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SOME MATHEMATICIANS OF PRE-ISLAMIC NORTH AFRICA1
Prof. Driss Lamrabet, Ph.D
Rabat, Morocco
I will be concerned in this part with scientists born on the north-African soil, independently of
the language they used in their writings. The most ancient we have knowledge of were natives
of Cyrene (now Shahhat, in Libya), a city founded by the Greeks in the VIIth century B.C.
This city was a very active intellectual centre, and harbored a well-known school of
philosophy: the Cyrenaics school. Other ancient north-African cities also gave birth to
mathematicians as will be seen later.
M1- Theodorus of Cyrene (Cyrene 465 –Cyrene 398 B.C.) : He was one of the greatest
philosopherrs of the cyrenaic school, and a famous geometer and astronomer. He was a
Pythagorean and a disciple of Protagoras (485-411 b.C). Plato, to whom he taught
mathematics during his stay in Cyrene, respected him for his knowledge of geometry and
other fields. In Theaetetus, he made Socrates praise Theodorus, and we learn through his
dialogues that Theodorus proved the incommensurability of lengths of sides of squares by
the unit, for lengths ranging from 3 to 17 (irrationality of 17,...,5,3 ).
Here are some extracts of dialogues illustrating these facts:
SOCRATES: If I cared enough about the Cyrenians, Theodorus, I would ask you whether
there are any rising geometricians or philosophers in that part of the world. But I am more
interested in our own Athenian youth […], and I see that a great many of them follow you, in
which they are quie right, considering your eminence in geometry and in other ways.
SOCRATES: And is Theodorus a painter?
THEAETETUS: I never heard that he was.
SOCRATES: Is he a geometrician?
THEAETETUS: Of course he is, Socrates.
SOCRATES: And is he an astronomer and calculator and musician, and in general an
educated man?
THEAETETUS: I think so.…
SOCRATES: In the first place, I should like to ask what you learn of Theodorus: something of
geometry, perhaps?
THEAETETUS: Yes.
SOCRATES: And astronomy and harmony and calculation?
THEAETETUS: I do my best.
SOCRATES: Yes, my boy, and so do I; and my desire is to learn of him, or of anybody who
seems to understand these things.
…
THEAETETUS: Theodorus was writing out for us something about roots, such as the roots of
three or five, showing that they are incommensurable by the unit: He selected other examples
up to seventeen --there he stopped. …
[Plato:Theaetetus ]
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From my book Introduction to the History of Maghrebian Mathematics (to appear within a few months); the
French (second) edition of the book is on Lulu website: http://www.lulu.com/shop/driss-lamrabet/introduction-
%C3%A0-lhistoire-des-math%C3%A9matiques-maghr%C3%A9bines/paperback/product-21257920.html

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…
Theod. By Ammon, the god of Cyrene, Socrates, that is a very fair hit; and shows that you
have not forgotten your geometry. I will retaliate on you at some other time, but I must now
ask the Stranger, who will not, I hope, tire of his goodness to us, to proceed either with the
Statesman or with the Philosopher, whichever he prefers. [Plato:Statesman]
[J O’Connor & E F Robertson : Indexes of biographies. http://www-history.mcs.st-
andrews.ac.uk/history/A mathematicians/ - Léon Robin and M.J Moreau (traduction and
notes): Platon; oeuvres complètes, tome II. Encyclopédie de la Pleiade- J.P. Colette, 1 : 57-
Becker & Hofmann, p. 62- C. Barabara, article Theodorus of Cyrene, in Ency. Universalis-
Plato : A) Theaetetus; b) Sophist; c) Statesman; translated by Benjamin Jowett ]
M2- Eratosthenes of Cyrene (Cyrene 276–Alexandria 194 B.C.): A mathematician,
astronomer, and a geographer; he studied under the supervision of: Lysanias of Cyrene, the
poet Callimarchus of Cyrene, and the philosopher Ariston of Chios, a disciple of Zeno.
Eratosthenes spent two years in Athens and was invited, in 245 B.C. by the king Ptolemy III
of Egypt to be his son's tutor and responsible in chief of Alexandria’s library.
This scientist is famous as an astronomer for having calculated accuratly the circumference of
the earth. He designed a map of the world and gave an estimate of the distance to the moon
and the sun. He also proposed a mechanical solution for the problem of the duplication of the
cube, and his solution was later used by Pappus and Theon of Alexandria. His name has
remained tied to the method of extracting prime numbers (sieve of Eratosthenes).
[J O’Connor & E F Robertson : Indexes of biographies. http://www-history.mcs.st-
andrews.ac.uk/history/A mathematicians - J.P. Colette, 1 :91- Becker & Hofmann, p. 88- J.
Kayas, article Eratosthène of Cyrene, in Encyc. Universalis]
M3- Nicoteles of Cyrene (around 250 B.C): This mathematician is mentioned by
Appolonius (262-190 B.C.) in his XIVth book on conics. Appolonius, who used the writings
of Conon (IIIth century B.C.) reports that some of his mathematical proofs (related to the
maximum number of intercept points of two conics) were severely criticized and completed
by Nicoteles of Cyrene.
[J O’Connor & E F Robertson : Indexes of biographies. http://www-history.mcs.st-
andrews.ac.uk/history/A mathematicians – J. Itard, article Alexandria (Ecole mathématique d’
), in Encyclopedia Universalis - Encyclopedia Britannica].
M4- Apuleus of Madaura (Madaure/Madauros circa 124- Carthag circa 170): A neo-
platonician philosopher and writer who was born in Madaura (now Madawrush ‫ماداوروش‬ in
Algeria), and is famous namely for his philosophical novel The Golden Ass. He is also the
author of one book in arithmetics and another one in astronomy. He translated the Arithmetics
of Nicomachus (c. 100 A.D.) from Greek to Latin. Apuleus also contributed to the
development of logic, and introduced the logical square concerning syllogistic relations,
known as the Apuleus square:

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The logical writings by this scholar were studied by A. Ben Maisa (1996) who pointed out
their originality.
[Abdessalam Ben Maissa (1996): Apuleus of Madaura and his Logical Works (in Arabic),
Publications de la faculté des lettres and sciences humaines de Rabat -Items : Apulée;
Opposition (concept of ); Logique (histoire de la) in Encyclopedia Universalis- Apulée, sa vie,
son oeuvre; Bibiliotheca Classica Selecta, on the web- Lucius Apuleius, in Forum Romanum,
on the web].
M5- Synesius of Cyrene (circa 370- circa 413): A neo-platonician philosopher then Christian
bishop. He studied mathematics and astronomy with the mathematician Hypathia of
Alexandria. He wrote an essay on making an astrolabe. Synesius played an important
political role in his region, the Cyrenaic. He is better known for his literary work, such as:
Hymni, On Kingship, In Praise of Baldness, Letters, on Providence, Dio, on Dreams,
Homelies.
[See http://www.livius.org/su-sz/synesius/synesius_cyrene.html (visited in November 2013)
where excerpts from Synesius’ work are available - R. Goulet, article Synésius in
Encyclopedia Universalis].
Fig. 5: Ruins of Cyrene in Libya
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