(Below, I refine what the commenter had to say with this comment.)
You cannot corrupt math, although it’s not because there aren’t mathematicians who wouldn’t corrupt it if it could be corrupted. Once mathematicians stray from math, their ability to be logical and unbiased is nothing but average. What can be corrupted is the application of math, and many people confuse the application of math with math.
Because the most useful of math is tied into an algebraic structure, such as the real numbers, then how could any corruption of note not be logically tracked down? And concerning the motive to corrupt math, isn’t useful math useless without the tools of quantity or distance, counting or measure? There’s true and false, but even the use of logic symbols requires counting. Interfere with quantity or measure, and you’re shaking the foundations of math based on quantity or measure, which is essentially all of mathematics. I use “essentially” only because using “all” is hazardous.
The foundation of the real numbers, and other algebraic structures, is standard set theory, standard logic, and the natural numbers. A corrupt mathematical construct would likely be at a higher level than the real numbers, and anything at a lower level, what would be the purpose of that? Very few people have a problem with the way we count or with the law of the excluded middle; it might be better to say that few people desire the awareness to be aware of such things.
You don’t have to corrupt math to corrupt an experimental-based application of math. You only have to find a set of unproved assumptions and a mathematical model that will take your assumptions where you want those assumptions to go.
The logic underpinning the mathematics will be rock solid, even if the math is wrong. One description of math would be “logical statements which do not require experiment to determine the logical validity of the statements.” The absence of experiment is important because the biggest problem with corrupt knowledge is not that false statements can be made, but that false statements can be made which definitively cannot be determined to be false.
In useful math, all statements are considered to be either true or false, a consequence which prevents any assumption from corrupting math. With math, no assumption in any hypothesis requires justification; any assumption will merely result in logical consequences.
Math is not an experimental science, and a person can get as creative with definitions, undefined terms, and axioms as desired. If the creative result conflicts with the logic of useful math long established, the result will be ignored or abandoned by others.
To corrupt experimental-based applications of math, there is no need to corrupt math, you merely need a set of unproved assumptions and a mathematical model that will take your assumptions where you want those assumptions to go. And in fact, given your unproved assumptions, why shouldn’t you be able to get the desired conclusion? At most, you might merely need some additional unproved assumptions. At most, you would merely need to practice the freedom of logic practiced in mathematics, and with the right credentials, you’d be good to go.
(With the above in mind, it should be apparent that talking about math and religion in the same sentence, conversation, or discussion is no threat to math. Math can be used to make religiously motivated, false statements about the world we live in, but that’s an application of math.)
Filed under: Math
