Photo of Jeff Oaks

Jeffrey A. Oaks

Professor and chair

Mathematics and Computer Science

Visiting professor, École des Hautes Études en Sciences Sociales (Paris, France) March 2014.

Office:  Lilly Science Hall 213


Phone: 317-788-3454

Ph.D. in mathematics (differential geometry) 1991, University of Rochester


Schedule for Winter 2014

MATH 380 Modern Geometries MWF 9:00-9:50 in LSH 308.

Research interests

History of Mathematics (mainly medieval Arabic algebra)


(to appear) (with Mahdi Abdeljaouad) "Al-Hawārī’s commentary on Ibn al-Bannāʾ’s Talkhīṣ: Contents and influences" Suhayl : Journal for the History of the Exact and Natural Sciences in Islamic Civilisation 12.

(to appear) "Al-Khwarizmi". The [Oxford] Encyclopedia of Philosophy, Science, and Technology in Islam.

2013 (with Jean Christianidis) "Practicing algebra in late antiquity:  The problem-solving of Diophantus of Alexandria".  Historia Mathematica 40, 127-163.

2012 "The series of problems in al-Khwarizmi's Algebra". Published online in HASTEC’s Carnet de Recherche:

2012 "Algebraic symbolism in medieval Arabic". Philosophica 87, 27-83. Available online:

2012  Four articles for Springer Verlag's Encyclopedia of Sciences and Religions: "Mathematics and Islam", "Arithmetic and Islam", "Algebra and Islam", and "Geometry and Islam".

2011  "Al-Khayyām's scientific revision of algebra".  Suhayl : Journal for the History of the Exact and Natural Sciences in Islamic Civilisation 10, 47-75.  Full pdf available here:

2011 "Geometry and proof in Abū Kāmil's algebra".  Pp. 234-256 in:  Actes du 10ème Colloque Maghrébim sur l'Histoire des Mathématiques Arabes  (Tunis, 29-30-31 mai 2010).  Tunis:  L'Association Tunisienne des Sciences Mathématiques.  Online version:

2010 "Equations and equating in Arabic mathematics".  Archives Internationales d'Histoire des Sciences 60, 265-298.

2010  "Polynomials and equations in medieval Italian algebra".  Bollettino di Storia delle Scienze Matematiche 30, 23-60.

2009  "Polynomials and equations in Arabic algebra".  Archive for History of Exact Sciences 63, 169-203.

2007  "Medieval Arabic algebra as an artificial language".  Journal of Indian Philosophy 35, 543-575.  This is my contribution to the meeting "The Generosity of Artificial Languages in an Asian Perspective" held in Amsterdam, May 18-20, 2006, and sponsored by the International Institute for Asian Studies.

2007 (with Haitham M. Alkhateeb)  "Simplifying equations in Arabic algebra".  Historia Mathematica 34, 45-61.

2005 (with Haitham M. Alkhateeb)  "Māl, enunciations, and the prehistory of Arabic algebra".  Historia Mathematica 32, 400-425.


2013    (with Mahdi Abdeljaouad) Al-Lubāb fī sharḥ Talkhīṣ aʿmāl al-ḥisāb (The Essential Commentary on [Ibn al-Bannāʾ's] Condensed Book on the Operations of Arithmetic). By ʿAbd al-ʿAzīz ibn ʿAlī ibn Dāwud al-Hawārī al-Miṣrātī. Tunis : Association Tunisienne de Didactique des Mathématiques. 270 p.

Book reviews

2012  "L'Eredità arabo-islamica nelle scienze e nelle arti del calcolo dell'Europa medievale (The Arabic-Islamic heritage in the sciences and arts of calculation in Medieval Europe) By Nadia Ambrosetti".  Historia Mathematica 39, 460-462.

2011  "Roshdi Rashed, ed., Al-Khwārizmī:  The Beginnings of Algebra.  London:  SAQI, 2009."  BSHM Bulletin:  Journal of the British Society for the History of Mathematics 26, 68-70.

2009  "Medieval Italian practical mathematics.  Jacopo da Firenze's Tractatus Algorizmi and Early Italian Abbacus Culture, by Jens Høyrup.  (Basel:  Birkhauser, 2007)."  Newsletter of the Canadian Society for the History and Philosophy of Mathematics.  Vol. 45, November 2009, 19-23.  The full 14-page review is on the Society's web page: (click on"archives").  Høyrup's answer is there, too, and my response to his answer can be found at  (Reviews by Menso Folkerts and Warren van Egmond agree with me, and Raffaella Franci has recently written an article explicitly supporting my conclusions.  "The history of algebra in Italy in the 14th and 15th centuries.  Some remarks on recent historiography" is available online:

2008  "Barnabas Hughes, ed., Fibonacci's De Practica Geometrie (Heidelberg:  Springer, 2008)"  Centaurus 51, 168-169.


2001-present.  I compiled an online Bibliography of Medieval Islamic Mathematics, arranged by topic:  Countless articles and books have been included so far.

Differential Geometry

1994  "Singularities and self-intersections of curves evolving on surfaces".  Indiana University Mathematics Journal 43, 959-981.  The main result and its proof can also be found in the 2001 book The Curve Shortening Problem by Kai-Seng Chou and Xi-Ping Zhu (CRC Press).

Railroad tie preservation and date nails

Not surprisingly, I am just about the only one around who studies the history of railroad tie preservation.  For more info click here:

1999  Date Nails and Railroad Tie Preservation, University of Indianapolis Archeology and Forensics Laboratory. 
A 560 page book in three volumes. In 2013 I put it online for free. Click on the link above.

In the April 2006 issue of Technology and Culture is Mark Aldrich's article "From Forest Conservation to Market Preservation:  Invention and Diffusion of Wood-Preserving Technology, 1880-1939".  The author makes many minor errors, he misses or misrepresents the major episodes in the history of tie preservation, and his main argument is completely wrong.  I wrote a rebuttal, which at 22 pages turned out to be too long for the journal.  The full version an be read here:
My reduced, two-page critique appeared as part of "Communications", Technology and Culture 48.3, July 2007, pp. 680-688.

The Roman Calendar

I collected exact dates of events in Roman history, and I compiled them by day of the year.  You can look up, for example, July 16, and find out what events form Roman history are known to have occurred on that day.  Over 1,500 events are listed:

1995  Ancient Roman Calendar.  Privately published.  For a .pdf file of the whole book, click here:

1996  "The Birth Dates of Valentinian II and Valentinian III:  A Correction to PLRE I", Medieval Prosopography 17.1, 147-148.

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