The Transmission of Mathematical Ideas from India and Islam to the West
Professor Victor Katz:

Abstract: In recent years there has been much research on the developments in 
mathematics in India and the Islamic world in such areas as trigonometry, algebra, 
number theory, geometry, and calculus.  Yet, it is still generally believed that in 
most cases, even when mathematical advances were made in these places, the 
knowledge of these advances did not reach Europe in time for the ideas to have 
an impact and therefore that the Europeans developed these ideas anew without 
any help.   A major question of current interest, then, is whether in fact that 
statement is true.  There seem to be more and more indications that ideas traveled 
to Europe through routes that were previously unknown.  In these two talks, we will 
consider some of the evidence for this transmission of ideas, including some evidence 
which now seems reasonably conclusive and other evidence which is still only 
circumstantial.  Areas of current research in this aspect of the history of mathematics 
will be discussed.


    The three references mentioned in the 2nd lecture on calculus ideas in India
are:

 David Bressoud, Was Calculus Invented in India?  College Mathematics
Journal 33 (2002), 2-13

 Victor Katz, Ideas of Calculus in Islam and India, Mathematics Magazine
68 (1995), 163-174

 Ranjan Roy, The Discovery of the Series Formula for Pi by Leibniz,
Gregory, and Nilakantha, Mathematics Magazine 63 (1990), 291-306

All of these articles will appear in a collection of MAA articles on the
history of mathematics, that I am editing, along with Robin Wilson and
Marlow Anderson.  This volume will probably come out by late summer.

Some of the other material from my two talks is in my textbook:  A History
of Mathematics:  An Introduction (Addison-Wesley, 1998).