This document summarizes three conferences on mathematical cultures organized by Dr. Brendan Larvor of the University of Hertfordshire. The first conference focused on diversity in mathematical cultures and included talks on topics like mathematics in ancient China, the Russian tradition of mathematics, and mathematical practices in Brazilian engineering schools. The second conference centered on values in mathematics, with talks addressing concepts like purity, explanation, rigor and generality. The third conference covered additional topics related to mathematical cultures, such as mathematics in fiction, morality and mathematics, and mathematics education for indigenous communities in Western Canada.

1. Mathematical Cultures
Brendan Larvor
www.herts.ac.uk/philosophy

3. Mathematical Cultures
The First Conference: Diversity
• Karine Chemla The meaning of parts in mathematical texts: The example of chapters in
mathematical writings from ancient China
• Ursula Martin Online/off line - mathematical culture in the age of the internet
• Slava Gerovitch. Creative Discomfort: The Culture of the Gelfand Seminar at Moscow
University
• Jean-Michel Kantor. The Russian tradition of mathematics: Philosophical, religious and
cultural roots of the Moscow school of mathematics through the last century.
• Silvia De Toffoli and Valeria Giardino. Low-dimensional Topology as Visual•Mathematics
• Christian Greiffenhagen The Materiality of Mathematics: Presenting Mathematics at the
Blackboard
• Anouk Barberousse, Rossana Tazzioli and Emma Sallent Del Colombo. A story about
vectors and tensors - Notation, aesthetic values, and mathematical cultures
• Rogério Siqueira. Mathematical practices in three engineering schools in the Brazilian First
Republic (1889-1930)
• Stav Kaufman. Two Dualities: an Anthropology of a Mathematical Result

4. Mathematical Cultures
The First Conference: Diversity
• Norbert Schappacher The Human Factor in Mathematics: On various actors’ reactions to
different crises 1914 - 1945
• Albrecht Heeffer. The Abbaco mathematical culture (1300 - 1500)
• Henrik Kragh Sørensen. 'The End of Proof'•? The integration of different mathematical
cultures as experimental mathematics comes of age
• Katalin Gosztonyi. Mathematical Culture and Mathematics Education in Hungary in the
XXth Century
• Alexandre Borovik. Specialist Mathematics Schools
• Snezana Lawrence What are we like - the view of mathematics and mathematicians in
mathematics education
• Paul Andrews Cultures, curricula and classrooms: The construction of school mathematics

5. Mathematical Cultures
The Second Conference: Values
• Alan Bishop "What would the mathematics curriculum look like if instead of techniques,
mathematical values were the focus?" See also this encyclopedia entry on values in
mathematics.
• David Corfield "Good mathematics as good narrative”
• Paul Ernest "Mathematics and Values: Overt and Covert”
• José Ferreirós "Purity as a value: contexts and implications in modern German
mathematics“
• Katalin Gosztonyi "Why don’t we like formalism?”
• Emily Grosholz "Explanation and Meaning in Modern Number Theory“
• Emmylou Haffner "From a rigorous and perfectly general standpoint: rigor and generality in
Richard Dedekind's mathematics.”
• Matthew Inglis and Andrew Aberdein "The Personality of Mathematical Proofs”
• Ursula Martin and Alison Pease "An experimental approach to mathematical values“

6. Mathematical Cultures
The Second Conference: Values
• John Mason and Gila Hanna "Qualities of Proofs Contributing to Memorability: Length,
Width, and Depth and Front, Back, and Sides”
• Morten Misfeldt and Mikkel Willum Johansen "Values of problem choice and
communication”
• Colin Jakob Rittberg "A Lakatosian Approach to Value Systems”
• Emil Simeonov "Values in mathematics – a top-down and a bottom-up approach”
• Henrik Kragh Sørensen "Cultures of mathematization: Tracing divergent views on
explanations”
• Manya Raman Sundström "On Beauty and Explanation in Mathematics”
• Oleksiy Yevdokimov "Mathematical explanation as the cornerstone of the road towards
understanding and appreciation of mathematics"

7. Mathematical Cultures
The Third Conference: Others
• Michael Harris The Science of Tricks
Tony Mann Mathematics in fiction: the novels of Catherine Shaw
• Heather Mendick Mathematical Popular Cultures
• Madeline Muntersbjorn Mathematics and Morality
• Tom Archibald and Veselin Jungic. Mathematics and First Nations in Western Canada:
From Cultural Destruction to a Re-awakening of Traditional Reflections on Quantity and
Form
• Michael Barany. Remunerative Combinatorics: Mathematicians and their Sponsors after
the Second World War
• Jean Paul Van Bendegem. The practice of proof rather than proof
• Alexandre Borovik. Mathematics in the new pattern of division of labour
• Paul Ernest. Questioning the Value of Mathematics
• Norma Beatriz Goethe. Leibniz on painting thoughts, playing with transmutations, working
with ´compendia´

8. Mathematical Cultures
The Third Conference: Others
• Albrecht Heeffer. Jesuit strategies for the recruitment of interest in mathematics after the
Ratio Studiorum (1599)
• Elizabeth Hind. Mathematics in STEM education – Where does it fit?
• Timothy Johnson. Is fairness a mathematical concept?
• Markus Pantsar. The Great Gibberish: Mathematics in Western Popular Culture
• Emil Simeonov. Is mathematics an issue of general education?
• Henrik Kragh Sørensen. Narrating Abel: Aesthetics as biography of the mathematical
persona in public culture

9. Mathematics and First Nations in Western Canada
Tom Archibald and Veselin Jungic
The history of the relationship between Indigenous peoples and European colonists in
Western Canada is one fraught with longstanding unresolved disputes that have typically
led, since the forming of Canada, to unilateral action on the part of the Canadian national
and provincial governments aiming at reaffirming the rights of the newcomers over native
rights. For a long period of time the principal aim was one of cultural destruction, as
evidenced by the mandated residential schools. These began in the nineteenth century as
private entities, but were transformed into a national program that was aimed at ending
the "Indian problem"; the last were closed in the 1990s. The treatment allotted to those
who did not learn mathematics well was the same as that given for not speaking English
or failing to adopt other required norms: beating. The attitudes to learning mathematics
(and formal learning generally) that this produced over several generations was quite
naturally negative, and efforts to provide a renewed system of education that addresses
the bad feelings while providing a full range of opportunities to Indigenous students have
met with many obstacles.

10. Mathematics and First Nations in Western Canada
Tom Archibald and Veselin Jungic
Yet it is our contention that the native cultures of western Canada are not "non-
mathematical". Experience both in examining older traditional sources and in discussing
mathematical ideas with elders, teachers, and students provides many examples of
mathematical questions and procedures that are culturally based. In this paper, following
a brief description of the historical roots of the present situation, we describe several
instances of culturally based mathematical problems and responses. We will also
describe the ``Math Catcher'' outreach program which seeks to identify and build on this
base. Its accompanying production of learning materials in Indigenous languages is one
effort to resituate mathematics at the core of a forward-looking yet traditionally acceptable
education for the fastest-growing school age population in the region, Indigenous youth

11. Cultures of Mathematics IV
March 2015 New Delhi, India

12. Who we are...
Isabel Cafezeiro
Universidade Federal Fluminense
Niterói
Ricardo
Kubrusly
Edwaldo
Cafezeiro
Ivan da Costa
Marques
Universidade Federal do Rio de Janeiro
Paulo Freire and mathematics, for
a situated approach of
mathematics

13. Betânia, Brasil, 2011

14. - We have to take it easy because students get angry. Natives have
a short fuse. They just want classes in Ticuna. But there is no
teaching materials in Ticuna. Crazy it here. We insist that the
Portuguese have to be the spoken language in school. But they are
offended. They think that we are putting down their language .
- I can not understand. It had to be
in Ticuna.
At school, the teachers complain:
And the natives retort:

15. Popular Mathematics I: String Figures
Eric Vandendriessche (Université Paris Diderot, France).

16. Popular Mathematics II: Kolem
Sunita Vatuk (City University of New York, U.S.A.)

17. The Königsberg Bridges : Not Mathematics?
But Euler Solved It Anyway

18. Mathematics: The Science of Patterns
A conception broad enough to find application in all cultures?

19. Who Was That?
Dr. Brendan Larvor
Reader in Philosophy and Head of
Philosophy
The University of Hertfordshire
b.p.larvor@herts.ac.uk
http://www.herts.ac.uk/philosophy
http://www.larvor.pwp.blueyonder.co.uk/