ruth M. Exploring Mathematics Through History. Young, LaiSang. Granville, Evelyn. moufang, ruth. Hamill, Christine http://www.unm.edu/~abqteach/math2002/02-02-10.htm

Return to Math Index Math and Games of Ancient Civilizations Tamara Werner Academic Setting For readers that are hoping to use my unit, I want to explain some statistics. These statistics have everything to do with why a lot of my students are having a hard time with academics in school. The majority of parents in the West Gate Community make below $25,000 annually. Actually 43% of the parents make this low wage. I hope that you can see how these children come from poor backgrounds. For a family of five or more, they make less than a teacher does. Parents who send their children to Truman make a low wage because most of them have only a high school diploma. Exactly 42% have such a Diploma. This seems low to me, because I come from a background where everyone at least gets through high school and graduates. Most even go and get some college education. But with the West Gate Community, many of them do not have that opportunity to be able to finish all their schooling. Then again we go back down with 19% not even finishing high school.

15. Flügge-Lotz, Irmgard Translate this page Flügge-Lotz, Irmgard. Herschel, Caroline Lucretia. Kovalevskaya, SofiaVasilyevna. moufang, ruth. Neumann, Hanna. Noether, Emmy Amalie. http://www.mathematikerin.de/auswahl.htm

Irmgard Herschel, Caroline Lucretia Kovalevskaya, Irmgard Herschel, Caroline Lucretia Kovalevskaya, ... Emmy Amalie

16. Gaston's Class NEW) Morawetz, Cathleen. moufang, ruth. Neumann, Hanna. Nicolson, Phyllis http://www.vermilionschools.org/teachlinks/gaston

Mr. Gaston's Math Homepage The project is complete! Click here to view the student works! This semester, the Algebra Classes will be presenting an in class project detailing the history of a particular mathematician from history. This will include an in class presentation as well as a written paper on the subject. These are the requirements students must meet for a satisfactory grade: Please read one of the biographies of a male or female mathematician from the following lists. Write a short summary. Create a poster, with at least 2 visual aids and attach your summary for display in class. Please include the following information in your summary: Mathematician's Name. Picture from biography file. Date of Birth and Current Age/or Date of Death. Geographical Location. Important contributions to Math. What you found most interesting about this person. At least two (2) sources must be cited in a bibliography page. Summaries should be at approximately three to four pages long (double-spaced, New Times Roman font, size 12). You are welcome to get additional information from the library if necessary. Here are the mathematicians students may choose from: The 100 most cross-referenced, with the most cross-referenced first. The number of other biographies in which each mathematician is cross-referenced is given in brackets) This list is from

17. Ruth Moufang By Walter Felscher ruth moufang by Walter Felscher. reply to this message post a messageon a new topic Back to mathhistory-list Subject ruth moufang http://mathforum.org/epigone/math-history-list/tysmolclerm

Ruth Moufang by Walter Felscher reply to this message post a message on a new topic Back to math-history-list Subject: Ruth Moufang Author: walter.felscher@uni-tuebingen.de Date: Sat, 15 Feb 1997 12:34:11 -0500 Ruth Moufang (1905-1977) was a student of Max Dehn and wrote a series of articles on projective planes, most of them between 1931 and 1937 and considered as ground breaking for this particular field of geometry. In 1936 , she obtained her Habilitation for mathematics at the Universitaet Frankfurt. While this was an academic promotion in the hands of the university, appointment to a salaried position was a matter of the state, and as in those years it was the state's policy not to appoint women [ a policy which changed 1940 after the outbreak of the war ], Miss Moufang had to look for other employment. She found it in Essen at the research institute of Krupp, the steel and arms manufacturer, where she worked from 1938 onwards. In 1946, she resumed her position at the Universitaet Frankfurt where, in 1955 and by an in-house appointment, she obtained a full professorship. W.F. The Math Forum

18. Ruth Moufang [was Re: In Memoriam...] By Julio Gonzalez Cabillon ruth moufang was Re In Memoriam by Julio Gonzalez Cabillon. reply to thismessage post a message on a new topic Back to mathhistory-list ruth moufang. http://mathforum.org/epigone/math-history-list/nimflefoi

Ruth Moufang [was Re: In Memoriam...] by Julio Gonzalez Cabillon reply to this message post a message on a new topic Back to math-history-list Subject: Ruth Moufang [was Re: In Memoriam...] Author: jgc@adinet.com.uy Date: http://www-groups.dcs.st-and.ac.uk./~history/Mathematicians/Moufang.html The Math Forum

19. Abstract property he called the moufang condition (in honor of ruth moufang's work in the early generalized polygons) which satisfy the moufang condition and using such a classification http://www.mth.msu.edu/~mccarthy/colloq.03.spring/weiss.abstract.html

Department of Mathematics Colloquium March 20, 2003 Buildings and the Moufang Property by Richard Weiss , Professor of Mathematics, Tufts University, Medford, Massachusetts Abstract In his famous Lecture Notes of 1974, Jacques Tits gave a classification of (thick irreducible) spherical buildings of rank at least three . He observed in the addenda to that work that every residue (the most important class of subbuildings) of rank at least two of such a building has a symmetry property he called the Moufang condition (in honor of Ruth Moufang's work in the early 1930's on projective planes) and proposed the two projects of classifying (thick irreducible) spherical buildings of rank two (equivalently, generalized polygons) which satisfy the Moufang condition and using such a classification to reprove the classification of spherical buildings of rank greater than two. In joint work with Tits, these two projects have now been completed. We will give a brief overview of this work. Last Revised: 12/23/02 Corrections: mccarthy@math.msu.edu

20. The Mathematics Genealogy Project - Ruth Moufang Translate this page ruth moufang Biography Dr. rer. nat. According to our current on-linedatabase, ruth moufang has 20 students and 82 descendants. http://www.genealogy.ams.org/html/id.phtml?id=34257

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