The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy

Important Vocabulary Words From The Video

logician

A logician is someone who specializes in logic. They use logic to figure out how things work and to make decisions.

  • The logician argued that the treaty was a bad idea because it would cause too many problems.
  • The logician argued that the treaty would be a good idea because it would prevent war.
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axiomatic

An axiomatic statement is a statement that is basic and obvious, and that cannot be disputed or questioned. The statement "two plus two equals four" is an example of an axiomatic statement.

  • An axiomatic statement is a statement that is selfevident.
  • It is an axiomatic truth that all statements are either true or false.
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disprove

To disprove something is to prove that it is not true. Scientists often use the term to refer to the process of testing a theory or hypothesis to see if it is true.

  • The scientist disproved the theory that the earth was the center of the universe.
  • The scientist disproved the theory that the moon was made out of cheese.
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paradoxes

A paradox is a situation that seems to be in conflict with itself. For example, it might be difficult to be both a successful and a popular person.

  • The paradox of the self is the idea that the self is contradictory.
  • The paradox of the frog is the idea that a frog can stay in water but it can't breathe.
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unprovable

Unprovable means that it cannot be proven. It's impossible to know for sure whether or not something is unprovable.

  • The claim that the moon is made of cheese is unprovable.
  • The claim that the moon landing was a hoax is unprovable.
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provable

Proven means that something has been demonstrated to be true. It can also mean that something is definitely true.

  • The theorem is provable, which means that it can be demonstrated using mathematical arguments.
  • The claim that the moon landing was faked is not provable, because there is no evidence that it was faked.
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provably

Provably means that you can be certain that something is the case. You can prove that something is true by doing something that is impossible to fake.

  • The algorithm is provably secure.
  • The vaccine is provably effective.
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fervently

fervently means very strongly. When you fervently believe in something, you have a lot of faith in it.

  • She fervently believed that the treatment would work.
  • He fervently believes that humans are the only intelligent creatures on Earth.
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