tag:blogger.com,1999:blog-5486692981606716948.post2576391252230588200..comments2020-01-31T19:33:17.922+05:30Comments on Prime Argument: C K Raju responds to Amir Aczel's claimsprimeargumenthttp://www.blogger.com/profile/13334888669233995058noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5486692981606716948.post-14963372493162425532017-12-10T08:33:11.495+05:302017-12-10T08:33:11.495+05:30This is not right. Calculus today is taught using ...This is not right. Calculus today is taught using (formal) "real" numbers which do not admit infinitesimals. See any high school or university text.<br /><br />Newton used fluxions (not infinitesimals) as described in my book Cultural Foundations of Math. <br /><br />The Jesuits stole the calculus because of the precise trigonometric values to which it led. Those precise values were of immense practical value to solve the European navigational problem, then the biggest scientific challenge in Europe. Thus, the top Jesuit Clavius published an interpolated version of the accurate Indian sine values (precise to 10 decimal places) in his name in 1607. Obviously this had the highest level of theological sanction, as did the Gregorian reform also authored by Clavius. <br /><br />Galileo abandoned the calculus and left it to his student Cavalieri because he had difficulties similar to those of Descartes: ("how is it possible to sum an infinite series exactly"). <br /><br />BTW, Brahmagupta did use infinitesimals, as in non-Archimedean arithmetic, as explained in my Springer articles. For a slightly more technical account see my USM lectures of 2010 or the more recent corrected version http://ckraju.net/sgt/technical-presentations-faculty/ckr-sgt-tech-presentation-2.pdf. C. K. Rajuhttp://ckraju.netnoreply@blogger.comtag:blogger.com,1999:blog-5486692981606716948.post-30476368857033410712017-07-26T11:36:14.114+05:302017-07-26T11:36:14.114+05:30Calculus owes its development to the idea of Infin...Calculus owes its development to the idea of Infinitesimals is well attested. Including the earlier war waged by the Jesuits on supporters of Infinitesimals because it was not seen as theologically correct.<br /><br />Amir Alexander covers this topic in his book "infinitesimal".<br /><br />His interesting interview is here on how Jesuit opposition destroyed the early shoots of science in Italy in 17th century Europe.<br /><br />http://www.npr.org/2014/04/20/303716795/far-from-infinitesimal-a-mathematical-paradoxs-role-in-history<br /><br />So the Jesuits waged a war of letters, threats and intimidation against the supporters of the infinitesimal, a group that included some of Italy's greatest thinkers — Galileo, Gerolamo Cardano, Federico Commandino and others. In Italy, the Jesuits' victory was complete.<br /><br />"Italy was — before the 17th century and into the 17th century — it was really the mathematical capital of Europe. It had the greatest mathematicians, the greatest mathematical tradition," Alexander says. "And by the time the Jesuits were done, that was gone. All of it. By the 1670s, Italy was a complete backwater in mathematics and the sciences."primeargumenthttps://www.blogger.com/profile/14552517971823796265noreply@blogger.com