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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Engineering
A close-up look at electronic paper reveals its exquisite patterns – and limitations
9 minutes
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Biography and memoir
The unique life philosophy of Abdi, born in Somalia, living in the Netherlands
29 minutes
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Cognition and intelligence
What’s this buzz about bees having culture? Inside a groundbreaking experiment
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Earth science and climate
The only man permitted in Bhutan’s sacred mountains chronicles humanity’s impact
22 minutes
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Cosmology
The Indian astronomer whose innovative work on black holes was mocked at Cambridge
13 minutes
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Ethics
For Iris Murdoch, selfishness is a fault that can be solved by reframing the world
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Death
A hunter’s lyrical reflection on the humbling business of being mortal
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Love and friendship
After his son’s terrorist attack, Azdyne seeks healing – and his granddaughter
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Astronomy
Seven years later, what can we make of our first confirmed interstellar visitor?
59 minutes