I'll explain why pure Mathematics is unquestionable to the same extent as deductive logic is unquestionable. I leave the other sciences to others better informed.
The modern notion of mathematics is very agnostic. You can invent your own language, logic and axioms and whatever conclusions you derive is valid mathematics (within your system). But mathematicians like to be able to work together, so they use a common system. The logic and axioms (the "ZFC" axioms) for this system would make sense even to a child, adding minimum possible additional rules (countable on one hand) for completeness (for cases we do not encounter in real life and thus have no "common sense" for).
Thus math has nothing to do with our universe (unlike other sciences). It is a completely invented thing. It has nothing to do with what is true in our existence. It only exists in and "talks about" its own system. As it doesn't deal with our world, it is safe from politics. No financial or other incentive to falsify results. No new discovery within our universe can affect it.
It is the only science where each student is required to fully verify everything he is taught (talking about university and higher pure math which comes with proofs for everything unlike school math which doesn't). In fact, math is verified every time it is learned because you can't understand it without also verifying it (all you need is pencil and paper). Thus, mathematics taught in universities has been checked and re-checked probably hundreds of thousands of times. Newly published math is verified in full during peer review (at least in quality journals), but more importantly, it will be by everyone who learns it in the future.The more it is learned, the more verified it becomes (i.e. the result is repeatable).
If you find an error in anyone's proof, you can publish a counterexample or derive a contradiction and be assured the mathematics community will accept it. There's zero tolerance for incorrectness and there is a strong urge for completeness and maximum generality. That's why I love math. It's a model for all sciences to emulate.
PS: Long ago there was a view that math represents some truth about our universe, so there was a notion of what should or shouldn't be math. But in the 20th century, that view became extinct, thanks to the crisis caused by Cantor's work.
As u/JuanTitor points out, when you take this pure math and try to apply it to our universe to make predictions, that requires interpretation and thus that process is art not science. The science part comes in when you verify this mathematical model against observations. Even if it checks out, it should only be accepted provisionally, not as truth. The absolute truth is unknowable through science.
I'll explain why pure Mathematics is unquestionable to the same extent as deductive logic is unquestionable. I leave the other sciences to others better informed.
The modern notion of mathematics is very agnostic. You can invent your own language, logic and axioms and whatever conclusions you derive is valid mathematics (within your system). But mathematicians like to be able to work together, so they use a common system. The logic and axioms (the "ZFC" axioms) for this system would make sense even to a child, adding minimum possible additional rules (countable on one hand) for completeness (for cases we do not encounter in real life and thus have no "common sense" for).
Thus math has nothing to do with our universe (unlike other sciences). It is a completely invented thing. It has nothing to do with what is true in our existence. It only exists in and "talks about" its own system. As it doesn't deal with our world, it is safe from politics. No financial or other incentive to falsify results. No new discovery within our universe can affect it.
It is the only science where each student is required to fully verify everything he is taught (talking about university and higher pure math which comes with proofs for everything unlike school math which doesn't). In fact, math is verified every time it is learned because you can't understand it without also verifying it (all you need is pencil and paper). Thus, mathematics taught in universities has been checked and re-checked probably hundreds of thousands of times. Newly published math is verified in full during peer review (at least in quality journals), but more importantly, it will be by everyone who learns it in the future.The more it is learned, the more verified it becomes (i.e. the result is repeatable).
If you find an error in anyone's proof, you can publish a counterexample or derive a contradiction and be assured the mathematics community will accept it. There's zero tolerance for incorrectness and there is a strong urge for completeness and maximum generality. That's why I love math. It's a model for all sciences to emulate.
PS: Long ago there was a view that math represents some truth about our universe, so there was a notion of what should or shouldn't be math. But in the 20th century, that view became extinct, thanks to the crisis caused by Cantor's work.
As u/JuanTitor points out, when you take this pure math and try to apply it to our universe to make predictions, that requires interpretation and thus that process is art not science. The science part comes in when you verify this mathematical model against observations. Even if it checks out, it should only be accepted provisionally, not as truth. The absolute truth is unknowable through science.