POM SIGMAA



POM Contributed Paper Sessions

August 2022 Mathfest, Philadelphia, PA
January 2022 JMM, Virtual (originally Seattle)
January 2021 JMM, Virtual
January 2020 JMM, Denver, CO
January 2019 JMM, Baltimore, MD
January 2018 JMM, San Diego, CA
January 2017 JMM, Atlanta, GA
January 2016 JMM, Seattle, WA
August 2015 Mathfest, Washington, DC
January 2015 JMM, San Antonio TX
January 2014 JMM, Baltimore, MD
August 2013 Mathfest, Hartford, CT
January 2013 JMM, San Diego CA
January 2012 JMM, Boston MA
January 2011 JMM, New Orleans LA
January 2010 JMM, San Francisco CA
August 2009 Mathfest, Portland OR
January 2008 JMM, San Diego CA
January 2007 JMM, New Orleans LA
January 2006 JMM, San Antonio TX
January 2005 JMM, Atlanta GA
January 2004 JMM, Phoenix AZ
January 2003 JMM, Baltimore MD

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Philadelphia, PA Mathfest, August 5 2022

Logic and Intuition in Everyday Mathematics

Many of us likely believe--and teach--that the role of proof is essential to the practice of pure mathematics. However, history is full of examples that suggest intuition may also play a meaningful role in the development of mathematical knowledge. Furthermore, computers can now supply (or at least verify) many of the logical steps in a mathematical proof, and even generate mathematical conjectures. This raises the question: what roles do logic and intuition play in mathematics? Is logic largely a scheme for demonstrating rigor and “correctness” after intuition has led us to a proposition that we believe to be correct? Or is logic more of an essential companion, informing our intuition and the very way think about our subject matter? This contributed paper session welcomes submissions reflecting on the relative roles of logic and intuition in mathematics, based on the contributor's historical/philosophical scholarship or lived experience as a working mathematician.

Organizers:
Jason Douma, University of Sioux Falls

Tom Morley, Georgia Institute of Technology










TimePresenterTitle
1:00 p.m. - 1:15 p.m.Chris Oehrlein Re-Imagining Theorem-and-Proof in a Guided-Inquiry Geometry Course for Future K-8 Teachers. Slides.
1:20 p.m. - 1:35 p.m.Benjamin Gaines Related Rates and Right Triangles: Developing Intuition in a Calculus Course . Slides.
1:40 p.m. -  1:55 p.m.Raul Rojas-Gonzalez Developing Mathematical Intuition with a History of Math Course. (cancelled)
2:00 p.m. - 2:15 p.m.Paul Christian Dawkins, Some Ways of Reasoning Productive for the Logic of Mathematical Reasoning . Slides.
Kyeong Hah Roh,

Derek Eckman,

Steven Ruiz, and

Anthony Tucci

2:20 p.m. - 2:35 p.m.Rick Sommer Logic, Intuition, and Infinity . Slides.

2:40 p.m. - 2:55 p.m.Rahmat Rashid and Defining Abstraction. Slides (pptx).
Mark Anderson

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Virtual JMM, April 6-7, 2022

Special Session on Competing foundations for mathematics: how do we choose?

Does the existence of many possible foundations of mathematics (some of which are mutually incompatible) pose a problem for mathematical realism/platonism? Is set theory or category theory the right foundation? For each, there are different versions. For example, for set theory, there’s Zermelo-Fraenkel (with or without the axiom of choice, with or without large cardinals, etc.), Cantor-von Neumann, Quine's NF, and others. And then there’s category theory, and topos theory. Each is importantly different from the others. But if realism about mathematics is correct, shouldn't there be just one correct foundational system? If so, which is correct? On the other hand, for physicists, a proliferation of theories does not call into question the reality of the external world. Why can mathematicians make important and meaningful contributions to their fields and yet simultaneously avoid, and indeed, often be ignorant of, mathematical foundations? How would we argue that a particular foundation is the correct choice? Or is realism wrong, and there is no one correct foundation? Should fruitfulness be the deciding mechanism? But can this lead to incorrect mathematics? In short, do specific formulations in mathematical foundations matter?

Day Time (PDT) Presenter Title
Apr. 68:00-8:45 amJohn BaldwinCategory theory and Model Theory: Symbiotic Scaffolds. Slides.
Apr. 69:00-9:45 amColin McLartyReality never has just one correct foundation
Apr. 610:00-10:45 amMichael ShulmanComplementary foundations for mathematics: when do we choose? Slides.
Apr. 611:00-11:45 amDiscussion
Apr. 61:00-1:45 pmJeremy AvigadThe Design of Mathematical Language. Slides.
Apr. 62:00-2:45 pmWilfried SiegMethodological Frames: Mathematical structuralism and proof theory. Slides.
Apr. 63:00-3:45 pmJames WalshOn the hierarchy of natural theories. Slides.
Apr. 65:00-5:45 pmDiscussion
Apr. 78:30-8:50 amJames HendersonRealism and Undeterminism in Mathematics and the Physical Sciences. Slides.
Apr. 79:30-9:50 amAlejandro CuneoAn Unorthodox Philosophy of Mathematics. Slides.
Apr. 710:00-10:20 amJohn BurkeStrict Finite Foundations of Mathematics. Slides.
Apr. 710:30-10:50 amThomas DruckerMathematics, Bivalence, and Alternative Logics
Apr. 711:00-11:45 amDiscussion

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Virtual JMM, January 6, 2021

Philosophy of Mathematics, in memory of Reuben Hersh

Philosophy of mathematics since the late 1970s owes a great debt to Reuben Hersh (1927-2020), who, arguably more than anyone else at the time, re-engaged mathematicians with questions on the nature of mathematics and proof. Hersh's writings on social constructivism (that the reality of mathematics is as a social, cultural, and historical construct), on actual proofs done by mathematicians (as opposed to formal proofs) and mathematics as a human activity (as opposed to a platonic ideal or a formal system) were and still are controversial. However, his work inspired many mathematicians to elucidate their own views on such matters, and the resulting discussions remain fruitful today. This session welcomes talks engaging with any of the many topics in the philosophy of mathematics that Hersh discussed.

2:15 p.m. MST1163-I5-1156Rachel RupnowAlgebraists' Metaphors for Sameness: Philosophies, Variety, and Commonality
2:35 p.m. MST1163-I5-1276Thomas DruckerWhy is There a Question About Why There is Philosophy of Mathematics At All?

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Denver, CO JMM, January 18, 2020

Role of Explanation in Mathematical Proofs

Mathematical proofs are a form of argument. We can say of arguments in general--and mathematical proofs specifically--that, when sound, they show us that the claim made is true. But often some arguments--and this includes some mathematical proofs--do more. They also explain to us why it is true. Proposed talks might discuss (but are not limited to) the following topics. What is it to explain why a mathematical theorem is true? Which mathematical proofs explain why the theorem proved is true? Some doubt that proofs by mathematical induction can. Is mathematical explanation different from, say, scientific explanation (which does not involve the use of mathematics)? Is it different from historical explanation? Or is there a unified sense of 'explanation' which is common to its use in all subjects, including mathematics? Are there instances of mathematical theorems which have multiple proofs, some of which are elegant and simple, but not explanatory, while the others are neither elegant nor simple, but explanatory? If so, does being explanatory count as a good reason to prefer one kind of proof over the other? If a mathematician finds a shorter proof of some theorem, will the shorter proof be more explanatory than the longer proof? All paper proposals which discuss the role of explanation in mathematical proofs will be considered.

8:00 a.m.1154-O1-487James Henderson, "Explanatory Proofs"
8:35 a.m.1154-O1-2227Jeremy Case, "Mathematical Explanation as an Aesthetic"
9:10 a.m.1154-O1-2672Paul Zorn, "Proofs that explain, proofs that don't, and proofs of the obvious"
9:45 a.m.1154-O1-716Bonnie Gold, "What makes proofs explanatory? Let's look at some examples"
10:20 a.m.1154-O1-2716Susan Ruff, "How logic is presented may obscure or enlighten"
11:00 a.m.1154-O1-1421Jeffrey Buechner, "Are mathematical explanations interest-relative?"

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Baltimore, MD JMM, January 18, 2019

Philosophy of Mathematics: Do Choices of Mathematical Notation (and Similar Choices) Affect the Development of Mathematical Concepts?

This session invites talks on any topic in the philosophy of mathematics. Our special theme this year is "Do Choices of Mathematical Notation (and Similar Choices) Affect the Development of Mathematical Concepts?" Once mathematical concepts have gelled, they tend to feel "natural" to mathematicians. But in the process of exploring and developing new concepts, mathematicians make choices, including of notation and terminology, that affect how the nascent concept solidifies. For example, to what extent does our decimal notation affect our understanding of numbers? Are there concepts and mathematical practices that can be understood in one notational framework and not in another? This session invites talks that look at this process, and the philosophical implications of the effect of our choice of mathematical notations on the development of mathematical concepts. Talks on the special theme will be given highest priority, but all talks on the philosophy of mathematics are welcome.

8:00 a.m.1145-L5-228 Thomas Morley, Feynman's Funny Pictures
8:30 a.m.1145-L5-1466Daniel Sloughter, What is a measure?
9:00 a.m.1145-L5-1790James Henderson, Multiplicity of Logical Symbols: Why Is That a Thing?
9:30 a.m.1145-L5-1687Kevin Iga, What does mathematical terminology say about linguistic determinism?
10:00 a.m.1145-L5-740Sergiy Koshkin, Mathematical Intuition and the Secret of Platonism
10:30 a.m.1145-L5-1961Jeffrey Buechner, What makes a notation for the natural numbers a good notation?
11:00 a.m.1145-L5-1343Ilhan Izmirli, Wittgenstein and Social Constructivism
11:30 a.m.1145-L5-1642Donald Palmer, Boundary Conditions: Numeric Representation and the Boundary of Pure and Applied Mathematics

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San Diego, CA JMM, January 12, 2018

Philosophy of Mathematics as Actually Practiced

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?"

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Atlanta GA JMM, January 7, 2017

Do Mathematicians Really Need Philosophy?

Nobel physicist Steven Weinberg famously declared that philosophers were useful to him only to defend him from other philosophers. Weinberg was complaining mostly about logical positivists, who don't seem to deal with mathematics much. But the philosophy of mathematics is a battleground for a number of warring schools, most prominently Platonists and constructivists. Does a practicing mathematician have to choose which school to join? Philosophical questions have been shown to have a huge positive effect in the teaching of mathematics, but need they come up during the development of a new branch of mathematics? Philosophy of mathematics has recently seen a movement toward "pluralism": let's accept everyone's philosophies, no matter how contradictory they may be. Is that a useful trend? Is it just a futile attempt to sweep a problem under the rug? This session, sponsored by POMSIGMAA, will give a forum for views from all sides of the issue, whether from the perspective of doing mathematical research, teaching mathematics, or more general philosophical fruitfulness. Other topics in the philosophy of mathematics will be considered as time allows.

1:00 p.m. 1125-C5-248 James R. Henderson, "Otavio Bueno's Mathematical Fictionalism"
1:30 p.m. 1125-C5-2521 Thomas Drucker, "Why Can't Those With Conflicting Views on the Foundations of Mathematics Just Get Along?"
2:00 p.m. 1125-C5-1670 Katalin Bimbó, "The unexpected usefulness of epistemological skepticism"
2:30 p.m. 1125-C5-507 Bonnie Gold, "Melding realism and social constructivism"

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Seattle WA JMM, January 7, 2016

Using Philosophy to Teach Mathematics

Courses in the philosophy of mathematics are rare, but philosophical questions frequently arise in the regular curriculum, often presenting difficulties to teachers who haven’t prepared to respond to them. In recent years a growing number of teachers of mathematics are discovering that addressing philosophical issues deliberately in their courses not only eases the strain but also enhances students’ ability to grasp difficult mathematical concepts. The upcoming MAA Notes volume, Using the Philosophy of Mathematics in Teaching Collegiate Mathematics, illustrates the ways a wide variety of teachers have found to introduce philosophical questions as an exciting part of presenting standard mathematical material. This session invites teachers at all levels to discuss ways they have found to include philosophy in the mathematics classroom. Papers on other topics in the philosophy of mathematics will be considered as time permits.

8:00 a.m. 1116-T5-103 Daniel C. Sloughter, "Making Philosophical Choices in Statistics"
8:30 a.m. 1116-T5-608 Sally Cockburn, "Senior Seminar in Set Theory as a Springboard for Mathematical Philosophy"
9:00 a.m. 1116-T5-2355 Thomas Drucker, "Role of Real Numbers in an Introduction to Analysis"
9:30 a.m. 1116-T5-2376 Brian R Zaharatos, "Statistics as a Liberal Art"
10:00 a.m. 1116-T5-177 James R Henderson, "Strange Bedfellows: Thomae's Game Formalism and Developmental Algebra"
10:30 a.m.1116-T5-2300 Luke Wolcott, "Gardens of Infinity: Cantor meets the real deep Web"
11:00 a.m. 1116-T5-2556 Martin Flashman, "Is Philosophy of Mathematics Important for Teachers?"

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Washington DC Mathfest, August 6, 2015

MathFest Centennial joint with Canadian Society for the History and Philosophy of Mathematics

Special Session on Philosophy of Mathematics

2:30 p.m. Elaine Landry, "Mathematical Structuralism and Mathematical Applicability"
3:00 p.m. Jean-Pierre Marquis, "Designing Mathematics: The Role of Axioms"
3:30 p.m. Alex Manafu, "Does the Indispensability Argument Leave Open the Question of the Causal Nature of the Mathematical Entities?"
4:00 p.m. Carl Behrens, "How Does the Mind Construct/Discover Mathematical Propositions?"
4:30 p.m. Jeff Buechner, "What is an Adequate Epistemology for Mathematics?"

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San Antonio TX JMM, January 13, 2015

Discovery and Insight in Mathematics

One new development in the philosophy of mathematics that mathematicians should welcome is an interest in the philosophy of mathematics as actually practiced by mathematicians. This session invites talks addressing philosophical issues concerning two related topics: how mathematics is discovered, and the role of insight in mathematical understanding and discovery. Epistemology studies how we come to know things. A distinction has been made between methods of discovery and methods of justification: that is, the way one discovers a mathematical truth – a conjecture, for example – may be quite different from how it is later justified (by a proof). What are the methods and grounds for such discoveries? What is the role insight plays in these discoveries? How do interconnections between mathematical concepts or subjects lead to discoveries? Talks addressing any of these issues within the philosophy of mathematics are appropriate for this session. Papers on other topics in the philosophy of mathematics will be considered as time permits.

Organizers: Dan Sloughter and Bonnie Gold

Session 1

8:00 a.m. 1106-C5-583 Daniel C Sloughter, “Insights Gained and Lost”
8:30 a.m. 1106-C5-443 James R Henderson, “Kepler's Mysterium Cosmographicum”
9:00 a.m. 1106-C5-2535 Horia I Petrache, “Removing bias: the case of the Dirac equation”
9:30 a.m. 1106-C5-1961 Ruggero Ferro, “An analogy to help understanding Discovery, Insight and Invention in Mathematics”
10:00 a.m. 1106-C5-1803 Carl E. Behrens, “How does the mind construct/discover mathematical propositions?”

Session 2

1:00p.m. 106-C5-1594 Reuben Hersh, “Mathematicians’ proof: ‘The kingdom of math is within you’”
1:30 p.m.1106-C5-1714 Thomas Drucker, “Explanatory and Justificatory Proofs”
2:00 p.m. 1106-C5-249 Bonnie Gold, “George Polya on methods of discovery in mathematics”
2:30 p.m. 1106-C5-2391 Tom Morley, “Some proofs and discoveries from Euler and Heaviside”
3:00 p.m. 1106-C5-2763 Kira Hylton Hamman, “Intuition: A History”
3:30 p.m. 1106-C5-838 Steven R Benson, “If you’re hoping for discovery, put away the handouts!”

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Baltimore MD JMM, January 16, 2014

Is Mathematics the Language of Science?

In 1960 physicist Eugene Wigner published an article entitled: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” in which he raised the question of the relationship between mathematics and the empirical sciences. Discussions of Wigner’s article often reflect the assumption that mathematics has relevance only as a means of exploring the physical world: as Wigner puts it, “in discovering the laws of inanimate nature.” Many mathematicians would find this an unacceptable restriction on the definition of their pursuits and activities. This session will explore the extent to which Wigner’s approach defines the role of mathematics, and entertain alternative or additional functions and purposes.

Organizers: Carl Behrens, Tom Drucker, Dan Sloughter

1:00 p.m. 1096-G1-1195Carl E. Behrens,"Mathematics Is a Science in its Own Right"
1:30 pm: 1096-G1-149 James R Henderson, "The Mathematics of Quantum Mechanics: Making the Math Fit the Philosophy"
2:00 pm: 1096-G1-2359 Horia I. Petrache, "A group theory perspective of mathematical constructs in physics"
2:30 pm:1096-G1-842 Mate Szabo, "The Roots Of Kalmar's Empiricism"
3:00 pm:1096-G1-2034 Ruggero Ferro,"No Surprise for the Effectiveness of Mathematics in the Natural Sciences"
3:30 pm:1096-G1-743 Ronald E. Mickens, "Mathematics as an Emergent Feature of the Physical Universe"
3:55 pm: 1096-G1-1414 Jeff Buechner, "A New Look at Wigner's `The Unreasonable Effectiveness of Mathematics in the Natural Sciences'"

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Hartford CT Mathfest, August 1 - 3, 2013

There were two types of sessions in Hartford: a session running throughout the meeting, of talks in either the history or philosophy of mathematics, and a session of talks on the interactions between history and philosophy of mathematics. Of the former, only the specifically philosophical talks during the daily sessions are listed.

Philosophy of Mathematics:

Friday, August 2

9 a.m. Matthew Clemens, "Fictionalism and Mathematical Practice," Keene State College
10 a.m. Robert H C Moir, "Rational Discovery of the Natural World: An Algebraic and Geometric Answer to Steiner"
11 a.m. Jean-Pierre Marquis, "Canonical Maps: Where Do They Come From and Why Do They Matter?"
3 p.m. Martin E Flashman, "Logic is Not Epistemology: Should Philosophy Play a Larger Role in Learning about Proofs?"

Interactions Between History and Philosophy of Mathematics

This session is geared specifically to interactions between the history and philosophy of mathematics. Talks will be expected either to approach specifically how each discipline informs the other in particular or general contexts, or to discuss issues and episodes that have implications for both the philosophy and the history of mathematics.

Organizers: Thomas Drucker, University of Wisconsin-Whitewater and Glen Van Brummelen, Quest University

Saturday, August 3

10:30 a.m.Thomas Drucker, "Zeno Will Rise Again"
11:00 a.m.Amy Ackerberg-Hastings,"Analysis and Synthesis in Geometry Textbooks: Who Cares?"
2:30 p.m.Robert S D Thomas, "Assimilation in Mathematics and Beyond
3:00 p.m.Lawrence D'Antonio, "Euler and the Enlightenment
3:30 p.m.Maryam Vulis, "Persecution of Nikolai Luzin"
4:00 p.m. Roger Auguste Petry,"Philosophy Etched in Stone: The Geometry of Jerusalem's 'Absalom Pillar'"
4:30 p.m. Jeff Buechner, "Understanding the Interplay between the History and Philosophy of Mathematics in Proof Mining"

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San Diego CA JMM, January 11, 2013

Philosophy, Mathematics and Progress.

Mathematics as a discipline seems to make progress over time, while philosophy is often taken to task for not having made such progress over the millennia. When philosophy comes to tackle issues related to mathematics, one natural topic is how mathematics succeeds in making progress while philosophy does not. One question to be addressed in this session is whether philosophy can help to explain the apparent progress displayed by mathematics. Another is whether the mismatch in progress between the disciplines is more apparent than real. As currents of mathematical change gather speed, perhaps a philosophical perspective is needed to make sure that current practitioners do not lose their footing. Papers addressing issues of progress in mathematics and philosophical ways of understanding that progress will help to continue conversations between mathematicians and philosophers.

Organizers: Thomas Drucker, University of Wisconsin-Whitewater and Daniel Sloughter, Furman University

1:00 p.m. 1086-L5-459 Deborah C. Arangno, “From Intuition to Esoterica
1:30 p.m. 1086-L5-71 Sean F. Argyle, “Mathematical Thinking: From Cacophony to Consensus
2:00 p.m. 1086-L5-618 Thomas Drucker, “Mathematical Progress via Philosophy
2:30 p.m. 1086-L5-1597 Daniel Sloughter, “Philosophical and Mathematical Considerationsof Continua
3:00 p.m.1086-L5-45 Amy Ackerberg-Hastings, “John Playfair, the Scottish Enlightenment, and ‘Progress’ in the History and Philosophy of Mathematics
3:30 p.m. 1086-L5-365 Ruggero Ferro, “Mathematics versus Philosophy
4:00 p.m. 1086-L5-209 James R. Henderson, “Progress in Mathematics: The Importance of Not Assuming Too Much
4:30 p.m. 1086-L5-874 Mate Szabo, “Kalmar’s Argument Against the Plausibility of Church’s Thesis

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Contributed Paper Session, Friday, January 6, 2012

Philosophy of Mathematics and Mathematical Practice

Philosophers search for insights into the most general epistemological and ontological questions: How do we know, and what is it that we know? Since mathematical knowledge is a significant piece of what we know, an explanation of the nature of mathematics plays an important role in philosophy. To this end, a philosopher of mathematics must pay careful attention to mathematical practice, what it is that mathematicians claim to know and how they claim to know it. A philosopher's explanation of mathematics cannot be a local explanation: it must fit within the larger picture of knowledge as a whole. A mathematician may have an account of mathematics which suffices for her work, but unless this account fits coherently into a larger epistemological and ontological picture, it will not suffice as a philosophy of mathematics. This session will address questions concerning the relationship between the philosophy and the practice of mathematics. We encourage papers to address questions such as: Should the philosophy of mathematics influence, or be influenced by, the practice of mathematics? Is it necessary for the philosophy of mathematics to influence the practice of mathematics for it to be relevant to mathematicians?

Organizers: Daniel Sloughter, Furman University and Bonnie Gold, Monmouth University

1:00 p.m.1077-K1-1196Daniel C. Sloughter, "The Consequences of Drawing Necessary Conclusions"
1:30 p.m.1077-K1-383 Thomas Drucker, "Thought in Mathematical Practice"
2:00 p.m.1077-K1-85 Joshua B. Wilkerson, "Beyond Practicality: George Berkeley and the Need for Philosophical Integration in Mathematics"
2:30 p.m.1077-K1-2002 Bonnie Gold, "Philosophy (But Not Philosophers) of Mathematics Does Influence Mathematical Practice"
3:00 p.m.1077-K1-1287 Sarah-Marie Belcastro, "Epistemological Culture and Mathematics"
3:30 p.m.1077-K1-904 Ruggero Ferro, "How Do I (We) Know Mathematics"
4:00 p.m.1077-K1-800 Jeff Buechner, "Formal mathematical proof and mathematical practice: a new skeptical problem"
4:30 p.m.1077-K1-1744 Nathaniel G. Miller,"CDEG: Computerized Diagrammatic Euclidean Geometry"

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New Orleans LA JMM, January 8, 2011

Philosophy of Mathematics in Teaching and Learning.

Mathematicians tend not to think about philosophical issues while teaching. Yet we are making ontological and epistemological commitments in much of what we do in the classroom. Every time we use a proof by induction or contradiction, discuss the existence or non-existence of a mathematical object, or refer to the discovery or creation of some piece of mathematics, we are endorsing some philosophical view of our subject.

The focus of this session is on the recognition and use of the philosophy of mathematics in the teaching and learning of mathematics. Can we understand mathematics without a philosophical context? Papers are encouraged to address questions such as: What philosophical issues (such as the nature of mathematical objects, the method of mathematical proof, and the nature of mathematical knowledge) should be treated in a mathematics course? How? In which course(s)? In what ways does the consideration of philosophical issues enhance a mathematics, or mathematics related, course? What does a learner gain by contact with issues from the philosophy of mathematics?

Other papers of a philosophical nature will be considered for inclusion as time permits.

Organizers: Dan Sloughter, Furman University, and Martin E. Flashman, Humboldt State University

1:00 p.m.1067-T1-1395Martin E. Flashman, "Square Roots: Adding Philosophical Contexts and Issues to Enhance Understanding"
1:30 p.m.1067-T1-2224Whitney Johnson and Bill Rosenthal, "Precalculus from an Ontological Perspective"
2:00 p.m.1067-T1-1766Thomas Drucker, "Putting Content into a Fictionalist Account of Mathematics for Non-Mathematicians"
2:30 p.m.1067-T1-2223Sheila K. Miller, "On the Value of Doubt and Discomfort"
3:00 p.m1067-T1-712Jeff Buechner, "Mathematical Understanding and Philosophies of Mathematics"
3:30 p.m.1067-T1-1527Ruggero Ferro, "Abstraction and objectivity in mathematics"
4:00 p.m.1067-T1-159James R. Henderson, "Causation and Explanation in Mathematics"
4:30 p.m.1067-T1-2327Andy D. Martin, "Claims Become Theorems, but Who Decides?"
5:00 p.m.1067-T1-2300Firooz Khosraviyani, Terutake Abe and Juan J Arellano, "Definitions in Their Developmental Stages: What should we call them?"

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San Francisco CA JMM, January 15, 2010

Philosophy of Mathematics for Working Mathematicians.

Philosophers have a wide range of views on the nature and existence of mathematical objects. How is it that mathematics continues to flourish, year after year, when philosophical questions about the fundamental nature of mathematical objects remain controversial and unsettled? This session invites papers that address, and clarify the relevance of, this issue, and propose views of mathematical objects that are consistent with mathematical practice.

Organizers: Carl Behrens, Alexandria, Virginia, and Bonnie Gold, Monmouth University

1:00 p.m.1056-M5-259James R. Henderson, “What Is the Character of Mathematical Law?
1:30 p.m.1056-M5-596 Carl E. Behrens, “John Stuart Mill's "Pebble Arithmetic" and the Nature of Mathematical Objects
2:00 p.m.1056-M5-1635 Thomas Drucker, “Dummett Down: Intuitionism and Mathematical Existence
2:30 p.m.1056-M5-1770 Martin Flashman, “The Articulation of Mathematics-A Pragmatic/Constructive Approach to The Philosophy of Mathematics
3:00 p.m.1056-M5-445 Lawrence A. D’Antonio, “Molyneux's Problem
3:30 p.m.1056-M5-1015 Jeff Buechner, “Mathematical practice and the philosophy of mathematics
4:00 p.m. 1056-M5-444 Daniel C. Sloughter, “Being a Realist Without Being a Platonist
4:30 p.m.1056-M5-1918 Ruggero Ferro, “An analysis of the notion of natural number

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Portland OR Mathfest, August 7, 2009

The History of Mathematics and its Philosophy, and Their Uses in the Classroom

Note: this session was joint with HOMSIGMAA. Most of the talks were history of mathematics; the talks listed below involved either only philosophy of mathematics, or both history and philosophy.

Organizers: Janet Beery, University of Redlands; Bonnie Gold, Monmouth University; Amy Shell-Gellasch, Pacific Lutheran University; Charlotte Simmons, University of Central Oklahoma

1:00 p.m.Martin E Flashman, "Which Came First? The Philosophy, the History, or the Mathematics?"
1:20 p.m.Daniel Sloughter, "Should My Philosophy of Mathematics Influence My Teaching of Mathematics?"
1:40 p.m.Bonnie Gold, "Philosophical Questions You DO Take a Stand on When You Teach First-year Mathematics Courses"
2:00 p.m.Jeff Buechner, "Using the Philosophy of Intuitionistic Mathematics to Strengthen Proof Skills"

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San Diego CA JMM, January 7, 2008

Organizers: Kevin Iga, Pepperdine University, and Bonnie Gold, Monmouth University

8:30 a.m.1035-Q1-1936Laura Mann Schueller, Mathematical Rigor in the Classroom
9:00 a.m.1035-Q1-25 Andrew G. Borden, Mathematics is a Meme(plex)
9:30 a.m.1035-Q1-1360 Carl E. Behrens, Are Euclid’s Postulates Really Essences?
10:00 a.m.1035-Q1-181 Daniel C. Sloughter, The De Continuo of Thomas Bradwardine
10:30 a.m. 1035-Q1-1461 Jeff Buechner, Ignoring the Obvious in Philosophical Applications of the Gödel Incompleteness theorems
11:00 a.m. 1035-Q1-94 James R Henderson, What Does It Mean for One Problem to Reduce to Another?
11:30 a.m.1035-Q1-1722 Ruggero Ferro, Remarks about the notion of EXISTENCE in mathematics

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New Orleans, LA JMM, January 6, 2007

Organizers: Bonnie Gold, Monmouth University, Charles Hampton, The College of Wooster

8:00 a.m.1023-N1-1867 Martin Flashman, What Place Does Philosophy Have in Teaching Mathematics?
8:40 a.m.1023-N1-1392 S. Stueckle, Mathematics as Representational Art
9:20 a.m.1023-N1-637 Ruggero Ferro, From an analysis of definitions to a view of mathematics,
10:00 a.m.1023-N1-973 Jeff Buechner, Searle's Metaphysics of Computation and Alternative Logics: A Surprising Connection,
10:40 a.m.1023-N1-882 Carl E. Behrens, Why do we all get the same answers? Kitcher's anti-apriorism and the problems of social constructivism
11:20 a.m.1023-N1-292 Andy D. Martin, In Praise of Cranks: Are You Thinking What I'm Thinking?
1:00 p.m.1023-N1-243 G. Edgar Parker,* James S. Sochacki, David C. Carothers, Why the Universe MUST be Complicated,
1:40 p.m.1023-N1-133 James Henderson, Catching the Tortoise: A Case Study in the Rules of Mathematical Engagement,
2:20 p.m.1023-N1-459 Nathaniel Miller, The Philosophical Status of Diagrams in Euclidean Geometry,
3:00 p.m.1023-N1-1387 Kenneth Manders, Representations in Knot Classification

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San Antonio TX JMM, January 12, 2006

Organizers: Roger A. Simons, Rhode Island College, Satish C. Bhatnagar, University of Nevada

8:00 a.m. 1014-A1-1158Carl E. Behrens, What Are Mathematical Objects? An Empiricist Hypothesis
8:30 a.m. 1014-A1-276 Bonnie Gold, Mathematical objects may be abstract, but they're NOT acausal
9:00 a.m. 1014-A1-1352Sarah-Marie Belcastro, How the way we `see' mathematics changes mathematics
9:30 a.m.1014-A1-1010 Martin E. Flashman, The Square Root of 2, Pi, and the King of France: Ontological and Epistemological Issues Encountered (and Ignored) in Introductory Mathematics Courses
10:00 a.m. 1014-A1-626 Sam Stueckle, Mathematics: An Aesthetic Endeavor
10:30 a.m. 1014-A1-500 James R Henderson, Propensities and the Two Varieties of Occult Qualities

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Atlanta GA JMM, January 7, 2005

Organizers: Charles Hampton, The College of Wooster, Bonnie Gold, Monmouth University

1:00 p.m.1003-P1-488 Bonnie Gold, What Is Mathematics II: A Possible Answer
1:25 p.m.1003-P1-652David W. Henderson, Daina Taimina, Strands in the history of geometry and how they affect our views as to what geometry is
1:50 p.m.1003-P1-830Robert E. Bradley, Object and Attribute: the case of Curves and Equations
2:15 p.m.1003-P1-522Homer S. White, Philosophy of Mathematics in Classical India: an Overview
2:40 p.m.1003-P1-655Daniel C. Sloughter, Realism and Mathematics: Peirce and Infinitesimals
3:05 p.m.1003-P1-405Thomas Drucker, Fictionalism and the interpretation of mathematical discourse
3:30 p.m.1003-P1-409Troy D. Riggs, Linguistic Relativity in Applied Mathematics
3:55 p.m.1003-P1-708Charles R. Hampton, Applied Mathematics---A Philosophical Problem
4:20 p.m.1003-P1-597Frederik S. Herzberg, Generalised likelihoods, ideals and infinitesimal chances - how to approach the "zero-fit problem,"

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Phoenix AZ JMM, January 9, 2004

2:00 p.m. 993-U1-528Charles R. Hampton, Philosophy of Mathematics: What, Who, Where, How and Why
2:25 p.m.993-U1-1331Padraig M. McLoughlin, On the Nature of Mathematical Thought and Inquiry: A Prelusive Suggestion
2:50 p.m.993-U1-185Paolo Rocchi, The Interpretation of Probability Is Perhaps an Ill-Posed Question
3:10 p.m. RECEPTION
3:40 p.m.993-U1-1266Joseph Auslander, When is a Proof a Proof?
4:05 p.m.993-U1-1080Jerry P. King, The Poetic View of Mathematics
4:30 p.m. 993-U1-376Lawrence D'Antonio, "You cannot solder an Abyss with Air" - the Role of Metaphor in Mathematics
(Note: this talk wasn't presented due to speaker's illness)
4:50 p.m.RECEPTION
5:20 p.m.993-U1-294Michael J. Bossé, The NonEuclidean Revolution Makes Relativism Available to the Rest of the World
5:45 p.m. 993-U1-1564Debasree Raychaudhuri, The Tension and the Balance Between Mathematical Concepts and Student Constructions of It
6:10 p.m.993-U1-408 G. Arthur Mihram* and Danielle Mihram, On Godel's Proof and the Relation Between Mathematics and the Physical World

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Baltimore MD JMM, January 17, 2003

1:00 p.m.983-S1-49 Thomas Drucker, Why Plato was not a Platonist
1:30 p.m.983-S1-351Daniel C Sloughter, Peirce, Zeno, Achilles, and the Tortoise
2:00 p.m.983-S1-544Kenneth Manders, Structuralist Mathematics and Mathematical Understanding
2:30 p.m.983-S1-546Roger A. Simons, Are Mathematical Objects Inside or Outside a Human Mind?
3:00 p.m.983-S1-341Bonnie Gold, What is Mathematics I: The Question
3:30 p.m.983-S1-429Sarah-marie Belcastro, A Conjecture about... Feminist Mathematics?
4:00 p.m.983-S1-137Michael J. Bossé, Defining Mathematical Esthetics within the NCTM Standards
4:30 p.m.983-S1-482John E Beam, Unfair Gambles in Probability (Preliminary Report)
5:00 p.m. 983-S1-551Satish C Bhatnagar, The Pedagogical Challenges of One to One Correspondence
5:30 p.m.983-S1-545M Anne Dow, A Unifying Principle Describing How Mathematical Knowledge Unfolds

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