Contents 1 Introduction 1.1 Proposals 1.1.1 Initial Proposal 1.1.2 Revised Proposal 1.2 Resources 1.3 Bibliographies 1.3.1 Bibliography 1.3.2 Tangential-Bibliography 1.3.3 Non-Bibliography 1.3.4 Yet-to-be-determined Bibliography 2 (Some) Research 2.1 Nineteenth Century Mathematicians and their Mathematics 3 Discussion 3.1 Communication 3.2 Thoughts

[edit] Introduction

This page reflects the progress of Matthew Reyna's independent study in the German program. In addition to providing a tangible record of my work, this page offers the means for regular review and facilitated communication within the Wiki environment. In particular, this site offers the independent study proposal, a working bibliography, and a collection of resources; most of this is currently under construction.

For now, this page is informal: there is an attention to but not an enforcement of spelling, grammar, and other conventions. This should facilitate contribution and review.

[edit] Proposals

[edit] Initial Proposal

The objective of this independent study is to lay the foundations for substantial research regarding mathematics and German. This two-semester endeavor naturally prepares for and leads into a senior honors thesis.

The results of the first semester, one-credit hour independent study will be the cultivation of a cross-disciplinary faculty involvement, the creation of a working bibliography, and the inception of a rudimentary lexicon of mathematics. The results of the second semester, two-credit hour independent study will be a tenable statement of thesis for a research paper, the development of a working bibliography, and the maturation of an original, self-written lexicon of mathematics.

Frequent communication with faculty will facilitate counsel for and review of my work. Weekly meetings with German and/or mathematics faculty and regular e-mail correspondence with my adviser will characterize the first semester of research, while biweekly meetings with faculty and regular e-mail correspondence with my adviser will characterize the second semester. Shorter, more frequent meetings of less than an hour will naturally progress into longer, more periodic meetings of approximately two hours when writing the lexicon takes the forefront of my efforts.

The accomplishments of each semester of independent study will be individually tangible. In particular, the results of the first semester of study will provide a basis for the later study of mathematics in German, and the results of the second semester of study will not only extend this basis but also incorporate linguistic, historical, and other cultural aspects of German, Germany, and the Germans as they relate to the appreciation of mathematics. Above all, the outcome of this two-semester undertaking has not only potential for further study but also sufficient merit of its own.

[edit] Revised Proposal

The objective of this independent study is the appreciation of "German" mathematics during the nineteenth century -- where German is understood in a broad but distinctly cultural sense. In general, I am interested in the interaction between German and mathematics during the nineteenth century; in particular, I am interested in the rise, fall, and intermediary heyday of German mathematics during the nineteenth and early twentieth centuries and the contributions of German mathematics to the abstraction and formalization of mathematics, especially in the areas of complex numbers, probability, group theory, set theory, algebra, analysis, and non-Euclidean geometry. This understanding of mathematics transcends national borders, but it is not timeless -- I am interested in the historical undercurrent of the times whenever it and mathematics are intertwined.

Counsel for and review of my work will occur through frequent faculty interaction. This site will facilitate communication with faculty and others. Weekly meetings with my adviser and correspondence with German and/or mathematics faculty as helpful will characterize the first semester of research, while biweekly meetings with my adviser and correspondence with faculty as helpful will characterize the second semester. Shorter, more frequent meetings will naturally progress into longer, more periodic meetings as my work grows more autonomous.

The accomplishments of each semester of independent study should be developing but individually tangible. In particular, the results of the first semester of study will provide a basis for the later study of mathematics in German, and the results of the second semester of study will not only extend this basis but also incorporate linguistic, historical, and other cultural aspects of German, Germany, and the Germans as they relate to the appreciation of mathematics. Above all, the outcome of this two-semester undertaking has not only potential for further study but also sufficient merit of its own.

[edit] Resources

The OCLC WorldCAT database features over 57,000,000 records of materials from over 400 languages -- but no request capabilities. I should admit that I was confused by this at first, but I asked a librarian for help. Two librarians responded, giving the following (paraphrased) advice:

(1) Search for items on a database, either on WorldCAT or one of the below databases.

(2) Search for the desired items on EuclidPLUS. If they are available, then pick them up at Kelvin Smith Library. Otherwise,

(3) Search for the desired items on OhioLINK. If they are available, request delivery at Kelvin Smith Library or another library of choice. Otherwise,

(4) Search for the desired items on ILLiad. If they are available, request delivery at Kelvin Smith Library or another library of choice.

Thanks to Janet Fowler and Karen Oye of Kelvin Smith Library for their prompt and helpful responses.

[edit] Bibliographies

[edit] Bibliography

Buckmire, Ron. "NUMB3RS: The Intersection between Mathematics and Hollywood is Not Empty." math Horizons. Sept. 2005: 10, 12.

Durham, William. Journey through Genius: The Great Theorems of Mathematics. New York: John Wiley & Sons, Inc., 1990.

Gerhardt, C. J. Geschichte der Mathematik in Deutschland. Munich: Oldenbourg, 1877. Rpt. 1965.

James, Glenn and Robert C. James, eds. Mathematics Dictionary: Multilingual Edition. Princeton: D. Van Nostrand Company, Inc., 1959.

Klaften, Berthold. Mathematisches Vokabular. München, Verlag für Wirtschaftswerbung, 1961.

Kolmogorov, A.N. and A.P. Yushkevich. Mathematics of the 19th Century. Basel: Birkhäuser Verlag: 2001.

O'Connor, John and Edmund Robertson. Birthplace Maps Index. Aug 2001. School of Mathematics and Statistics, University of St. Andrews, Scotland. 25 Oct. 2005. <http://www-history.mcs.st-andrews.ac.uk/BirthplaceMaps/MapIndex.html>.

Comment: The map of German and European birth places may, in particular, be useful to the complex anthropological issue of German ethnicity and the even thornier issue of German mathematical ethnicity [above].

O'Connor, John and Edmund Robertson. MacTutor History of Mathematics archive, The. Aug. 2005. School of Mathematics and Statistics, University of St. Andrews, Scotland. 25 Oct. 2005. <http://www-history.mcs.st-andrews.ac.uk/index.html>.

Comment: The University of St Andrews runs a helpful website [above].

Pfeil, Traute. Mathematischer Fachwortschatz. Jena: Friedrich-Schiller-Universität, 1980.

Pierpont, James. "History of Mathematics in the Nineteenth Century, The". 21 Dec. 1999. Bulletin (New Series) of the American Mathematical Society. Volume 37, Number 1, Pages 9-24. S 0273-0979(99)00804-6. 6, Nov. 2005. <http://www.ams.org/bull/2000-37-01/S0273-0979-99-00804-6/S0273-0979-99-00804-6.pdf>

Rosenberg, Adam. "Another Mathematician Looks at NUMB3RS." math Horizons. Sept. 2005: 11-12.

Siegmund-Schultze, Reinhard. Rockefeller and the Internationalization of Mathematics Between the Two World Wars. Basel: Birkhäuser, 2001.

Yun, Jae, et al. The Nineteenth - Century Mathematics of Germany - Modern Mathematics. Moon Young Academy. 7 Nov. 2005. <http://seoul-gchs.seoul.kr/~contest/tq/mathematics/emh1700.htm>.

[edit] Tangential-Bibliography

The following items kind-of made the cut. I determined that they were probably outside the scope of my research, but I am keeping track of them because they are tangentially related or because they are just plain interesting.

Fadiman, Clifton. Fantasia mathematica. New York: Copernicus, 1997.

[edit] Non-Bibliography

The following items just did not make the cut. I determined that they were outside the scope of my research, but I am keeping track of them in case the scope of my research changes and so that I do not accidentally browse through them again. These items are listed without the conventions of citations because they are not part of the "official" bibliography.

Orlov, V.B., et al. Russko-anglo-nemetsko-frantsuzskii matematicheskii slovar : osnovnye terminy. Moskva: Russkii iazyk, 1987.

[edit] Yet-to-be-determined Bibliography

The following books are awaiting evaluation and eventual placement in either of the above bibliography sections. These items are listed without the conventions of citations because they are not part of the "official" bibliography.

[edit] (Some) Research

The following is (some) research that I have posted on the Wiki.

[edit] Nineteenth Century Mathematicians and their Mathematics

To be written.

[edit] Discussion

The following is interaction in the Wiki environment. Anyone is welcome to post.

[edit] Communication

Monday, 3 October 2005:

Question for M. Reyna: When did German replace Latin as the language for mathetmatical texts and teaching?

FYI: Marie-Sophie Germain was the woman who used a pseudonym to hide her gender. The male mathematician with whom she corresponded was Lagrange.

Questions on cultural identity: is Bolyai a German mathematician? An important if not the most important part of his mathematical education was in Goettingen (German speaking) where he met Gauss, with whom he continued to correspond. Can Abel be considered a German mathematician? He was Norwegian at a time when there was no nation of Norway and published at least some articles in French.

Sunday, 9 October 2005:

Question: When did German replace Latin as the language for mathematical texts and teaching?

Response: The simple answer is the early 1800s. The German mathematician Carl Friedrich Gauss wrote in Latin at least as late as the early 1800s in his Disquisitiones Arithmeticae, and the German mathematician Georg Friedrich Bernhard Riemann wrote in German at least as early as the mid 1800s in his Über die Anzahl der Primzahlen unter einer gegebenen Grösse. New mathematicians, and not merely new decades, are inevitably responsible for the change of language for mathematical publication and instruction, so the cultural, historical, and other factors that produced these new generations are of essential importance. Accordingly, the better answer is more complicated but more interesting. Of course, there will be more on this topic later.

Question: Is Bolyai a German mathematician? An important if not the most important part of his mathematical education was in Goettingen (German speaking) where he met Gauss, with whom he continued to correspond.

Response: Bolyai also studied in Vienna. From my perspective, the question of whether Bolyai, or any mathematician, is or is not German is richer than simple nationality. I think that the question has a reciprocal relationship between the mathematics and the mathematician: how was Bolyai influenced by mathematics (by his Hungarian father, the Viennese university where he studied, the German mathematician Gauss with whom he corresponded, etc.) and how did Bolyai influence mathematics (with a treatise written in Vienna, etc.). I agree, even if Bolyai was not born German, German is at least part of both equations.

Question: Can Abel be considered a German mathematician? He was Norwegian at a time when there was no nation of Norway and published at least some articles in French.

Response: I think that the same consideration of German influence on Abel and Abel's influence on German applies here. Abel grew up in Norway, studied briefly in German, and studied even more briefly in France before his death. While the most of his education occurred in Oslo, the pinnacle of his mathematical study occurred in Berlin and Freiberg, and his most memorable contributions to the field of mathematics (some of which have trickled into my abstract algebra course) occurred in Freiberg; he was so under appreciated and hardly known in France that he sought appointment in Germany. More than for Bolyai, Bolyai seems to have enjoyed a substantial contribution from and to German mathematics.

Comment: I understand that Wikipedia, as an anonymous source of user contributions, is not something from which papers are written, but I think that it is reliable enough to guide research into something more substantial, i.e., good for guidance, bad for citation.

[edit] Thoughts

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