There is a bizarre number in maths referred to simply as ‘i’. It appears to break the rules of arithmetic - but turns out to be utterly essential for applications across engineering and physics. We are talking about the square root of -1, which makes no sense.Professor Fry waxes lyrical about the beauty and power of this so-called ‘imaginary’ number to a sceptical Dr Rutherford. Dr Michael Brooks, author of The Maths That Made Us, tells the surprising story of the duelling Italian mathematicians who gave birth to this strange idea, and shares how Silicon Valley turned it into cold hard cash. Professor Jeff O’Connell, Ohlone College California, demonstrates that it is all about oscillations, and Dr Eleanor Knox, philosopher of physics at KCL and a senior visiting fellow at the University of Pittsburgh reveals that imaginary numbers are indispensable for the most fundamental physics of all - quantum mechanics.

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