Mathematics is ultimately based upon bits of simple assumptions drawn from our everyday experiences and common sense.
For example we believe that
The above assumptions are purely based upon our common sense and logic from our everyday experiences and do not have any ‘deeper’ supporting maths to prove them.
So, mathematics is ultimately based upon our assumptions which we believe as true in our everyday life. Then how could any mathematical model make predictions that go against our common sense and logic? How can any theory challenge its own basic pillars of foundation and still be valid?
Mathematics is just a language
Mathematics is simply a language which uses numbers and symbols to express. Despite correct grammar, a weird statement doesn’t become right just because that is expressed in Greek language or a correct logic doesn’t become weird just because one couldn’t express the same in Greek.
Similarly, just because something is expressed in terms of weird numbers and symbols, a weird expression doesn’t automatically become a fact or law. 2×5=6 is obviously a wrong statement. So a mathematical expression can’t be right if it violates logic.
And, just because a logical argument or fact is not expressed in maths, it doesn’t automatically become wrong. Facts like we the humans exist on this Earth or the Earth rotates around the Sun remain facts though we can’t express the same in the language of mathematics.
A mathematical statement to be considered as correct, it must be built upon correct logic. And that is true with any statement in any language. The language doesn’t per se decides the truthfulness of a statement. It is the underlying logic which decides whether some statement is a fact or not.
So a mathematical statement can’t be considered beyond logic and one can’t swear by maths and overthrow logic.
Just like how wrong assumptions lead to wrong statements in any language, wrong assumptions (constant speed of light, constant speed of snail etc) will lead to wrong maths. And if one believes and goes by that wrong statement, one will be forced to make further wrong predictions.
Most importantly, something that can be explained in mathematical terms can also be expressed in terms of logical statements in any language. And there isn’t any puzzle that will only ‘yield’ to mathematics but not to logic. Of course, some factual statements may be better and more conveniently expressed in mathematical terms while some may be better expressed in conventional sentences.
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