Dating back to ancient Greece, the idea that any mathematical statement can ultimately be proven true or false, and any apparent contradiction ultimately erased, was as enticing as it was intuitive for many logicians and mathematicians. However, this long-dominant belief was upended in the early 20th century when the logician Kurt Gödel converted a written paradox – ‘This statement cannot be proved’ – into an equation, shattering the notion that mathematics could be built on structures of total certainty. This animation from TED-Ed traces how Gödel was able to use words to transform mathematics forever, and how his ‘incompleteness theorem’ has led to breakthroughs in both his field and the digital world.
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History of science
Ideas ‘of pure genius’ – how astronomers have measured the Universe across history
29 minutes
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Values and beliefs
Why a single tree, uprooted in a typhoon, means so much to one man in Hanoi
7 minutes
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Meaning and the good life
Why Orwell urged his readers to celebrate the spring, cynics be damned
11 minutes
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Making
On the Norwegian coast, a tree is transformed into a boat the old-fashioned way
6 minutes
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Animals and humans
One man’s quest to save an orphaned squirrel, as narrated by David Attenborough
14 minutes
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Computing and artificial intelligence
A future in which ‘artificial scientists’ make discoveries may not be far away
9 minutes
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History
Hags, seductresses, feminist icons – how gender dynamics manifest in witches
13 minutes
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Earth science and climate
Images carved into film form a haunting elegy for a disappearing slice of Earth
3 minutes
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Meaning and the good life
Leading 1950s thinkers on the search for happiness in trying times
29 minutes