Jeffrey A. Oaks

Professor of mathematics

Office:  Martin Hall 367

Phone: 317-788-3454


Schedule for Fall 2017

MATH 190 Calculus and Analytic Geometry I MWRF 10:00-10:50 somewhere in Martin Hall
MATH 191 Calculus and Analytic Geometry II MWRF 1:00-1:50 somewhere in Martin Hall
MATH 270 Calculus and Analytic Geometry III MTWF 9:00-9:50 somewhere in Martin Hall

Research interests

History of Mathematics (mainly medieval Arabic algebra)


(to appear) “The legacy of al-Khwārizmī in history of algebra”. To appear in the proceedings of the seminar “Al-Khwārizmī’s Contribution to Human Civilization” hosted by Muḥammad bin Hamad al-Thani Center for Muslin Contributions to Civilization, at Hamad bin Khalifa University, Doha, Qatar, on November 21, 2016. 21 p.

(to appear) “Arithmetical proofs in Arabic algebra”. To appear in: Actes du 12ème Colloque Maghrébin sur l'Histoire des Mathématiques Arabes (Marrakech, 26-27-28 mai 2016). 31p.

(to appear) “Ibn a-Bannāʾ al-Marrākushī”, “al-Jawharī”, and “al-Karajī”. Three articles to appear in: Encyclopedia of Islam, third edition. Leiden : Brill.

(to appear) “Diophantus, al-Karajī, and quadratic equations”. To appear in: Michalis Sialaros, ed., Revolutions and Continuity in Greek Mathematics. Berlin : de Gruyter.

(to appear) “Algebra according to early Arabic authors”. To appear in: Karine Chemla, Tian Miao, edd., A Worldwide Approach to the Early History of Algebra. Heidelberg : Springer.

(to appear) “Irrational ‘coefficients’ in Renaissance algebra”. Science in Context.

2016 “Excavating the errors in the Mathematics’ chapter of 1001 Inventions”. Pp. 151-171 in: Sonja Brentjes, Tanner Edis, Lutz Richter-Bernberg, edd., 1001 Mistakes: How (Not) to Narrate Histoey of Science, Medicine, and Technology in Non-Western Cultures. Wurzburg : Ergon.

2016 (with Mahdi Abdeljaouad) De la découverte d'al-Lubāb fī sharḥ talkhīṣ aʿmāl al-ḥisāb d'al-Hawārī al-Miṣrātī”. Pp. 15-34 in: Abdelmalek Bouzari, ed., Actes du 11ème Colloque Maghrébin sur l'Histoire des Mathématiques Arabes.

2015 “Series of problems in Arabic algebra: The example of ʿAlī al-Sulamī”. Alain Bernard et al, edd., Les Séries de Problèmes, un Genre au Carrefour des Cultures. 16p. Les Ulis: EDP Sciences.

2014 Al-Khwārizmī. The [Oxford] Encyclopedia of Philosophy, Science, and Technology in Islam, Vol I, pp. 451-459.

2014 Al-Khayyām. In: Helaine Selin, ed., Encyclopedia of the History of Science, Technology, and Medicine in Non-Western Cultures, third edition (3p).

2013 (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, 9-44.

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

2015 "Roshdi Rashed. Histoire de l'Analyse Diophantienne Classique (French) [History of Classical Diophantine Analysis] Berlin : Walter de Gruyter, 2013. x+349 pp.'' Mathematical Reviews.

2015 "Abū Kāmil : Algèbre et Analyse Diophantienne. Edition, translation and commentary by Roshdi Rashed". Aestimatio 11, 24-49.

2014 "Roshdi Rashed. Apollonius de Perge, La section des droites selon des rapports (French) [Apollonius of Perge, The cutting off of a ratio] Berlin, New York : Walter de Gruyter, 2010. vii+493 pp.'' Mathematical 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: In the past few years I have slacked off, so it is not up-to-date.

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.