Email: auranteacus at gmail com
Brief Professional Bio
In reverse-chronologic order:
2017 (June 30) This talk, given for RIPS17 at IPAM, follows one year after the first talk for RIPS16: Leibniz used Calculus to solve the Catenary Problem, but he presented it as a Euclidean Construction without Explanation. In a private letter, Leibniz explained his analysis. He wrote: ``Let those who don't know the new analysis try their luck!'' This talk presents his elegant construction and analysis. Paradoxically, the construction isn't possible as strictly Euclidean, but it doesn't really matter! I present the analysis in Leibniz's own idiom of differential calculus. A YouTube video was prepared by IPAM's expert videographer, Kayleigh Steele.
This was a slight modification of an invited talk at Dartmouth for the Dartmouth Mathematics Colloquium, April 13.
2017 (January 4) The Leibniz Catenary Construction: Geometry vs Analysis in the 17th Century, an invited talk for the Special Session on the History of Mathematics at JMM 17 in Atlanta. This talk positions the publication of Leibniz's construction at the time when mathematicians were turning away from Descarte's dictate to present curves as geometric constructs toward analytic presentations. Leibniz played it both ways: he published a construction that could only have been derived using calculus but did not disclose the derivation publicly.
2016 (July 6) An invited talk for RIPS16 at IPAM: How did Leibniz Solve the Catenary Problem? A Mystery Story.
Turned out not to be a mystery after all! I learned after this talk that Leibniz explained his solution in a private letter to Rudolph Von Bodenhausen of 1691. In ignorance of Bodenhausen, this talk features an independent solution that demonstrates directly how the hyperbolic functions can be easily discovered at the heart of the catenary problem. In the most recent talk at IPAM (June 30), I explained Leibniz's analysis in detail. (For a discussion of the Bodenhausen letter, see supplementary notes.)
I worked with IPAM staff and the late Robert Borrelli of Harvey Mudd College to create the RIPS program in 2001, and then to continue developing the program over the fifteen summers of my directorship. I enjoyed working with the many students and academic mentors who participated in RIPS over all those years.
My approach to managing the RIPS program, was presented to the panel Starting and maintaining a student industrial research progam in the mathematical sciences at the MAA's MathFest of Aug 4, 2007 in San Jose, CA.
RIPS continued in the summer of 2016 under the directorship of the talented Spanish mathematician and teacher Prof. Susana Serna of the Autonomous University of Barcelona. Prof. Serna had been an academic mentor for RIPS teams for the previous eight summers.
2011 Participated in review panel for the NSF and for the S. -T. Yau High School Mathematics Awards.
Photos and Slide shows