Imaginary Numbers

In Our Time

BBC

History

4.6 • 9.2K Ratings

🗓️ 23 September 2010

⏱️ 43 minutes

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Summary

Melvyn Bragg and his guests discuss imaginary numbers. In the sixteenth century, a group of mathematicians in Bologna found a solution to a problem that had puzzled generations before them: a completely new kind of number. For more than a century this discovery was greeted with such scepticism that the great French thinker Rene Descartes dismissed it as an "imaginary" number.The name stuck - but so did the numbers. Long dismissed as useless or even fictitious, the imaginary number i and its properties were first explored seriously in the eighteenth century. Today the imaginary numbers are in daily use by engineers, and are vital to our understanding of phenomena including electricity and radio waves. With Marcus du SautoyProfessor of Mathematics at Oxford University Ian StewartEmeritus Professor of Mathematics at the University of WarwickCaroline SeriesProfessor of Mathematics at the University of WarwickProducer: Thomas Morris.

Transcript

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0:00.0	Just before this BBC podcast gets underway, here's something you may not know.
0:04.7	My name's Linda Davies and I Commission Podcasts for BBC Sounds.
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0:39.0	For more details about In Our Time and for our terms of use, please go to BBC.co. UK forward slash radio for. I hope you enjoy
0:46.5	the program. I know sometime in the 1530s a group of mathematicians in Northern Italy
0:52.4	made an alarming discovery.
0:54.0	In solving a problem that had perplexed scholars for thousands of years,
0:58.0	they stumbled across another, an entirely new type of number.
1:01.0	Mysteriously, it didn't fit into their conventional number system
1:04.6	and was apparently useless for counting or measuring things.
1:07.4	For more than 100 years, a new number attracted hostility from mathematicians who
1:11.3	regarded it as fictitious, impossible or meaningless.
1:14.5	The French thinker René Descartes shared this opinion but also gave it a name.
1:18.8	He called it the imaginary number.
1:21.7	But since the 18th century mathematicians have come to accept imaginary numbers as both genuine and very useful.
1:27.0	They underpin some of the modern world's most essential technologies from Main's electricity to radio.
1:32.0	Without imaginary numbers, you wouldn't be listening to
1:34.3	Radio for now.
	...

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