CRC Seminar Series - Prof. Joachim von zur Gathen

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Joachim von zur Gathen

Prof. Joachim von zur Gathen

9th Feb 2023, 4:00pm – 5:00pm (GST)



Glimpses at the history of Arab science: cryptography and mathematics


In the first centuries after the hijrah, Arab scientists began the first serious scientific investigations after the Greek and Roman antiquity. This talk will concentrate on two areas whose modern versions are close to my heart: cryptography and mathematics.

The caliph al-Ma’mūn established the Bait al-Ḥikmāh, House of wisdom, in Baghdād, often considered to be the first university in the world. The outstanding figure is Abū Yūsuf al-Kindī (185-256 H, 801-873 CE). This universal scholar is considered the “father of Muslim philosophy”, translated Greek scientific treatises into Arabic and thus preserved them, also later for Western scientists, wrote about medical and many other subjects, and the first scientific studies of cryptography. His book Risālah fī istikhrāj al-mu,mmah, Manuscript on deciphering encrypted messages is the oldest existing book on cryptography. After studying the distribution of consonants in Arabic and classifying cryptographic methods, al-Kindī introduced the surprisingly modern tool of frequency analysis, explaining lucidly how this method can break the then prevalent type of cryptosystems. Others carried this work further.

As to mathematics, the towering figure is Muḥammad ibn Mūsā Al-Khwārizmī (c. 158-228 H, c. 780-850 CE), who also worked at the Bait alḤikmah. His book ḥisāb al-jabr w’al-muqābala, Computing by breaking and rearranging) introduced fairly general techniques for solving linear equations, by moving terms around: “breaking and rearranging”. And for solving quadratic equations, he used “completing the square”. Two major fields of modern mathematics and computer science owe their name to his work: algorithm, from his name, and algebra, from al-jabr in his book title.

Lamentably, Western sources often—but not always—pay insufficient respect to these historical advances in science. It will be very interesting to see how efforts like the TII influence modern technological thinking and science in Arab countries, standing in a millenium-old tradition.


Joachim von zur Gathen has held full-professor positions at the universities of Toronto (Canada), Paderborn and Bonn (both in Germany), where he is now an Emeritus. His research interests have evolved over time: first complexity theory, then computer algebra, and currently cryptography. His book (with a coauthor) Modern Computer Algebra is widely considered as the standard text on the subject and enjoys thousands of citations. His book CryptoSchool presents the foundations of modern cryptography including the mathematical bases. Both books include numerous historical excursions illustrating his life-long interest in understanding the sources of our sciences.

His publication record spans a period of about 45 years and several areas. In factorization of polynomials, some of his ideas shaped the progress of research. This is of interest in some cryptographical situations, and with his research group, he provided some software and hardware world records: factoring a polynomial of degree one million, elliptic curve cryptography with a single SMS, fastest elliptic signatures on hardware (FPGAs).