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**History of POM SIGMAA **

By Bonnie Gold

The philosophy of mathematics (as with the philosophy of many other fields) is an interdisciplinary subject, asking philosophical questions about the content and methods of mathematics. In the last two hundred years, it went through two major shifts: one, starting in the 1800s, from a wide range of philosophical questions to a focus almost exclusively on foundations; and then, starting in the mid 1900s, back to the broader philosophical approach, with foundations becoming largely a technical mathematical field. The mathematical community was actively involved in the first change of direction, which came in response to assorted problems or developments in mathematics (including the apparent inconsistencies in calculus, leading to more careful definitions of basic concepts such as limits and the real numbers; the discovery of non-Euclidean geometries; the development of transfinite numbers and the paradoxes of set theory). However, after Gödel’s work the broader mathematical community began to lose interest in the foundational problems, which largely became the concern of logicians. The Association for Symbolic Logic (ASL) was formed to serve the interest of mathematicians and philosophers interested in foundational issues, and represents those interests at national meetings of both mathematicians and philosophers. However, discussion of the broader range of philosophical questions has largely remained in the philosophical community until recently, with the exception of the development of social constructivism by mathematicians such as Philip Davis and Reuben Hersh.

### Forming POMSIGMAA

The idea to form POMSIGMAA occurred as soon as the MAA announced the SIGMAA program in December, 1999. Many mathematicians have at least a passing interest in the philosophy of mathematics, but this interest is often kept in the closet, possibly because so many other mathematicians quickly express disdain for any kind of philosophy, or identify it with foundations. As a result, prior to the formation of POMSIGMAA, the large mathematics meetings offered very few talks involving the philosophy of mathematics beyond technical work in foundations, and still today the philosophy of mathematics does not have its own number in the AMS’s Mathematics Subject Classification. (It is listed as a sub-sub classification, 00A30, of General and Overarching Topics.) A special interest group seemed the ideal way to allow those with this interest to “come out of the closet” and share ideas with each other. It would also give a forum for informing the rest of the mathematical community about new developments in the philosophy of mathematics beyond the foundational issues covered by the ASL.

As a trial balloon, Joseph Auslander and Bonnie Gold put together a panel discussion on “The Philosophy of Mathematics: That Which Is of Interest to Mathematicians.” It was co-sponsored by the AMS and the MAA at the Joint Mathematics Meetings (JMM) in January 2001 in New Orleans. The panel consisted of three mathematicians (Chandler Davis, Reuben Hersh, and Saunders Mac Lane) and two philosophers of mathematics (Kenneth Manders and Timothy Bays). The room was filled to overflowing, with about 200 people. They probably did not all come to hear about the philosophy of mathematics: for example, this was a rare opportunity to hear Saunders Mac Lane. But the subject itself and the controversiality of Reuben Hersh’s views also seemed to have drawing power. Moved by the size of the crowd, Gold passed around a sheet for those interested in forming a SIGMAA for the philosophy of mathematics; about 75 people signed.

Gold contacted those people in March 2001, to recruit charter members for POMSIGMAA, and she circulated, among those who responded, a first draft of a proposed charter. This led to a discussion of whether the philosophy of mathematics belonged with the already-approved History of Mathematics SIGMAA. Should those interested in the philosophy of mathematics propose that it become a SIGMAA for the History and Philosophy of Mathematics? Concern was raised that the philosophy of mathematics enthusiasts might get lost in the already large history of mathematics group. But some joint activities would probably be appropriate. A vote was put to those who were participating in the charter discussions, and the vast majority preferred starting a separate SIGMAA for the philosophy of mathematics. The group edited the charter via email, mostly in the summer of 2001.

In October, 2001, the Committee on SIGMAAs was sent an application for a new SIGMAA for the Philosophy of Mathematics, with a proposed charter and a list of 27 charter members. In February 2002, the Committee asked for a preliminary list of POMSIGMAA officers. The slate of officers (below) was selected from those who had contributed to the development of the charter, and was elected by the members in July 2002. The charter was approved by the MAA Committee on SIGMAAs in October 2002, and, after some further revisions, approved by the MAA Executive Committee in November 2002. By then the membership had grown to 31. The initial officers of POMSIGMAA were:

Chairperson: | Bonnie Gold, Monmouth University |

Chair-elect: | Roger Simons, Rhode Island College |

Program Director: | Satish C. Bhatnagar, University of Nevada, Las Vegas |

Secretary: | Joseph Auslander, University of Maryland (retired) |

Treasurer: | Charles Lindsey, Florida Gulf Coast University |

Newsletter Editor/Web Page Manager: | Charles R. Hampton, College of Wooster |

### The early years

Membership at first rose dramatically, and then leveled off at around 300. A significant number of members are also members of at least one other SIGMAA - nearly half are also members of HOMSIGMAA, and about 1/5 are members of the SIGMAA on RUME (Research in Undergraduate Mathematics Education).

POMSIGMAA’s first official activities were a reception and business meeting at the joint winter meetings in Baltimore in January 2003, along with its first Contributed Paper Session. Since that time, POMSIGMAA has sponsored annual contributed paper sessions and invited speakers at JMM (and a few contributed paper sessions at MathFest when the meeting was joint with the Canadian Society for the History and Philosophy of Mathematics), an invited speaker at MathFest through 2017, several discussions, a panel, a minicourse, a listserv, and a web page that is kept updated. Turnout declined substantially at MathFest, and a decision was made to have invited speakers only at the January joint meetings. Unfortunately, a year after that decision was made, in October 2018, the MAA decided to stop co-organizing JMM, and as of this writing (June 2020) POMSIGMAA is trying to figure out what to do about speakers at future meetings.

More specifically, POMSIGMAA has sponsored a contributed paper session at every JMM except 2009 (a proposal was submitted but rejected). These sessions differ significantly from most. Normally philosophers reserve approximately twice as much time for discussion of a paper after it is presented as for the presentation of the paper itself. Mathematicians, by contrast, normally feel that two or three minutes for questions at the end of a talk is more than adequate. POMSIGMAA sessions are a median between these modes: approximately half as much time as a speaker has spoken is reserved for discussion of what the speaker has said, and even then, it is often necessary to cut off discussion to allow the next speaker the full allotted time. While maintaining a high standard of scholarship for the material of the presentations, the talks tend to be less intense in technical details compared with talks presenting mathematical proofs, and are aimed at a broader audience. Also, audience members bring to talks their own mathematical experiences and philosophical viewpoints. Hence many audience members are interested in interacting with the speaker.

### Ongoing activities

Although initially POMSIGMAA contributed paper sessions were quite generic, which organizers believed would draw the widest range of proposed talks, the committee that selects sessions declined to approve yet another general session on the philosophy of mathematics for the 2009 joint meetings. To avoid that issue, contributed paper sessions since then have focused on specific topics. This has encouraged contributions from a broad spectrum of mathematicians with assorted viewpoints, and covered a good range of topics. For example, in 2010 the topic was “Philosophy of mathematics for working mathematicians”; in 2011, “Philosophy of mathematics in teaching and learning”; in 2012, “Philosophy of mathematics and mathematical practice.” A full list of the sessions can be found at http://sigmaa.maa.org/pom/CPS.shtml. Philosophy of mathematics unfortunately tends to attract more than its fair share of cranks. This was learned the hard way when one of the speakers at the second contributed paper session gave a diatribe against Gödel’s theorem, although he hadn’t even read the paper presenting the theorem. Since then organizers of the sessions have been more careful to inquire further when a proposed abstract appears to be a bit strange.

Over the years 74 different people have given talks at these sessions (as of 2020), 21 of them more than once (the record as of 2020 is talks at 13 different sessions, held by POMSIGMAA’s former treasurer, James Henderson). Several of these speakers came from abroad.

POMSIGMAA also sponsored one Contributed Paper Session with HOMSIGMAA at the summer MathFest 2009, “The History of Mathematics and its Philosophy, and Their Uses in the Classroom” and again jointly sponsored sessions with HOMSIGMAA and the Canadian Society for the History and Philosophy of Mathematics (CSHPM/SCHPM) at MathFest 2013. (MathFest itself was co-sponsored with that organization, as the MAA Centennial.)

### Guest speakers

At MathFest 2004, POMSIGMAA had its first invited speaker, Philip Davis of Brown University, on “The Decline, Fall, and Current Resurgence of Visual Geometry.” Since then there has been a POMSIGMAA invited speaker at almost all national MAA meetings. There has been an attempt to invite both well-known mathematicians with philosophical interests and well-respected local philosophers of mathematics. Given the very limited income of SIGMAAs, coming from low annual membership dues, POMSIGMAA cannot afford to pay significant speaker travel expenses. So POMSIGMAA invites mathematicians who would attend the meeting anyway, or philosophers who live near the city in which the meeting is to be held. This strategy has yielded a quite outstanding series of talks, held in the late afternoon just prior to dinner, including mathematicians such as Jon Borwein, Chandler Davis, Keith Devlin, Reuben Hersh, and Barry Mazur, and philosophers such as John Burgess, Charles Chihara, Penelope Maddy, Michael Resnik, and Stewart Shapiro. (For a full list of the invited speakers and titles of their talks, see the appendix.) The talks by mathematicians have presented a range of issues that the philosophy of mathematics community is often not yet discussing, while the talks by philosophers have introduced the mathematical community to developments (such as a new philosophical school, structuralism) and controversies currently actively engaging philosophers of mathematics.

The Joint Meetings in January 2012 presented an unprecedented opportunity, given the wealth of both mathematicians and philosophers of mathematics in the Boston area. In addition to the usual contributed paper session, POMSIGMAA applied for a joint AMS-MAA Invited Paper Session, “Recent Developments in the Philosophy of Mathematics.” We made a list of a few dozen potential speakers, and to our astonishment, all but one of our top six choices responded positively to the invitation (the sixth was due to be out of town). The session featured a distinguished mathematical physicist, Arthur Jaffe of Harvard University, who spoke on “Is Mathematics the Language of Physics?” and five outstanding philosophers of mathematics, Jody Azzouni of Tufts University, who spoke on “Formal logic and informal-rigorous mathematical proof ”; Juliet Floyd of Boston University, who spoke on “Turing and Wittgenstein”; Charles Parsons of Harvard University, who spoke on “Structuralism and its discontents”; Agustin Rayo of MIT, who spoke on “A Trivialist Account of Mathematics” and Stephen Yablo, also of MIT, who spoke on “Explanation and Existence.” The invited evening speaker at that meeting was Barry Mazur, speaking on “Why is it Plausible” at the business meeting and reception.

### Other POMSIGMAA activities

At MathFest 2003, Bonnie Gold led an open discussion on “What is Mathematics,” and at MathFest 2009, Martin Flashman led an open discussion on “The Role of The Philosophy of Mathematics in Teaching and Learning.” At JMM 2008, Martin Flashman, Humboldt University, gave a minicourse, “Teaching and the Philosophy of Mathematics.” At JMM 2009, POMSIGMAA sponsored a panel jointly with HOMSIGMAA, “The Intersection of the History and Philosophy of Mathematics” with panelists Thomas Drucker (University of Wisconsin-Whitewater), Kenneth Manders (University of Pittsburgh) and Daniel Sloughter (Furman University). At the New Jersey MAA section meetings, Bonnie Gold led lunch discussion tables several times on topics in the philosophy of mathematics. In September 2019, two former chairs of POMSIGMAA, Thomas Drucker and Dan Sloughter, organized an AMS special session on Recent Work in the Philosophy of Mathematics at the AMS Central Sectional Meeting in Madison, Wisconsin (details of the session available at https://www.ams.org/meetings/sectional/2267_program_ss4.html#title).Two MAA books have been published related to the work of POMSIGMAA, edited by former chairs of POMSIGMAA: Proof and Other Dilemmas, edited by Bonnie Gold and Roger Simons, containing short articles both by mathematicians and philosophers, aiming to introduce mathematicians to current discussions in the philosophy of mathematics; and Using the Philosophy of Mathematics in Teaching Undergraduate Mathematics, edited by Bonnie Gold, Carl Behrens, and Roger Simons, with articles suggesting ways to introduce the philosophy of mathematics in a wide range of mathematics courses.

In March, 2005, the POMSIGMAA listserv was started. At first discussion was very lively. Since then, it tends to come in bursts in response to a question or assertion started by a member. In January 2020, the MAA started migrating membership activities to MAA Connect, and in June, 2020, the listserv was moved to this platform.

Charter changes, primarily concerning the election process and changing the title of the Newsletter/ Web-page editor to Public Information Officer were approved at the business meeting at JMM 2008. A second set of charter changes were necessitated by the Committee on SIGMAA’s review of POMSIGMAA in 2015, mostly minor changes to bring the charter into alignment with the preferred SIGMAA charter. The most significant changes were combining the roles of secretary and treasurer (since SIGMAAs no longer needed to submit budget requests and reports), adding a nominating committee, and a change in quorums for meetings and elections. This revision was approved in April 2018. The most recent review, finished in May 2020 praised POMSIGMAA as a potential model SIGMAA and did not require any further charter revisions.

The web page must be updated at least twice a year to reflect the upcoming talks and sessions, changes in officers, and events in philosophy of mathematics not sponsored by POMSIGMAA but of potential interest to its members.

### Looking to the future

Challenges for the future for POMSIGMAA include keeping the momentum it has developed, figuring out how to respond to the MAA’s decision to largely remove itself from the winter joint meetings (and to not allow SIGMAAs to spend any of their funds there) and continuing to develop a core of mathematicians actively interested in philosophy of mathematics who can keep the organization lively and responsive to changes in mathematics that affect philosophical views.