Abstract: Mathematics is about abstract concepts, precise idealizations, relations, calculations, and notations, all of which are made possible by the amazing (albeit limited) workings of the human mind and the biological apparatus that supports it. Over the past 50 years the scientific study of mental phenomena has made enormous progress in understanding their psychological, linguistic, and neurological underpinnings. Traditional approaches in Philosophy of Mathematics such as Platonism, Formalism, Logicism, and Intuitionism - developed many decades, if not centuries prior to these developments - could not benefit from these findings. I argue that today, in the 21st century, philosophical investigation - e.g. What is mathematics? What is it for? How does it work? - should be informed by, and be compatible with findings in the sciences of the mind. I'll illustrate my arguments with research addressing issues in hyperset theory, infinitesimal calculus, and mathematical induction.
Rafael Núñez is Full Professor at the Department of Cognitive Science at UCSD. He has co-authored, with George Lakoff, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being.
We will have our reception at 5:30 pm, then a business meeting at 6:00 pm, followed by the guest lecture at 6:15 pm.
Description: The philosophy of mathematics has often failed to account for actual mathematical practice, concentrating only on the finished product, theorems and proofs, and even then, not proofs as mathematicians give them, but the formal proofs by which they could be replaced. In the last quarter of the 20th century, many philosophers of mathematics began to be interested in considering mathematics as it is actually developed, leading to the formation, in 2009, of the Association for the Philosophy of Mathematical Practice. This kind of approach requires that the philosopher of mathematics have a good understanding of mathematics, how it develops, and how it is taught and learned. It therefore requires a significant interaction with the mathematical community. This session invites contributions that discuss philosophical issues involved with mathematics as it is actually practiced. Papers that bring out issues that have not yet been discussed by philosophers but that involve philosophical issues with current mathematical practice are especially welcome. Other topics in the philosophy of mathematics will be considered as time allows.
8:00 a.m. 1135-A5-144 David M. Shane, "The Eroding Foundation of Mathematics"
8:30 a.m. 1135-A5-362 James Henderson, "When Physicists Teach Mathematics"
9:00 a.m. 1135-A5-609 Daniel C. Sloughter, "Hardy, Bishop, and Making Hay"
9:30 a.m. 1135-A5-301 Jae Yong John Park, "Fictionalism, Constructive Empiricism, and the Semantics of Mathematical Language"
10:00 a.m. 1135-A5-814 Chandra Kethi-Reddy, "Gian-Carlo Rota and the Phenomenology of Mathematics"
10:30 a.m. 1135-A5-1883 sarah-marie belcastro, "Does Inclusivity Matter in Mathematical Practice?"
The deadline for submission of abstracts has passed. Thank you to all who submitted abstracts.
Also of interest at the JMM 2018 meeting:
8:00 a.m. (1135-03-2) John Stillwell, "The Brouwer Fixed Point Theorem"
9:00 a.m. (1135-01-302) Jemma Lorenat "Algebraic symbols and geometrical reality: the algebraic geometry of Charlotte Angas Scott"
9:30 a.m. (1135-01-852) Kenneth L Manders "On Proofs of the Quadratic Reciprocity Theorem"
10:00 a.m. (1135-11-173) Roger B. Nelsen "Alternative Proofs in Number Theory"
10:30 a.m. (1135-00-53) Rebecca Lea Morris "Alternative proof presentations"
11:00 a.m. (1135-03-584) Wilfried Sieg "The Cantor-Bernstein Theorem: How many proofs?"
POMSIGMAA sponsored our first ever invited paper session at the 2012 AMS/MAA Joint Meeting in Boston. The speakers were Arthur Jaffe at Harvard University on "Is Mathematics the Language of Physics" and Charles Parsons at Harvard University on "Structuralism and its Discontents", Jody Azzouni at Tufts University on "The Relationship of Derivations in Artificial Languages to Ordinary Rigorous Mathematical Proof", Juliet Floyd at Boston University on "Turing and Wittgenstein", Agustin Rayo at MIT on "A Trivialist Account of Mathematics" and Stephen Yablo at MIT on "Explanation and Existence."
POMSIGMAA has sponsored contributed paper sessions at
the 2003 AMS/MAA Joint Meeting in Baltimore,
the 2004 AMS/MAA Joint Meeting in Phoenix,
the 2005 AMS/MAA Joint Meeting in Atlanta,
the 2006 AMS/MAA Joint Meeting in San Antonio,
the 2007 AMS/MAA Joint Meeting in New Orleans,
the 2008 AMS/MAA Joint Meeting in San Diego,
MathFest 2009 in Portland, OR, jointly with HOMSIGMAA, "The History of Mathematics and its Philosophy, and Their Uses in the Classroom",
the 2010 AMS/MAA Joint Meeting in San Francisco, "Philosophy of Mathematics for Working Mathematicians,"
the 2011 AMS/MAA Joint Meeting in New Orleans, "Philosophy of Mathematics in Teaching and Learning,"
the 2012 AMS/MAA Joint Meeting in Boston, "Philosophy of Mathematics and Mathematical Practice."
the 2013 AMS/MAA Joint Meeting in San Diego, "Philosophy, Mathematics, and Progress."
the 2013 MathFest, in conjunction with CSHPM and HOMSIGMAA, daily sessions on history of mathematics and philosophy of mathematics, and one session on the Interactions Between the History and Philosophy of Mathematics.
the 2014 AMS/MAA Joint Meeting in Baltimore, "Is mathematics the Language of Science?"
the 2015 AMS/MAA Joint Meeting in San Antonio, "Discovery and Insight in Mathematics."
the 2016 AMS/MAA Joint Meeting in Seattle, "Using Philosophy to Teach Mathematics."
the 2017 AMS/MAA Joint Meeting in Atlanta, "Do Mathematicians Really Need Philosophy?"
At MathFest 2017 in Chicago, IL, July 26 - 29, John Baldwin, Emeritus Professor at the University of Illinois at Chicago, gave the POMSIGMAA Invited Address, "Philosophical implications of the paradigm shift in model theory."
At 2017 AMS/MAA Joint Meetings in Atlanta, GA, January 4 - 7, Jeff Buechner, of the philosophy department at Rutgers University Newark and the Saul Kripke Center, CUNY Graduate Center, gave the POMSIGMAA Invited Address, "Computers, mathematical proof, and the nature of the human mind: a surprising connection."
At MathFest 2016 in Washington, DC, August 3 - 6, Stewart Shapiro, of Ohio State University, gave the POMSIGMAA Invited Address, "Potential infinity: a modal account." Full text (pdf)
At the 2016 AMS/MAA Joint Meetings in Seattle, WA, January 6 - 9, Bonnie Gold, of Monmouth University, gave the POMSIGMAA Invited Address, "Is School Mathematics 'Real' Mathematics?" Full text (pdf)
At MathFest 2015 in Washington, DC, August 5 - 8, John Burgess, of Princeton University, gave the POMSIGMAA Invited Address, "What are mathematical objects, and who cares?"
At the 2015 AMS/MAA Joint Meetings in San Antonio, TX, January 10 - 13, Matt Jones, of California State University Dominguez Hills, gave the POMSIGMAA Invited Address, "Mathematical Authority and Inquiry-Based Learning."
At MathFest 2014 in Portland, OR, August 6 - 9, Paul Zorn of St. Olaf College gave the POMSIGMAA Invited Address, “Math-Speak: Syntax, Semantics, and Pragmatics.”
At the 2014 AMS/MAA Joint Meetings in Baltimore, MD, January 15 - 18, Steve Gimbel of Gettysburg College gave the POMSIGMAA Invited Address, "Hermann Minkowski – The Quiet Genius."
At MathFest 2013 in Hartford, CT July 31 - August 3, the MAA met jointly with the Canadian Society for the History and Philosphy of Mathematics. POMSIGMAA cosponsored contributed paper sessions running throughout the meeting, as well as a plenary talk (the Kenneth O. May Lecture) on Saturday, August 3 by Jeremy Gray, of the University of Warwick and the Open University, on "Henri Poincaré: Mathematician, Physicist, Philosopher."
At the 2013 AMS/MAA Joint Meetings in San Diego, CA, January 9 - 12, Mark Balaguer of California State University, Los Angeles, gave the POMSIGMAA invited address “A Guide for the Perplexed: What Mathematicians Need to Know to Understand Philosophers of Mathematics.” Full text (pdf) Handout (pdf)
At MathFest 2012 in Madison, WI August 2 - 4, Janet Follina, of Macalester College, gave the POMSIGMAA invited address, "Is the Proof in the Picture? Seeing, Believing, and Provings."
2011 in Lexington, KY, August 4 - 6, Neil
Tennant, of the Department of Philosophy of The Ohio State
University gave the POMSIGMAA invited address, "Natural
Logicism for Mathematics." Full text
At the 2011 AMS/MAA Joint Meeting in New Orleans, LA, January 6 - 9, Keith Devlin of the Center for the Study of Language and Information at Stanford University gave the invited address, "Will the real philosophy of mathematics please stand up?"
At MathFest 2010 in Pittsburgh, PA, August 5 - 7, Wilfried Sieg, of Carnegie Mellon University, gave the POMSIGMAA invited address, "Structural Proof Theory: Uncovering capacities of the mathematical mind." Full text (pdf) PowerPoint slides
At the 2010 AMS/MAA Joint Meeting in San Francisco, CA, January 13 - 16, Charles Chihara (Philosophy Department, University of California at Berkeley) gave the invited POMSIGMAA address, "What is Philosophy of Mathematics? A Case Study of Fictionalism."
At MathFest, August 6-8, 2009 in Portland, OR, POMSIGMAA held a Reception and Moderated Discussion led by Martin Flashman, Humboldt State University, Past-Chair POM SIGMAA, on "The Role of The Philosophy of Mathematics in Teaching and Learning."
At the 2009 AMS/MAA Joint Meeting in Washington, DC, Chandler Davis (University of Toronto) gave an invited address, jointly sponsored by HOMSIGMAA (the SIGMAA for the History of Mathematics), "The Role of the Untrue in Mathematics". It will be published in the Mathematical Intelligencer; a preliminary version is available here as a Word document, but it is copyrighted by the Mathematical Intelligencer, all rights reserved. At that meeting, there was also a panel jointly with HOMSIGMAA (the History of Mathematics SIGMAA), "The Intersection of the History and Philosophy of Mathematics" with panelists Thomas Drucker (University of Wisconsin-Whitewater, current POMSIGMAA treasurer), Kenneth Manders (University of Pittsburgh) and Daniel Sloughter (Furman University).
At MathFest 2008, in Madison, WI, Morris W. Hirsch (University of Wisconsin) gave an invited POMSIGMAA address, "Mathematics: the divine madness."
At the 2008 AMS/MAA Joint Meeting in San Diego, Penelope Maddy, of the Department of Logic and Philosophy of Science of the University of California at Irvine, gave an invited address at the POMSIGMAA session, "How applied mathematics became pure." Charter changes were approved at the business part of this session. Our 2007-2009 Chairperson, Martin Flashman also gave a minicourse, "Teaching and the Philosophy of Mahtematics," at these joint meetings.
At Mathfest 2007, in San Jose, Michael Beeson, of San Jose State University, gave an invited address at the POMSIGMAA session, "The meaning of existence in mathematics."
At the 2007 AMS/MAA Joint Meeting in New Orleans, Klaus Peters, of AK Peters LTD, gave an invited address at the POMSIGMAA session, "Does a proof exist if nobody has read it?"
At Mathfest 2006, in Knoxville, TN, Michael Resnik, of the University of North Carolina, Chapel Hill, gave an invited address at the POMSIGMAA session, "Some Problems and Solutions in Contemporary Philosophy of Mathematics."
At the 2006 AMS/MAA Joint Meeting in San Antonio, Paul Humphreys, of the University of Virginia, gave an invited address on "Pure and Applied Computational Mathematics: Some Philosophical Morals".
At MathFest 2005 in Albuquerque, NM, Reuben Hersh gave an invited address, "Subversive essays on the nature of mathematics".
At the 2005 AMS/MAA Joint Meeting in Atlanta, Jonathan Borwein, of Dalhousie University, gave an invited address, "Philosophical Implications of Experimental Mathematics"
At MathFest 2004 in Providence, RI, Philip Davis, of Brown University, gave an invited address sponsored by POM SIGMAA. Professor Davis was introduced by Roger Simons (Chair-elect) and his talk was entitled "The Decline, Fall, and Current Resurgence of Visual Geometry." It was followed by a brief POM SIGMAA business meeting led by POM SIGMAA Chairperson, Bonnie Gold.
At the MathFest 2003 in Boulder, CO there was an
80 minutes open discussion involving approximately 25 people, on
the topic, "What is Mathematics?" Bonnie Gold moderated
this discussion and it included representatives of most of the
modern points of view: social constructivism, formalism,
versions of platonism. The discussion ebbed and flowed,
sometimes being fairly carefully focused, sometimes wandering a
bit off the topic.