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

## Important Vocabulary Words From The Video

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.

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.

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.

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.

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.

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.

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.

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.