Chalk: Materials and Concepts in Mathematics Research

So recounts an admiring biographer the pedagogical exploits of AugustinLouis Cauchy, a towering figure of early nineteenth-century mathematics. Cauchy was trained and then taught at the prestigious Ecole Polytechnique, a school for military engineers that not long before Cauchy’s matriculation became one of the first to make systematic use of a new mode of advanced mathematical instruction: lessons at a blackboard. Today, chalk and blackboards are ubiquitous in mathematics education and research. Chalk figures prominently in the imaginations and daily routines of most mathematicians. ∗Corresponding author (mbarany@princeton.edu). Princeton University, Program in History of Science. Barany’s work was supported by a Marshall Scholarship and a National Science Foundation Graduate Research Fellowship (Grant No. DGE-0646086). †University of Edinburgh, School of Social and Political Science. Valson 1868, 1:253, our translation from the French original.

[1]  C. Wylie.  Teaching manuals and the blackboard: accessing historical classroom practices , 2012 .

[2]  B. Latour.  Drawing Things Together , 2011 .

[3]  Christian Greiffenhagen,et al.  Video Analysis of Mathematical Practice? Different Attempts to "Open Up" Mathematics for Sociological Investigation , 2008 .

[4]  Eric Livingston,et al.  The Context of Proving , 2006 .

[5]  Philip Mirowski,et al.  Masters of Theory: Cambridge and the Rise of Mathematical Physics. , 2005 .

[6]  Michael Aschbacher,et al.  Highly complex proofs and implications of such proofs , 2005, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  G. Lakoff,et al.  Where mathematics comes from : how the embodied mind brings mathematics into being , 2002 .

[8]  N. Guicciardini.  Squaring the Circle. The War between Hobbes and Wallis , 2001 .

[9]  Judith B. Krauss,et al.  A fresh look , 2001 .

[10]  Eric Livingston,et al.  Cultures of Proving , 1999 .

[11]  Hélène Mialet.  Do Angels Have Bodies? Two Stories About Subjectivity in Science: , 1999 .

[12]  R. Netz.  The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History , 1999 .

[13]  Elinor Ochs,et al.  Down to the wire: The cultural clock of physicists and the discourse of consensus , 1997, Language in Society.

[14]  Andrew Pickering,et al.  The mangle of practice : time, agency, and science , 1997 .

[15]  Martina Merz,et al.  Deconstruction in a `Thinking' Science: Theoretical Physicists at Work , 1997 .

[16]  J. Lave,et al.  Understanding Practice: Perspectives on Activity and Context , 1996 .

[17]  B. Rotman.  Thinking Dia-Grams: Mathematics, Writing, and Virtual Reality , 1995, Mathematics, Science, and Postclassical Theory.

[18]  W. Thurston.  On Proof and Progress in Mathematics , 1994, math/9404236.

[19]  Elinor Ochs,et al.  Interpretive Journeys: How Physicists Talk and Travel through Graphic Space , 1994 .

[20]  B. Rotman.  Ad Infinitum... The Ghost in Turing's Machine: Taking God Out of Mathematics and Putting the Body Back In. An Essay in Corporeal Semiotics , 1993 .

[21]  Herbert Mehrtens,et al.  Moderne Sprache, Mathematik : eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme , 1992 .

[22]  J. Lave.  Cognition in Practice: Outdoors: a social anthropology of cognition in practice , 1988 .

[23]  L. Suchman.  Representing practice in cognitive science , 1988 .

[24]  Steve Woolgar,et al.  Time and documents in researcher interaction: Some ways of making out what is happening in experimental science , 1988 .

[25]  Mary Elizabeth Lynch,et al.  The externalized retina: Selection and mathematization in the visual documentation of objects in the life sciences , 1988 .

[26]  Eric Livingston,et al.  The Ethnomethodological Foundations of Mathematics , 1986 .

[27]  Michael Lynch,et al.  Art and Artifact in Laboratory Science: A Study of Shop Work and Shop Talk in a Research Laboratory , 1985 .

[28]  Steve Woolgar,et al.  Laboratory Studies: A Comment on the State of the Art , 1982 .

[29]  Philip J. Davis,et al.  The Mathematical Experience , 1982 .

[30]  David Bloor,et al.  Polyhedra and the Abominations of Leviticus , 1978, British Journal for the History of Science.

[31]  Richard J. Lipton,et al.  Social processes and proofs of theorems and programs , 1977, POPL.

[32]  D. Bloor,et al.  Knowledge and Social Imagery , 1977 .

[33]  David Bloor,et al.  Wittgenstein and Mannheim on the sociology of mathematics , 1973 .

[34]  David Kirshner,et al.  Situated cognition : social, semiotic, and psychological perspectives , 2009 .

[35]  Catherine Porter,et al.  Weaving Self-Evidence: A Sociology of Logic , 2008 .

[36]  D. Kaiser.  Growing Explanations: Historical Perspectives on Recent Science , 2006 .

[37]  David Kaiser.  Drawing Theories Apart: The Dispersion of Feynman Diagrams in Postwar Physics , 2005 .

[38]  Wes Sharrock,et al.  Gestures in the blackboard work of mathematics instruction , 2005 .

[39]  Donald MacKenzie,et al.  Mechanizing Proof: Computing, Risk, and Trust , 2001 .

[40]  Bettina Heintz,et al.  Die innenwelt der mathematik : zur kultur und praxis einer beweisenden disziplin , 2000 .

[41]  Elinor Ochs,et al.  Interaction and grammar: “When I come down I'm in the domain state”: grammar and graphic representation in the interpretive activity of physicists , 1996 .

[42]  K Széll,et al.  [The lecture]. , 1994, Orvosi hetilap.

[43]  B. Rotman.  Toward a semiotics of mathematics , 1988 .

[44]  Brian Rotman,et al.  Towards a Semiotics of Mathematics , 1988 .

[45]  E. Schegloff.  Structures of Social Action: On some gestures' relation to talk , 1985 .

[46]  B. Latour,et al.  Laboratory Life: The Construction of Scientific Facts , 1979 .

[47]  M. L'hermite,et al.  La vie et les travaux du Baron Cauchy, membre de l'Académie des Sciences , 1868 .