Leila Schneps
Pen nameCatherine Shaw
  • Mathematician
  • Author
  • English
  • French
  • German
Alma materUniversity of Paris
ChildrenCoralie Colmez

Leila Schneps is an American mathematician and fiction writer at the Centre national de la recherche scientifique working in number theory. Schneps has written general audience math books and, under the pen name Catherine Shaw, has written mathematically themed murder mysteries.


Schneps earned a B.A. in Mathematics, German Language and Literature from Radcliffe College in 1983.[1] She completed a Doctorat de Troisième Cycle in Mathematics at Université Paris-Sud XI-Orsay in 1985 under the supervision of John H. Coates with a thesis on p-adic L-functions attached to elliptic curves,[2][3] a Ph.D. in Mathematics in 1990 with a thesis on p-Adic L-functions and Galois groups,[4][5] and Habilitation at Université de Franche-Comté in 1993, with a thesis on the Inverse Galois problem.[6][1]

Professional experience

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.[1] 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.[7]



Schneps has published academic papers on various aspects of analytic number theory since the late 1980s. Her early work explored p-adic L-functions,[8] which became the topic of her first thesis, and around 2010 she was continuing to work on the related fields of zeta functions.[9]

Since the late 1990s she focused on aspects of Galois theory, including Galois groups, geometric Galois actions, and the inverse Galois problem,[10] and has been described by Jordan Ellenberg as "the arithmetic geometer . . . who taught me most of what I know about Galois actions on fundamental groups of varieties".[11] Her work led to her study of the related Grothendieck–Teichmüller group,[12][13][14][15] and she has become a member of a group preserving the works and history of Grothendieck. In the early 2010s she published research investigating various aspects of Lie algebras.[16][17][18]


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[19] and contributed an article to the series,[20] was an editor for a text on the Inverse Galois Problem,[10] and edited a book on Galois groups.[21] She was a co-author of a text on Field Theory[22] and co-editor of another on Galois–Teichmüller Theory.[23]

In 2013, Schneps and her daughter, mathematician Coralie Colmez, published the book Math on Trial: How Numbers Get Used and Abused in the Courtroom.[24] Targeted at a general audience, the book uses ten historical legal cases to show how mathematics, especially statistics, can affect the outcome of criminal proceedings, especially when incorrectly applied or interpreted. The mathematical concepts covered include statistical independence (discussed using the examples of the Sally Clark case and the murder of Meredith Kercher), Simpson's paradox (UC Berkeley gender bias case) and statistical modeling using a binomial distribution (Howland will forgery trial).[24]

While not written as a textbook, some reviewers found it suitable for students, as an introduction to the topic and to "get them thinking, talking and even arguing about the issues involved",[25] 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",[26] and another finding the book suitable "for parents trying to support teenagers in their studies of mathematics – or in fact, law".[27]

While most reviews were positive, there was 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, 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.[28] Another suggests the book was 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.[29]


Schneps has produced English-language translations of several French-language books and papers, including Invitation to the mathematics of Fermat-Wiles,[30] Galois theory,[31] A Mathematician Grappling With His Century,[32] Hodge Theory and Complex Algebraic Geometry II,[33] p-adic L-Functions and p-Adic Representations,[34] and Renormalization methods : critical phenomena, chaos, fractal structures.[35]

Grothendieck Circle

Mathematician Alexander Grothendieck 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".[36] 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.[37] She also assisted with the translation of his correspondence with Jean-Pierre Serre.[38]

Fiction writing

In 2004, Schneps published (as Catherine Shaw) The Three Body Problem, a Cambridge Mystery,[39] 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".[40] When another reviewer contacted the author, she confirmed that Catherine Shaw was a pseudonym and that she was actually an academic and practicing mathematician but preferred to remain anonymous.[41] It has since been revealed that Catherine Shaw is the pseudonym of Leila Schneps.[42]

Schneps, as Catherine Shaw, has published four historical novels in the series, all featuring the same main character Vanessa Duncan, and all following mathematical themes:

As Shaw, Schneps has also published a non-fiction guide to solving Sudoku and Kakuro puzzles.[53]


Schneps promotes public awareness of the importance of the proper use of mathematics and statistics in criminal proceedings.[24][54] Schneps is a member of the Bayes and the Law International Consortium.[55]

Personal life

Coralie Colmez is the daughter of Schneps and Pierre Colmez.[56][57]


  1. ^ a b c Schneps, Leila, Curriculum Vitae (PDF), retrieved 2013-12-22
  2. ^ Leila Schneps, 2014, Mathematics Genealogy Project, retrieved 2013-12-22
  3. ^ 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
  4. ^ Fonctions l p-adiques, et construction explicite de cetains groupes comme groupes de galois, Theses.fr, January 1990, retrieved 2013-12-23
  5. ^ 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
  6. ^ 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
  7. ^ Grants Awarded in 1998, France Berkeley Fund, archived from the original on 2014-03-09, retrieved 2014-01-02
  8. ^ 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
  9. ^ 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, S2CID 16250943
  10. ^ a b 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
  11. ^ Ellenberg, Jordan (2013-03-28), Math on Trial, by Leila Schneps and Coralie Colmez, 2014, retrieved 2013-12-30
  12. ^ 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
  13. ^ Lochak, Pierre; Schneps, Leila (2006), "Open problems in Grothendieck–Teichmüller theory", Proceedings of Symposia in Pure Mathematics, 75: 165–186, CiteSeerX, doi:10.1090/pspum/074/2264540, ISBN 9780821838389
  14. ^ Lochak, Pierre; Schneps, Leila (2013), "Grothendieck–Teichmüller groups", Grothendieck–Teichmüller Groups, Deformation and Operads, archived from the original on 2014-03-09, retrieved 2014-01-02
  15. ^ 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
  16. ^ Schneps, Leila (2012-01-25), Double Shuffle and Kashiwara–Vergne Lie algebras, arXiv:1201.5316, Bibcode:2012arXiv1201.5316S
  17. ^ 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, S2CID 55057070
  18. ^ Baumard, Samuel; Schneps, Leila (2013), Relations dans l'algèbre de Lie fondamentale des motifs elliptiques mixtes, arXiv:1310.5833, Bibcode:2013arXiv1310.5833B
  19. ^ Schneps, Leila (1994), "The Grothendieck Theory of Dessins D'Enfants", Lecture Note Series, london: Cambridge University PRess, 200, ISBN 9780521478212
  20. ^ 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
  21. ^ 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
  22. ^ 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
  23. ^ 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
  24. ^ a b c Schneps, Leila; Colmez, Coralie (2013), Math on Trial: How Numbers Get Used and Abused in the Courtroom, New York: Basic Books, ISBN 978-0465032921
  25. ^ Hayden, Robert (2013-12-24), "Math on Trial: How Numbers Get Used and Abused in the Courtroom", MAA Reviews
  26. ^ Hill, Ray (September 2013). "Review: Math on Trial" (PDF). Newsletter of London Mathematical Society. 428. London Mathematical Society. Retrieved 2014-02-08.[permanent dead link]
  27. ^ Tarttelin, Abigail (2013). "Book Review: Math On Trial by Leila Schneps and Coralie Colmez". Huffington Post Blog. Retrieved 2014-02-08.
  28. ^ Finkelstein, Michael (Jul–Aug 2013), "Quantitative Evidence Often a Tough Sell in Court" (PDF), SIAM News, 46 (6), archived from the original (PDF) on 2016-04-16, retrieved 2014-03-09
  29. ^ 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
  30. ^ Hellegouarch, Yves (2002), Invitation to the Mathematics of Fermat-Wiles, London: Academic Press, ISBN 978-0-12-339251-0
  31. ^ Escofier, Jean-Pierre. (2001), Galois theory, Graduate texts in mathematics, 204, New York: Springer, ISBN 978-0387987651, retrieved 2013-12-30
  32. ^ Schwartz, Laurent. (2001), A mathematician grappling with his century, Basel ; Boston: Birkhäuser, ISBN 978-3764360528
  33. ^ 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
  34. ^ 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
  35. ^ Lesne, Annick. (1998), Renormalization methods : critical phenomena, chaos, fractal structures, Chichester ; New York: J. Wiley, ISBN 978-0471966890
  36. ^ Leith, Sam (2004-03-20), "The Einstein of maths", The Spectator, retrieved 2014-01-03
  37. ^ "Grothendieck Circle". www.grothendieckcircle.org. Retrieved 2019-12-26.
  38. ^ Grothendieck, A.; Serre, Jean-Pierre (2004), Grothendieck–Serre correspondence, Providence, R.I.: American Mathematical Society, ISBN 9780821834244
  39. ^ Shaw, Catherine (2005), The three body problem : a Cambridge mystery, Long Preston, ISBN 978-0750522892
  40. ^ Montgomery, Richard (October 2006), "The Three Body Problem, A Cambridge Mystery" (PDF), Notices of the American Mathematical Society, 53 (9): 1031–1034
  41. ^ Kasman, Alex (2004), "The Three Body Problem", Mathematical Fiction, retrieved 2013-12-31
  42. ^ Shaw, Catherine, 1961-, Library of Congress, 2009
  43. ^ Shaw, Catherine (2005), Flowers stained with moonlight, London: Allison & Busby, ISBN 978-0749083083
  44. ^ Douglas, Lord Alfred (1984), "Two Loves", The Chameleon, 1 (1)
  45. ^ Nesvet, Rebecca (May 2005), Review: Flowers Stained with Moonlight
  46. ^ Shaw, Catherine. (2007), The library paradox, London: Allison & Busby, ISBN 9780749080105
  47. ^ Gill, Sunnie (July 2007), Review: The Library Paradox
  48. ^ Kasman, Alex, Review: The Library Paradox, Mathematical Fiction
  49. ^ Shaw, Catherine (2009), The riddle of the river, New York: Felony & Mayhem Press, ISBN 9781934609330
  50. ^ Review: The Riddle of the River, Historical Novel Society, 2013-12-30
  51. ^ Shaw, Catherine (2013), Fatal Inheritance, Allison & Busby, ISBN 978-0749013226
  52. ^ Review: Fatal Inheritance, Hisotircal Novel Society, 2013
  53. ^ Shaw, Catherine (2007), How To Solve Sudoko & Kakuro, Allison & Busby
  54. ^ Schneps, Leila; Colmez, Coralie (2013-03-26), "Justice Flunks Math", The New York Times, The Opinion Pages
  55. ^ Fenton, Norman (2013-12-30), Bayes and the Law
  56. ^ "Allow me to explain, Your Honour". The Economist. 2 May 2013. Retrieved 2 October 2020.
  57. ^ Tsui, Diana (9 January 2018). "The Mathematician Who Moonlights As a Rock-Band Violinist". The Cut. Retrieved 2 October 2020.