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## Main Question or Discussion Point

Hello.

The following is the content taken from here. It is a summary or map of mathematics.

"Foundation:

This area tries to work out with properties of mathematics itself and asks what the basis of all rules of mathematics is and is there complete set of fundamental rules or axioms from which all mathematics comes from and

My question is:

Why do I need to talk about consistency in mathematics? What does it mean if mathematics is said to have consistency with itself? I am unable to understand what the text highlighted in red (above) means.

Thank you.

The following is the content taken from here. It is a summary or map of mathematics.

"Foundation:

This area tries to work out with properties of mathematics itself and asks what the basis of all rules of mathematics is and is there complete set of fundamental rules or axioms from which all mathematics comes from and

**can we prove it is consistent with itself**? Mathematical theory, set theory and category theory try to answer this and the famous result in mathematical logic is Gödel incompleteness theorem which for most people means that mathematics does not have complete and consistent set of axioms which means it is all kind of made up by humans."My question is:

Why do I need to talk about consistency in mathematics? What does it mean if mathematics is said to have consistency with itself? I am unable to understand what the text highlighted in red (above) means.

Thank you.

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