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A talk at Jodrell Bank September 24, 2008

Posted by Alexandre Borovik in Uncategorized.

Yesterday I gave a talk “Social life of Infinity: from mathematics to Kitsch” at “Arts meet Science” event held at Jodrell Bank.  I mentioned in the talk that kisch is virtually unknown in mathematics and was presented with a counterexample: one of the speakers, sci-fi writer David  McIntee, gave me a Sudocube bought in the Visitor Centre shop. I proudly display a photo.

Back to Zeno, again and again… September 7, 2008

Posted by Alexandre Borovik in Uncategorized.
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A very interesting survey of the old conundrum written by a physicist, Zurab Silagadze.  Abstract:

“No one has ever touched Zeno without refuting him”. We will not refute Zeno in this paper. Instead we review some unexpected encounters of Zeno with modern science. The paper begins with a brief biography of Zeno of Elea followed by his famous paradoxes of motion. Reflections on continuity of space and time lead us to Banach and Tarski and to their celebrated paradox, which is in fact not a paradox at all but a strict mathematical theorem, although very counterintuitive. Quantum mechanics brings another flavour in Zeno paradoxes. Quantum Zeno and anti-Zeno effects are really paradoxical but now experimental facts. Then we discuss supertasks and bifurcated supertasks. The concept of localization leads us to Newton and Wigner and to interesting phenomenon of quantum revivals. At last we note that the paradoxical idea of timeless universe, defended by Zeno and Parmenides at ancient times, is still alive in quantum gravity. The list of references that follows is necessarily incomplete but we hope it will assist interested reader to fill in details.”

New Directions in Philosophy of Mathematics September 2, 2008

Posted by Alexandre Borovik in Uncategorized.
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MIMS Workshop on New Directions in Philosophy of Mathematics

Manchester, Saturday 4 October 2008.     

This workshop is part of the MIMS (Manchester Institute for Mathematical Sciences) New Directions series of workshops taking place in MIMS throughout 2008.

Mathematics and philosophy have a long history of involvement with each other. Profound changes to both disciplines have occurred through this interaction from the Greek exploration of the foundations of geometry, through the early modern philosopher-mathematicians, such as Descartes (analytic geometry) and Leibniz (calculus), to Frege and the beginnings of analytic philosophy under Russell. In recent times, however, this involvement has largely dwindled. For the most part philosophy’s interest in mathematics over the past half century has been of no interest to mathematicians. There has been a growing unrest with this state of affairs, and we are beginning to see encouraging signs of efforts to bridge the gulf between these great disciplines.

These new approaches range from studies which pay close attention to the cognitive, historical, or sociological aspects of mathematical practice, through to those which see developments within recent mathematics as being of philosophical importance, whether model theory, category theory, or the current intense interaction between mathematics and physics. The workshop will explore these themes, and will allow philosophers and mathematicians the chance to hear each other’s views on the direction forward for the philosophy of mathematics.

Organisers: Alexandre Borovik (School of Mathematics, University of Manchester), David Corfield (Department of Philosophy, University of Kent).

Programme, Saturday 4 October 2008:

10:00 Coffee

10:30 Mary Leng (Liverpool) Creation and discovery in mathematics

11:30 George Joseph (Manchester) History of Non-Western Mathematics: New Perspectives

12:30-13:00 Lunch, to be served on premises

13:00 Marcus Giaquinto (UCL) Curves in Proofs

14:00 Angus Macintyre (QMUL) The Impact of Incompleteness on Pure Mathematics

15:00 David Corfield (Kent) The Reality of Mathematics

16:00 Panel discussion, with some wine being served.

17:00 End

Venue: All talks will take place in Frank Adams Room in MIMS in the Alan Turing Building at the University of Manchester. The building is 20 minutes walk from the city centre and 15 minutes walk from Piccadilly or Oxford Road train stations.  

Directions to MIMS are available.

Night before, Friday 3 October: for those particiapants, who come on Friday to stay overnight, or who are local, we suggest an informal get-together at 19:00 at Lass O’Gowrie  with the aim of having dinner at 20:00 at East Z East Ibis Hotel on Princess street. Since an advanced booking for East Z East is needed, please notify me in advance that you are coming for dinner.

 If you wish to attend, please, send an e-mail by Friday 26 September to

Trimble on Category Theoretic Foundations September 1, 2008

Posted by dcorfield in Uncategorized.
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Todd Trimble has an excellent post on the Elementary Theory of the Category of Sets. He promises us more and asks for feedback.