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J. Sullivan (1999)
"The Optiverse" and other sphere eversionsarXiv: Geometric Topology
(1994)
The knot book. Providence: American Mathematical Society
G. Budworth (1983)
The Knot Book
(1986)
Grammatica del Vedere: Saggi su Percezione e Gestalt
(2003)
Envisioning Transformations-The Practice of Topology Corfield
Could Hilbert
An Introduction to the Philosophy of Mathematics
W. Thurston (1994)
On Proof and Progress in MathematicsBulletin of the American Mathematical Society, 30
P. Kitcher (1985)
The nature of mathematical knowledge
J. Ferreirós (2015)
Mathematical Knowledge and the Interplay of Practices
Jessica Carter (2010)
Diagrams and Proofs in AnalysisInternational Studies in the Philosophy of Science, 24
Katherine Kinzler, E. Spelke (2007)
Core systems in human cognition.Progress in brain research, 164
M. Giaquinto (2007)
Visual thinking in mathematics
J. Hoorn (2005)
Distributed cognitionCognition, Technology & Work, 7
(1998)
A credo of sorts
J. Alexander (1928)
Topological invariants of knots and linksTransactions of the American Mathematical Society, 30
By Alexander (1923)
A Lemma on Systems of Knotted Curves.Proceedings of the National Academy of Sciences of the United States of America, 9 3
D. Corfield, Brian Davies (2011)
TOWARDS A PHILOSOPHY OF REAL MATHEMATICSNotices of the American Mathematical Society, 58
P. Mancosu, Klaus Jørgensen, S. Pedersen (2005)
Visualization, Explanation and Reasoning Styles in Mathematics
V. Jones (1985)
A polynomial invariant for knots via von Neumann algebrasBulletin of the American Mathematical Society, 12
J. Avigad (2007)
Philosophy of Mathematics: 5 Questions
W. Aspray, P. Kitcher (1988)
History and Philosophy of Modern Mathematics
I. Starikova (2012)
From Practice to New Concepts: Geometric Properties of Groups
K. Chemla (2005)
The Interplay Between Proof and Algorithm in 3rd Century China: The Operation as Prescription of Computation and the Operation as Argumento
(1998)
The optiverse . Narrated videotape ( 7 min )
(2012)
Braids . A movie
I. Starikova (2010)
Why do Mathematicians Need Different Ways of Presenting Mathematical Objects? The Case of Cayley GraphsTopoi, 29
P. Mancosu (2008)
The Philosophy of Mathematical PracticeHistory and Philosophy of Logic, 30
(1999)
Euclid or descartes: Representation and responsiveness, unpublished
I. Lakatos, J. Worrall, E. Zahar (1976)
Proofs and Refutations: Frontmatter
B. Larvor (2012)
How to think about informal proofsSynthese, 187
D. Rolfsen (2003)
Knots and Links
Silvia Toffoli, Valeria Giardino (2015)
An Inquiry into the Practice of Proving in Low-Dimensional Topology
Silvia Toffoli, Valeria Giardino (2014)
Forms and Roles of Diagrams in Knot TheoryErkenntnis, 79
J. Høyrup (2005)
Tertium Non Datur: On Reasoning Styles in Early Mathematics
(1997)
An introduction to knot theory (Graduate Texts in Mathematics)
[The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the target of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitive capacities demanded to the practitioners; and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology—the proof of Alexander’s theorem—is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to light philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on various notations, and the constant and fruitful feedback from one representation to another. Finally, some suggestions for further research are given in the conclusion.]
Published: May 26, 2016
Keywords: Mental Model; Braid Group; Mathematical Practice; Collective Dimension; Jones Polynomial
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