Leila Schneps (born December 22, 1961) is an American mathematician, living in France, employed by Centre national de la recherche scientifique, and based at the Institut de Mathématiques de Jussieu of Pierre and Marie Curie University, France, where she specializes in number theory. In addition to academic publication, she has edited several text books on aspects of mathematics, written a popular book and articles on the use and abuse of mathematics in criminal proceedings, and, under the pseudonym Catherine Shaw, written a series of mathematically themed murder mysteries.
|Born||December 22, 1961|
Waltham, Massachusetts, United States
|Pen name||Catherine Shaw|
|Alma mater||University of Paris|
Schneps earned a B.A. in Mathematics, German Language and Literature from Harvard/Radcliffe University in 1983, then took up graduate studies in France. She completed a Doctorat de Troisième Cycle in Mathematics at Université Paris-Sud XI-Orsay in 1985, with a thesis studying p-adic L-functions attached to elliptic curves, a Ph.D. in Mathematics in 1990, with a thesis on p-Adic L-functions and Galois groups, and Habilitation at Université de Franche-Comté in 1993, with a thesis on the Inverse Galois problem.
Schneps held various teaching assistant positions in France and Germany until the completion of her Ph.D. in 1990, then worked as a postdoctoral assistant at the ETH in Zurich, Switzerland for one year. In 1991 she was awarded a tenured research position at CNRS, the French National Centre for Scientific Research, at the University of Franche-Comté in Besançon, where she still works. During the late 1990s Schneps also had short-term visiting researcher assignments at Harvard University, Princeton's Institute for Advanced Study, and MSRI at Berkeley.
Schneps has published academic papers on various aspects of analytic number theory since the late 1980s. Her early work explored p-Adic L-functions, which became the topic of her first thesis, and she continues to work on the related fields of zeta functions.
Since the late 1990s she focused on aspects of Galois theory, including Galois groups, geometric Galois actions, and the inverse Galois problem, and has been called, by one mathematics professor, "the arithmetic geometer . . . who taught me most of what I know about Galois actions on fundamental groups of varieties". Her work led to her study of the related Grothendieck–Teichmüller group, and she has become a member of a group preserving the works and history of Grothendieck. Her most recent work has investigated various aspects of Lie algebras.
Schneps has also edited and contributed to several mathematics textbooks in number theory. She edited a series of lecture notes on Grothendieck's theory of dessins d'enfants and contributed an article to the series, was an editor for a text on the Inverse Galois Problem, and edited a book on Galois groups. She was a co-author of a text on Field Theory and co-editor of another on Galois–Teichmüller Theory.
Schneps' latest book is Math on Trial: How Numbers Get Used and Abused in the Courtroom, which she co-authored with her daughter, mathematician Coralie Colmez. This book, targeted for a general audience, uses 10 historical legal cases to show how mathematics, especially statistics, can affect the outcome of criminal proceedings, especially when incorrectly applied or interpreted. While not written as a textbook, some reviewers have found it suitable for students, as an introduction to the topic and to "get them thinking, talking and even arguing about the issues involved", with another agreeing that, "they have struck the right balance of providing enough mathematics for the specialist to check out the details, but not so much as to overwhelm the general reader", and another finding the book suitable "for parents trying to support teenagers in their studies of mathematics – or in fact, law".
While most reviews are positive, there has been some criticism concerning its over-simplification of mathematics' influence in complex trial proceedings. One reviewer finds that, while the book's description of the weakness of some mathematics presented in courtrooms is valid, that the text magnifies mathematics' role in legal proceedings, which traditionally feature evidentiary analysis at appellate as well as trial stages and have preexisting standards for treating certain types of evidence. Another suggests the book influenced by the authors' selection of cases to show a "disastrous record of causing judicial error", thus attributing insufficient weight to the counterbalancing traditionally inherent in legal proceedings—as lawyers attack opposing evidence and experts with their own, and appellate judges write to influence the conduct of trial judges faced with various types of ordinary and expert testimony.
Schneps has produced English-language translations of several French-language books and papers, including Invitation to the mathematics of Fermat-Wiles, Galois theory, A Mathematician Grappling With His Century, Hodge Theory and Complex Algebraic Geometry II, p-adic L-Functions and p-Adic Representations, and Renormalization methods : critical phenomena, chaos, fractal structures.
Alexander Grothendieck, author of the theories upon which some of the above works are based, became a recluse in 1991 and removed his published works from circulation. More than a decade later, Schneps and Pierre Lochak located him in a town in the Pyrenees, then carried on a correspondence. Thus they became among "the last members of the mathematical establishment to come into contact with him". Schneps became a founding member of the Grothendieck Circle, a group dedicated to making information by and about Grothendieck available, and created and maintains the Grothendieck Circle website, a repository of information regarding Grothendieck, including his own unpublished writings. She also assisted with the translation of his correspondence with Jean-Pierre Serre.
As Catherine ShawEdit
In 2004, new author Catherine Shaw published The Three Body Problem, a Cambridge Mystery, a murder mystery novel involving mathematicians in Cambridge in the late 1800s, working on the three-body problem. The title is a double entendre, referring to both the mathematical problem and the three murder victims. While a mathematician reviewing the book disliked the Victorian writing style, he found the math accurate, and the mathematicians' personalities and sociology "well portrayed". When another reviewer contacted the author, she confirmed that Catherine Shaw was a pseudonym and that she was, in reality, an academic and practicing mathematician but preferred to remain anonymous. It has since been revealed that Catherine Shaw is the pseudonym of Leila Schneps.
Schneps, as Catherine Shaw, has published four more historical novels in the series, all featuring the same main character Vanessa Duncan, and all following mathematical themes:
- Flowers Stained with Moonlight was called a mystery that was "very easy to solve", as the book's title is from a poem by Lord Alfred Douglas, which strongly hits at the solution to the crime.
- The Library Paradox also has a double entendre title, as the story is a classic locked room mystery set in a library, but also alludes to Russell's paradox, which arises from the question of whether a library catalog should include itself in its contents. The murder victim in the story was antisemitic, and the story mentions the Dreyfus affair and explores the issues of "being Jewish in 1896 London".
- The Riddle of the River explores "the theatre world, the late 19th century craze for séances, [and] the Marconi revolution which will lead to the invention of the telegraph".
- Finally, Fatal Inheritance explores "the importance of heredity and how it might influence the nation's health; Dr Freud's latest theories; and . . . the dubious 'science' of eugenics".
Seminars and lecturesEdit
Schneps lectures and presents at mathematics conferences and seminars. In 2004 she gave talks on the Grothendieck–Teichmüller group, on curve complexes, tensor categories, and fundamental groupoids, and on Lie algebras, at a workshop at the American Institute of Mathematics in Palo Alto; she gave a series of lectures on Grothendieck–Teichmüller theory at the Massachusetts Institute of Technology in 2012; and she presented talks on Grothendieck–Teichmüller theory, Lie algebras, and moduli spaces of curves in 2009 and 2013 at the Isaac Newton Institute for Mathematical Sciences in Cambridge. As part of the 2014 Sampson Lectures at Bates College, she gave a technical talk on Multiple Zeta Values and a general-level talk based on her book Math on Trial.
Schneps promotes public awareness of the importance of the proper use of mathematics and statistics in criminal proceedings. In addition to her book on the subject, she has written newspaper articles and she is a member of the Bayes and the Law International Consortium.
- Leila Schneps, 2014, Mathematics Genealogy Project, retrieved 2013-12-22
- Schneps, Leila (January 1987), "On the μ-invariant of p-adic L-functions attached to elliptic curves with complex multiplication", Journal of Number Theory, 25 (1): 20–33, doi:10.1016/0022-314X(87)90013-8, ISSN 0022-314X
- Fonctions l p-adiques, et construction explicite de cetains groupes comme groupes de galois, Theses.fr, January 1990, retrieved 2013-12-23
- Schneps; Henniart (1990), Fonctions L p-Adiques, et Construction Explicite de Cetains Groupes Comme Groupes de Galois, [S.l.]: Université Paris Sud, retrieved 2013-12-18
- Archives des habilitations à diriger des recherches (HDR) soutenues au LMB [Archive of Habilitations supported at the LMB], Laboratoire de mathématiques de besançon, retrieved 2014-01-01
- Schneps, Leila, Curriculum Vitae (PDF), retrieved 2013-12-22
- Grants Awarded in 1998, France Berkeley Fund, archived from the original on 2014-03-09, retrieved 2014-01-02
- Colmez, Pierre; Schneps, Leila (1992), "p-adic interpolation of special values of Hecke L-functions" (PDF), Compositio Mathematica, 82 (2): 143–187, retrieved 2014-01-02
- Brown, Francis; Carr, Sarah; Schneps, Leila (2010), "The algebra of cell-zeta values", Compositio Mathematica, 146 (3): 731–771, arXiv:0910.0122, Bibcode:2009arXiv0910.0122B, doi:10.1112/S0010437X09004540
- Schneps, Leila.; Lochak, P. (1997), 2. The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups, London Mathematical Society lecture note series ; 242-243, Cambridge ; New York: Cambridge University Press, ISBN 9780521596411
- Ellenberg, Jordan (2013-03-28), Math on Trial, by Leila Schneps and Coralie Colmez, 2014, retrieved 2013-12-30
- Harbater, David; Schneps, Leila (2000), "Fundamental groups of moduli and the Grothendieck–Teichmüller group" (PDF), Trans. Amer. Math. Soc., 352 (7): 3117–3149, doi:10.1090/S0002-9947-00-02347-3, ISSN 0002-9947, retrieved 2013-12-31
- Lochak, Pierre; Schneps, Leila (2006), "Open problems in Grothendieck–Teichmüller theory", Proceedings of Symposia in Pure Mathematics, 75: 165–186, CiteSeerX 10.1.1.511.6401, doi:10.1090/pspum/074/2264540, ISBN 9780821838389
- Lochak, Pierre; Schneps, Leila (2013), "Grothendieck–Teichmüller groups", Grothendieck–Teichmüller Groups, Deformation and Operads, retrieved 2014-01-02
- Schneps, Leila (2003), "Fundamental groupoids of genus zero moduli spaces and braided tensor categories", Moduli Spaces of Curves, Mapping Class Groups and Field Theory, SMF/AMS Texts and Monographs, ISBN 978-0-8218-3167-0, retrieved 2014-01-02
- Schneps, Leila (2012-01-25), Double Shuffle and Kashiwara–Vergne Lie algebras, arXiv:1201.5316, Bibcode:2012arXiv1201.5316S
- Baumard, Samuel; Schneps, Leila (2011-09-17), "Period polynomial relations between double zeta values", The Ramanujan Journal, 32: 83–100, arXiv:1109.3786, Bibcode:2011arXiv1109.3786B, doi:10.1007/s11139-013-9466-2
- Baumard, Samuel; Schneps, Leila (2013), Relations dans l'algèbre de Lie fondamentale des motifs elliptiques mixtes, arXiv:1310.5833, Bibcode:2013arXiv1310.5833B
- Schneps, Leila (1994), "The Grothendieck Theory of Dessins D'Enfants", Lecture Note Series, london: Cambridge University PRess, 200, ISBN 9780521478212
- Schneps, Leila (1994), "Dessins d'enfants on the Riemann Sphere" (PDF), The Grothendieck Theory of Dessins d'Enfants, 200: 47–78, doi:10.1017/CBO9780511569302.004, ISBN 9780511569302
- Schneps, Leila (2003), Galois groups and fundamental groups, Mathematical Sciences Research Institute publications ; 41, Cambridge, U.K. ; New York: Cambridge University Press, ISBN 978-0521808316
- Buff, Xavier; Fehrenbach, Jérôme; Lochak, Pierre; Schneps, Leila; Vogel, Pierre (2003), Moduli Spaces of Curves, Mapping Class Groups and Field Theory, 9, AMS and SMF, ISBN 978-0-8218-3167-0
- Nakamura, Hiroaki; Pop, Florian; Schneps, Leila; et al., eds. (2012), Galois–Teichmüller Theory and Arithmetic Geometry, 63, Tokyo: Kinokuniya, ISBN 978-4-86497-014-3
- Schneps, Leila; Colmez, Coralie (2013), Math on Trial: How Numbers Get Used and Abused in the Courtroom, New York: Basic Books, ISBN 978-0465032921
- Hayden, Robert (2013-12-24), "Math on Trial: How Numbers Get Used and Abused in the Courtroom", MAA Reviews
- Hill, Ray (September 2013). "Review: Math on Trial" (PDF). Newsletter of London Mathematical Society. 428. London Mathematical Society. Retrieved 2014-02-08.
- Tarttelin, Abigail (2013). "Book Review: Math On Trial by Leila Schneps and Coralie Colmez". Huffington Post Blog. Retrieved 2014-02-08.
- Finkelstein, Michael (Jul–Aug 2013), "Quantitative Evidence Often a Tough Sell in Court" (PDF), SIAM News, 46 (6)
- Edelman, Paul (2013), "Burden of Proof: A Review of Math on Trial" (PDF), Notices of the American Mathematical Society, 60 (7): 910–914, doi:10.1090/noti1024, retrieved 2013-12-22
- Hellegouarch, Yves (2002), Invitation to the Mathematics of Fermat-Wiles, London: Academic Press, ISBN 978-0-12-339251-0
- Escofier, Jean-Pierre. (2001), Galois theory, Graduate texts in mathematics ; 204, New York: Springer, ISBN 978-0387987651, retrieved 2013-12-30
- Schwartz, Laurent. (2001), A mathematician grappling with his century, Basel ; Boston: Birkhäuser, ISBN 978-3764360528
- Voisin, Claire (2002), Hodge theory and complex algebraic geometry, Cambridge studies in advanced mathematics ; 76-77, Cambridge ; New York: Cambridge University Press, ISBN 978-0521802833
- Perrin-Riou, Bernadette. (2000), p-adic L-functions and p-adic representations, SMF/AMS texts and monographs, v. 3, Providence, RI: American Mathematical Society, ISBN 978-0821819463
- Lesne, Annick. (1998), Renormalization methods : critical phenomena, chaos, fractal structures, Chichester ; New York: J. Wiley, ISBN 978-0471966890
- Leith, Sam (2004-03-20), "The Einstein of maths", The Spectator, retrieved 2014-01-03
- Grothendieck, A.; Serre, Jean-Pierre (2004), Grothendieck–Serre correspondence, Providence, R.I.: American Mathematical Society, ISBN 9780821834244
- Shaw, Catherine (2005), The three body problem : a Cambridge mystery, Long Preston, ISBN 978-0750522892
- Montgomery, Richard (October 2006), "The Three Body Problem, A Cambridge Mystery" (PDF), Notices of the American Mathematical Society, 53 (9): 1031–1034
- Kasman, Alex (2004), "The Three Body Problem", Mathematical Fiction, retrieved 2013-12-31
- Shaw, Catherine, 1961-, Library of Congress, 2009
- Shaw, Catherine (2005), Flowers stained with moonlight, London: Allison & Busby, ISBN 978-0749083083
- Douglas, Lord Alfred (1984), "Two Loves", The Chameleon, 1 (1)
- Nesvet, Rebecca (May 2005), Review: Flowers Stained with Moonlight
- Shaw, Catherine. (2007), The library paradox, London: Allison & Busby, ISBN 9780749080105
- Gill, Sunnie (July 2007), Review: The Library Paradox
- Kasman, Alex, Review: The Library Paradox, Mathematical Fiction
- Shaw, Catherine (2009), The riddle of the river, New York: Felony & Mayhem Press, ISBN 9781934609330
- Review: The Riddle of the River, Historical Novel Society, 2013-12-30
- Shaw, Catherine (2013), Fatal Inheritance, Allison & Busby, ISBN 978-0749013226
- Review: Fatal Inheritance, Hisotircal Novel Society, 2013
- Shaw, Catherine (2007), How To Solve Sudoko & Kakuro, Allison & Busby
- Schneps, Leila (2004-04-23), "The Grothendieck Teichmüller Group" (PDF), Lectures at AIM, retrieved 2014-01-03
- Schneps, Leila (2004-04-23), "Curve Complexes, Tensor Categories, Fundamental Groupoids" (PDF), Lectures at AIM, retrieved 2014-01-03
- Schneps, Leila (2004-04-23), "Five Lie Algebras" (PDF), Lectures at AIM, retrieved 2014-01-03
- "Theory of motives, homotopy theory of varieties, and dessins d'enfants", Lectures at AIM, 2004-04-23, retrieved 2014-01-03
- Schneps, Leila (2012), An introduction to Grothendieck–Teichmüller theory, MIT
- Schneps, Leila (2009-10-06), "Relations between multi-zeta values and Grothendieck–Teichmueller theory", Non-Abelian Fundamental Groups in Arithmetic Geometry
- Schneps, Leila (2013-04-12), Elliptic Grothendieck–Teichmueller theory, Isaac Newton Institute for Mathematical Sciences
- Lochak, Pierre; Schneps, Leila (2013), "Grothendieck–Teichmüller groups", Grothendieck–Teichmüller Groups, Deformation and Operads
- Schneps, Leila; Lochak, Pierre (2013-02-27), "Lie algebras I", Grothendieck–Teichmüller Groups, Deformation and Operads
- Lochak, Pierre; Schneps, Leila (2013-02-20), "Moduli spaces of curves, curve complexes", Grothendieck–Teichmüller Groups, Deformation and Operads
- "Lectures to feature a mystery-writing mathematician and a noted inventor". Bates College. 2014-02-25. Retrieved 2014-03-03.
- Schneps, Leila; Colmez, Coralie (2013-03-26), "Justice Flunks Math", The New York Times, The Opinion Pages
- Fenton, Norman (2013-12-30), Bayes and the Law