All the math you know may be wrong. Or it could be right. It depends.
Around 1900, Bertrand Russell and Alfred Whitehead spent decades developing the beginnings of a totally rigorous and absolutely excruciating basis for the logical foundations of math. I think the first volume of the 3 volumes published got up to 1+1=2. German logician and mathematician Kurt Gödel didn't like Russel and his approach to logic. He published his incompleteness theorems in the 1930's which basically destroyed Russell's premise that you could build an absolutely complete and self consistent basis for a mathematical system. Bertrand Russel quit math and went on to become a antiwar activist. Gödel fled Hitler and wound up in Princeton NJ in 1946 at the Advanced Research Center where he starved himself to death fearing that people were going to poison him.
Gödel also put the first nail in the coffin in the debate whether the Continuum Hypothesis was correct. This was identified in 1900 as No. 1 in the most important problems in mathematics at the time. In the late 1800s, Georg Cantor postulated that the real number line ("The Continuum"" had a smaller infinite set (Aleph Naught which could be either rationals, algebraic irrationals, or other denumberable sets) and larger infinite set (Aleph One = transcendentals which could not be mapped one to one against an orderly infinite set). The CH said that a number of different infinities were embedded in the real number line, but no set of infinities between the two mentioned existed. Cantor spent years working on this problem and had multiple nervous breakdowns and stays in mental institutions. Godel and later Cohen, basically said the CH could be either proved true or false depending on the preferred set of conditions assumed.
And so it goes in mathematics. The long held concept has been that mathematics is always correct. Once you proved a theorem, it became a law, absolutely iron tight and no future discoveries would invalidate it (unlike science which has very few laws). Euclidean geometry was presumed inviolable until someone decided to challenge the foundation assumptions and came up with non-Euclidean (Riemann and other) geometries. Same way in set theory.
So in mathematics, you have absolutely correct structures, based on the set of initial assumption you made. My personal opinion is that more people are becoming open to the multiverse approach that our existing mathematical structures are only a portion of whats out there and that alternate mathematical structures can be found. It just depends on your premises.
So go hug a math teacher and then ask em about this.
BTW, you could do the same thing with Music Theory. Make your intervals different than 12 or non equally tempered and voila....fuel for multiple future TB flame wars.
