C. Comments: 
 
This is a very strong proposal to continue work on a software package that has already made a significant impact in many fields of mathematics and applications.  The Sage package collects a wide variety of open source mathematics packages (more than 100) into a unified framework, and has the potential to largely replace the need for many commercial software packages such as Matlab, Mathematica, and Maple that are in wide use. 
 
The advantages of this open source unified alternative goes well beyond the financial benefit to the user or university. In particular the Sage notebook, a web based interface, is unique and very powerful.   One of the specific goals of this RRF is to further develop the notebook as a teaching tool, by improving the efficiency to allow many students to simultaneously use it on a single server.  I believe this has the potential to help revolutionize the way mathematics is taught, not only at UW but at the many other universities where Sage is already in use. 
 
Another specific goal is to improve the symbolic manipulation facilities in Sage, which are currently based on the package Maxima. This aspect of Sage is one that is widely used as an alternative to Mathematica or Maple and improving its efficiency would greatly enhance its usability. 
 
On the negative side, Stein has obtained substantial outside support for Sage and already has a wide-spread reputation for his work on this project. So it is not clear how well this proposal fits into the RRF framework.  However, I believe that he makes a good case that improvement in these two specific areas will greatly enhance the ability to attract even more outside funding, much of which has been used to support UW students and postdocs working on this project. Stein has worked with a large number of students on these projects, including many undergraduates. 
 
Although many others are working on the Sage project, including volunteers from around the world on specialized topics, the development of major enhancements requires substantial involvement from the main developer.  Much of the success of Sage is due to the intense hands-on involvement of Stein, and support as an RRF Scholar for a quarter would almost certainly lead to significant progress.

 

C. Comments (continue onto additional pages as necessary): 

1. Research Performance Competance.  The SAGE mathematical software project is unique and uniquely valuable -- in the broadest sense.  There is nothing comparable (in the world) to its quality and usefulness to pure and applied mathematicians.  It has won international prizes and has no competitor.  However this project is critically dependent on its leader, William Stein.  It is his vision, leadership, and energy that are the engine that drives this project.  There is no doubt that he is top person in the world in the development of this type of broadly applicable mathematical software.   

2. and 3.  Intrinsic merit and utility and relevance of the research.  The response of the mathematical community is a certification that SAGE is uniquely useful.  For example SAGE played a crucial role in the computation of the character table of E8, a spectacular achievement that was widely reported in international news.  The site http://www.sagemath.org/library/stories.html has an extensive file of testimonials.  Professor Stein proposes to make SAGE more useful to an undergraduate audience as a teaching tool.  This is a very good idea and will surely demand an intense effort.  It is certainly correct that it will require at least 12 weeks of hard work. 

4.  Effect of the research on the university infrastructure.  In addition to supporting Professor Stein's own research, the latest development of SAGE will mean that faculty, graduate students, undergraduates, and instructors will be able to efficiently study computationally hard problems in a way never before possible.  We are extremely lucky to be the center and world leader of this activity.  This work must be supported. Professor Stein is SAGE. 
1. Research performance competence —  

Superb.  In addition, investigator is uniquely situated to achieve research goals -- not clear, actually, that anyone else could accomplish them! 

2. Intrinsic merit of the research —  

This proposal is superb on all accounts.  The objectives -- to enhance symbolic computation and collaborative interfaces for a proven, comprehensive, open-source mathematical software package -- obviously important to the scientific community on a very large scale, and the investigator has put forth a focused and specific plan of attack that clearly will be greatly accelerated by RRF support. The impact seems very likely to greatly enhance the prominence of UW across the sciences and mathematics writ large, all while creating a highly unique and important research and education resource.   

Best of all proposals I've read. 

4. Effect of the research on the university infrastructure —  

The proposer is senior, but the proposal seems exactly in line with the intent of the RRF scholar program.  It seems clear that a focused quarter of research is necessary for these tasks to be completed.  The result of the research will be a direct enhancement of university infrastructure in a critical area essential across mathematics, the sciences, and engineering.