Do We Need a Separate Philosophy of Geometry?
Summary:
The philosophy of mathematics has long been focused primarily on topics such as the ontology of numbers and sets and the epistemology of results in the theory of numbers (arithmetic) and sets through issues of axioms and proofs for these theories. Though much of mathematics today seems to involve geometry in one form or another, the philosophical issues of geometry seem to receive little attention, treated as subservient to the general philosophy of mathematics or considered a part of the philosophy of physics. The author will consider why the issues of geometry could use a distinct discussion of its philosophical issues for both intrinsic and pedagogical reasons.
Registration Closed
Duration: 60 minutes
Format: Online seminar via Zoom web meeting software with questions and discussion. Detailed instructions for joining the seminar will be emailed to registered participants.
Presenter:
Martin Flashman graduated from Brandeis University in 1967 with a B. A. cum laude with honors in mathematics where he also completed both masters and doctoral degrees in mathematics. He then attended New York University School of Law and earned a law degree (J.D.).
Professor Flashman preferred to follow a career in mathematics. He had taught at Mount Holyoke College, Baruch College of CUNY, and Bard College before spending over 35 years mainly at Humboldt State University(HSU) where he is now retired as Professor Emeritus of Mathematics. Before retiring he had taught geometry to both majors and nonmajors, as well as history and philosophy of mathematics. Since fall, 2017, he has been a visiting scholar at the University of Arizona.
For too many years Professor Flashman has been working on a draft of the Sensible Calculus Book. He was book and media editor for UME TRENDS in which he wrote the column “Noteworthy Books and Such” until it ceased publication in 1996, and was a member the MAA committee on Calculus Reform And The First Two Years (CRAFTY) for 6 years ending in January, 1999. He was chair of the MAA Special Interest Group in the Philosophy of Mathematics from 2007 to 2009. In summer 2013 he started work on a resource for mapping diagrams: Mapping Diagrams from A(lgebra) to C(alculus) and D(ifferential) E(quation)s. A Reference and Resource Book on Function Visualizations Using Mapping Diagrams which is available on the internet in a working draft version using GeoGebra. He has made numerous presentations at local, national, and international conferences on his work visualizing functions with mapping diagrams.
His main hobbies currently revolve around music and trying to be on time.