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In this week's programme Adam Walton is in conversation with Marcus Chown whose new book, 'Breakthrough' celebrates the 'magicians' of science who've predicted the existence of planets, black holes, gravitational waves and the Higgs Boson entirely through mathematics - and often years before other scientists were able to provide experimental proof.

Those 'magicians' include Urbain Le Verrier who in 1846 used mathematical calculations to predict the existence - indeed the exact position - of the planet Neptune. We also hear about physicist Paul Dirac whose mathematical equation led to the inescapable conclusion that a universe of antimatter existed.

'Breakthrough: Spectacular Stories of Scientific Discovery from the Higgs Particle to Black Holes' by Marcus Chown is published by Faber