p15 courtesy of Clay Mathematics Institute; © 2000 Clay Mathematics Institute, All Rights Reserved; pp21, 42 and 133 Science Photo Library; p37 SCALA, Florence; p73 Universitätsbibliothek Göttingen; p177 Cambridge University Library; p214 Photography by Ingrid von Kruse, Freibildnerische Photographie; p221 photo courtesy of Andrew Odlyzko; p229 photo courtesy of Professor Leonard M. Adleman.
Material from Contact by Carl Sagan: Copyright © 1985, 1986, 1987 by Carl Sagan. Reprinted with the permission of Simon & Schuster Adult Publishing Group and Orbit, a Division of Time Warner Books, UK.
The quotes by Julia Robinson in section ‘From the chaos of uncertainty to an equation for the primes’ in Chapter Eight are taken from Reid, C., Julia, A Life in Mathematics (Washington, DC: Mathematical Association of America, 1996). The quotes by André Weil in section ‘Speaking in many tongues’ in Chapter Twelve are taken from Weil, A., The Apprenticeship of a Mathematician (Basel: Birkhäuser, 1992). The quotes by G.H. Hardy throughout the book are taken from Hardy, G.H., A Mathematician’s Apology (Cambridge: Cambridge University Press, 1940) and from other articles by Hardy listed in Further Reading.
All reasonable efforts have been made by the author and the publisher to trace the copyright holders of the images and material quoted in this book. In the event that the author or publisher are contacted by any of the untraceable copyright holders after the publication of this book, the author and the publisher will endeavour to rectify the position accordingly.