


History of Mathematics
Org: Len Berggren (SFU) [PDF]
 LEN BERGGREN, Simon Fraser University, Burnaby, BC V5A 1S6
Creating Mathematics Textbooks in the Thirteenth Century: The
Case of Nasir alDin alTusi and Aristarchos of Samos
[PDF] 
Aristarchos of Samos was a Greek astronomer who worked in the early
third century B.C. and wrote a treatise on the sizes of the sun and
moon and their distances from the earth. About a century and a half
later, beginning with the work of Hipparchos of Rhodes, astronomers
began to develop simpler ways of solving the questions that
Aristarchos addressed in his treatise. This work continued through
Ptolemy some 300 years later, and reached new heights with the
trigonometry developed by Islamic astronomers in the 10th century.
Yet, in the 13th century, Nasir alDin alTusi, who was well up on the
mathematics of his day, produced a new edition of Aristarchos's work
that completely ignored all these intervening improvements. Why, and
how, Nasir alDin did this, will be the subject of our talk.
The talk represents joint work with Dr. Nathan Sidoli.
 HARDY GRANT, York University, Toronto
The Curious Case of the "Mathematicals" in Greek Antiquity
[PDF] 
Plato assigned to mathematics an ontological status intermediate
between the realm of Forms and the physical world, and Aristotle based
on this tripartition of being an influential classification of
knowledge. But Plato placed something else between the intelligible
world and physical objects, namely soul; whence, in later centuries,
repeated attemptsstrange in our eyesto actually identify soul
with the objects of the mathematical sciences. In this endeavour,
astronomyone of the four disciplines considered "mathematical"
since the 5th centuryplayed a special role. I shall try to sketch
the interplay among these ideas, a story that reaches into late
antiquity.
 ALEXANDER JONES, University of Toronto
The Euclid Enigma
[PDF] 
Euclid is usually said to have lived about 300 B.C. at Alexandria, and
he is thought of primarily as a compilator and organizer of older
work. I will argue that he was more likely active in the second half
of the third century B.C., thus a contemporary of Archimedes and
Eratosthenes, and that he was initially best known as an original
mathematician working on the problems current in his time. Only in
the time of the Roman Empire do we find his name almost exclusively
associated with the text for which he is now remembered, the
Elements.
 NATHAN SIDOLI, Simon Fraser University
Ratio in the Late Ancient Commentators
[PDF] 
Ratio was one of the foundations of ancient Greek mathematics.
Although a general ratio theory is developed in book five of the
Elements, Greek mathematical practice was in fact much more
diverse than this foundation would suggest. In particular, the theory
of compound ratio seems never to have been fully established, despite
the fact that the best mathematicians in all fields used compound
ratios to produce new results. This lacuna was apparently conspicuous
to the late ancient commentators. Both Theon and Eutocius offer
meager attempts to give a theoretical foundation to the practices they
found in the texts they were studying. Although these discussions are
trivial from a mathematical perspective, they introduce interesting
and important shifts in the underlying definitions. These late
ancient views were then incorporated into the mainstreams of
mathematical practice when they were taken over, and built upon, by
the Arabic mathematicians.
 GLEN VAN BRUMMELEN, Bennington College
Controversies in the Early History of Trigonometry
[PDF] 
Few mathematical disciplines have been claimed to have begun in as
many different times and places as trigonometry, covering one and a
half millennia and three cultures. When applied to ancient
mathematics, the boundaries of the disciplineeven the meaning
of the wordare obscure and open to different interpretations. The
apparently safer ground of Hellenistic Greece is filled with claims
and counterclaims of paternity, from Eudoxus to Hipparchus. Later
developments are no clearer; spherical trigonometry may go back to
Hipparchus, or only to Menelaus over two centuries later. The
achievements of Claudius Ptolemy's Almagest are unquestioned, but what
Ptolemy contributed (or merely borrowed) is another matter. Finally,
the transmission of Greek astronomy to India opens up a series of
questions about both cultures. We shall survey the evidence and
arguments, with an eye toward establishing a conservative chronology
of the subject.
 BYRON WALL, York University, 4700 Keele St., Toronto, ON M3J 1P3
John Venn's Opposition to Probability as Degree of Belief
[PDF] 
John Venn is known as one of the clearest expounders of the
interpretation of probability as the frequency of a particular outcome
in a potentially unlimited series of possible events. This view he
held to be incompatible with the alternate interpretation of
probability as a measure of the degree of belief that would rationally
be held about a certain outcome based upon the reliability of
testimony and other prior information. This paper explores the
reasons why Venn may have been so opposed to the degreeofbelief
interpretation, and suggests that it may have been a way for him to
resolve a conflict in his own mind between his ideas of proper
scientific methods of inference and the religious beliefs that he held
as a young man.

