Math also fails sometimes, we’ve had to invent new math along the way because math is always correct only in the given constraints of how we currently understand math. If those constraints are challenged math evolves.
Example, imaginary numbers weren’t a thing for a good while and some stuff didn’t work correctly. All math stands upon 1+1=2, we don’t know if that always holds true, for now we asume it.
In fact, the entire foundation of math – its system of axioms – has had to be fixed due to contradictions existing in previous iterations. The most well known perhaps being Russell’s paradox in naive set theory: “Let X be the set of all sets that do not contain themselves. Does X contain itself?”
In fact, there have been many paradoxes that had to be resolved by the set theory we use today.
There are no correct axioms. You can change the axioms as you wish and make your own math2.0. And you will be able to apply it to things that follow thoose axioms but finding such things that follow them is the only hard part. We define 1+1=2 and that is true because we define it that way. If it does not hold true in any physical or something then it is that you are applying a correct math for a system which doesnt work with that math(i.e, you are the problem for assuming the same axiom is true for the real system)
I might go even further and say there’s no “math”. There are a wide variety of axiomatic systems (eg. games). None has the sole claim to being “math”. Maybe they’re all “math”.
(On the other hand… I guess any system that contains the “natural numbers” would be sufficient for the bulk of what’s widely considered “math”.)
(I belive math and mathematics are different. What is commonly called math is just numbers and stuff. But mathematics fits the general description of all axioms)
Example, imaginary numbers weren’t a thing for a good while and some stuff didn’t work correctly
And here’s Lewis Carroll to regale us with a tale that absolutely won’t be misunderstood and taken at face value by later generations about how foolish these silly mathematicians are with their wonky numbers.
Math also fails sometimes, we’ve had to invent new math along the way because math is always correct only in the given constraints of how we currently understand math. If those constraints are challenged math evolves.
Example, imaginary numbers weren’t a thing for a good while and some stuff didn’t work correctly. All math stands upon 1+1=2, we don’t know if that always holds true, for now we asume it.
In fact, the entire foundation of math – its system of axioms – has had to be fixed due to contradictions existing in previous iterations. The most well known perhaps being Russell’s paradox in naive set theory: “Let X be the set of all sets that do not contain themselves. Does X contain itself?”
In fact, there have been many paradoxes that had to be resolved by the set theory we use today.
There are no correct axioms. You can change the axioms as you wish and make your own math2.0. And you will be able to apply it to things that follow thoose axioms but finding such things that follow them is the only hard part. We define 1+1=2 and that is true because we define it that way. If it does not hold true in any physical or something then it is that you are applying a correct math for a system which doesnt work with that math(i.e, you are the problem for assuming the same axiom is true for the real system)
I might go even further and say there’s no “math”. There are a wide variety of axiomatic systems (eg. games). None has the sole claim to being “math”. Maybe they’re all “math”.
(On the other hand… I guess any system that contains the “natural numbers” would be sufficient for the bulk of what’s widely considered “math”.)
I’ll pick my side. They are all mathematics
(I belive math and mathematics are different. What is commonly called math is just numbers and stuff. But mathematics fits the general description of all axioms)
And here’s Lewis Carroll to regale us with a tale that absolutely won’t be misunderstood and taken at face value by later generations about how foolish these silly mathematicians are with their wonky numbers.
Axioms serve as a starting point.