You can at least predict things using maths
No, you cannot. You can make stuff up, and you can know stuff (and you can prove that you know stuff). You can't predict in maths that 1 + 1 = 2, you can define 1, 2, +, and =, so that it is necessarily true 1 + 1 = 2.
I disagree that Euclidean geometry is a tautology
Not all of it. Euclid's 5 postulates are arbitrarily made up, baseless, unprovable statements.
"Let the following be postulated":
- "To draw a straight line from any point to any point."
- "To produce [extend] a finite straight line continuously in a straight line."
- "To describe a circle with any centre and distance [radius]."
- "That all right angles are equal to one another."
- The parallel postulate: "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles."
Everything else in Euclidean geometry is tautologies. For example, the statement "In Euclidean geometry, if a convex polygon has
n sides, then its interior angle sum is given by the following equation:
S = (
n −2) × 180°." is a tautology that tells you nothing that you didn't already know. To prove a theorem is true, you need to prove that it tells you nothing you didn't already know.
All things in math consist of three categories (everything in each category is synonymous with everything else):
1) arbitrarily made up statements such as postulates, axioms, definitions, premises, assumptions, etc: these are considered true for no other reason than that someone said so, and no attempt is made to prove them.
2) things known to be true, such as theorems and tautologies; theorems are proved to be true by showing that they can be deduced from or are equivalent to a tautology
3) things that are known to be false, such as contradictions (which are the negation of a tautology).
Anyways, saying "of course that is true I already knew that" isn't a very good argument against something.
Who said that?
You called "survival of the fittest" a tautology, which means that you said that you knew it has to be true and that it tells you nothing you didn't already know. A tautology is a statement of the form "If A then A" or "A or not A" -- by logical necessity, both true and technically uninformative. Note however, that all theorems in mathematics are just fancy tautologies, which technically are no more informative that "A or not A".