# Human Dimension of Mathematics

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## Abstract

Human Dimension of Mathematics Alexandre Borovik April 2007 MIMS EPrint: 2008.38 Manchester Institute for Mathematical Sciences School of Mathematics The University of Manchester Reports available from: http://www.manchester.ac.uk/mims/eprints And by contacting: The MIMS Secretary School of Mathematics The University of Manchester Manchester, M13 9PL, UK ISSN 1749-9097 Human Dimension of Mathematics A Mathematician’s Look at History, Philosophy, Politics of Mathematics Alexandre Borovik Ankara, 5 April 2007 I. Social dimension of Mathematics II. Adam Smith and mathematics III. What is mathematics, really? IV. Mathematics and the brain V. What should mathematicians do? 2 I. Social dimension of Mathematics 3 Let us look at something practical. 4 A case study: RSA • On of the most widely used cryptographic systems. • Security is not proven. • Trust in RSA is rooted in the fact that, allegedly, USA and USSR adopted it in the systems of control of compliance with the Threshold Nuclear Ban Treaty (1974). 5 A case study: RSA • Breaking RSA is equivalent to breaking integers like 6, 15, 21, 35, . . . into product of smaller integers: 6 = 2× 3, 15 = 3× 5, 21 = 3× 7, . . . • The latter problem is assumed to be very difficult: can you decompose 391? 589? • But no-one ever offered any definite proof that the problem is indeed difficult. •Why could not it happen that some clever trick breaks RSA? 6 A case study: RSA By the way, 391 = 17× 23 589 = 19× 31 RSA routinely uses 150-digit numbers. 7 A case study: RSA • Our faith that RSA is secure is based on 2000 years of collective negative experience of mathematicians, who tried and failed decompose large numbers. • It is hard to imagine anything firmer rooted in the social and cultural practices of humankind. 8 Disclaimer for philosophers—if there are any in the audience. I am not a social constructivist: I insist that some of of mathematics associated wit

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