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And now, sometime in the 1530s a group of mathematicians in

Northern Italy made an alarming discovery. In solving a problem that had perplexed

scholars for thousands of years they stumbled across another an entirely new type of

number. Mysteriously it didn't fit into their conventional number system and was apparently

useless for counting or measuring things. For more than a hundred years a new number attracted

hostility from mathematicians who regarded it as fictitious, impossible or

meaningless. The French thinker René Descartes shared this opinion but also gave it

a name. He called it the imaginary number. But since

the 18th century mathematicians have come to accept imaginary numbers as both genuine

and very useful. They underpin some of the modern world's most essential technologies from Main's electricity to radio. Without imagery numbers, you wouldn't be listening to radio for now.

They led to complex number

which goes into the search of for instance complex molecules such as insulin viruses even DNA.

With me to discuss the discovery and uses of imaginary numbers are Marcus

Eusotoy professor of Mathematics at Oxford University,

Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick,

and Caroline Series Professor of Mathematics also at the University of Warwick.

Mark Usoto, before we go to imaginary numbers,

let's start with real ones.

What is a real number and how did our number system come into being?

Well, our real numbers are actually very rich and came out of the problem of solving equations which is where this

...