2 Added reference to Agrippa's Trilemma
source | link

Yes, mathematics (and classical logic) are based upon beliefs and assumptions.

Some of these are spelled out explicitly, as axioms.

Others generally go unstated. A good example of this is found in Lewis Carroll's seminal paper What the Tortoise Said to Achilles

It appears that what appeared to be air tight logic is actually full of paradoxes, circularity and relativity

That is indeed the case. Try not to let it get you down.

EDIT:

For why this is necessarily the case, see Agrippa's Trilemma.

Yes, mathematics (and classical logic) are based upon beliefs and assumptions.

Some of these are spelled out explicitly, as axioms.

Others generally go unstated. A good example of this is found in Lewis Carroll's seminal paper What the Tortoise Said to Achilles

It appears that what appeared to be air tight logic is actually full of paradoxes, circularity and relativity

That is indeed the case. Try not to let it get you down.

Yes, mathematics (and classical logic) are based upon beliefs and assumptions.

Some of these are spelled out explicitly, as axioms.

Others generally go unstated. A good example of this is found in Lewis Carroll's seminal paper What the Tortoise Said to Achilles

It appears that what appeared to be air tight logic is actually full of paradoxes, circularity and relativity

That is indeed the case. Try not to let it get you down.

EDIT:

For why this is necessarily the case, see Agrippa's Trilemma.

1
source | link

Yes, mathematics (and classical logic) are based upon beliefs and assumptions.

Some of these are spelled out explicitly, as axioms.

Others generally go unstated. A good example of this is found in Lewis Carroll's seminal paper What the Tortoise Said to Achilles

It appears that what appeared to be air tight logic is actually full of paradoxes, circularity and relativity

That is indeed the case. Try not to let it get you down.