Michael Melch and Quinn Suydam -- Christopher Clavius' Lasting Influence

   This is a good discussion of Clavius' contributions and your oral presentation
   was excellent.  But there are a few inaccuracies (see comments below), and 
   I don't think you quite understood the main point of the Amir Alexander book 
   "Infinitesimal" (see comment 3).  

   Apart from those smaller points, the main issue I have is that you have not done 
   a very good job of documenting and citing your sources.  There are several direct 
   quotations that are not attributed.  In addition, you need to get into the habit 
   of giving citations for facts that you are taking from your sources and statements
   of opinion that you did not develop yourself.  For this sort of paper, I
   know it's a lot but that's the way academic writing works and you should
   expect to have multiple footnotes on every page.  

   I know you are not intentionally trying to pass off work of others as yours.  
   But I have to tell you that other professors here at Holy Cross might be 
   inclined to "write you up" for plagiarism on the basis of what you did here.  
   I'm not going to do that, but you really need to make this a standard part 
   of all the research papers you write from now on!

   Specific comments:

   1) A lot of the points in the paragraph at the bottom of page 1 really
      deserve attribution (i.e. citation of sources) -- they are not your
      opinions.  

   2) "The Jesuits had been known for their involvement with education"
  
      > Yes, but it's interesting that if you look at the early years,
      say 1540 - 1550, then the Jesuits did not really have a plan to
      get involved with running schools.  That just sort of grew out of
      their other ministries.  

   3)  page 2:  "A large percentage of this growth in Jesuit institutions 
       can be contributed to Christopher Clavius for his commitment and 
       devotion to education."  

       > This is an overstatement, I think. Clavius was important for his
       promotion of mathematics as a subject of study.  But I don't think
       it's correct to attribute the growth of the system of Jesuit schools
       to his influence the way you are claiming.  

   4)  page 3:  The history behind the theory of "indivisibles" that Amir 
       Alexander discusses is more subtle than you appreciate and there
       are a lot of historians of mathematics who would disagree with elements
       of his book "Infinitesimal ... ."  The mathematics that Clavius
       was objecting to was what became the basis for the subject we
       know as *differential and integral calculus* and, as we know now,
       much of the scientific revolution came out the ways calculus lets
       us study change in the physical world and predict the future effects of 
       actions in the present(!)  It is possible to argue that Clavius' objections 
       to the foundations of calculus (admittedly imprecise at the time) were 
       a mistaken effort to try hold up progress (that's Alexander's point of 
       view, which I don't think you understood completely).  Other people 
       might say that objections like his forced the developers and users of 
       calculus to justify their methods and that actually helped progress.  
       It's quite subtle and Clavius' religious objections to the theory of 
       infinitesimals should really seem strange to us if they are examined 
       closely.  In any case, if you think about it, it is also strange that 
       someone who was as influential as Clavius was spent so much time fighting 
       a mathematical theory that is a central part of the subject today(!)   

   5)  page 4:  Where did you find the quote about the eclipse?  Document 
       your sources!

   6)  page 5:  Where did you find the quote about mathematics?  Document 
       your sources!

   7)  page 6:  At bottom, the sentence: "He began this process by recruiting and 
       training instructors who would be thorough in their teaching of math."  should
       really be the start of a new paragraph.  You're changing the subject.  

   8)  page 11:  "He also includes his own proof of Euclid’s fifth postulate in his
       version of Elements."  

       > Yes, but in fact we know today that what he said was *incorrect* and 
       it is, in fact impossible to prove Euclid's 5th Postulate from the others.
       It is independent of them, and there are other mathematical geometrical
       theories in which Euclid's 5th Postulate *does not hold* (!)
       

   Final Project Grade Computation 
  
   Bibliography:   7/10  

   Paper:         53/60

   Presentation:  30/30

   Total:         90/100