I understand how the steps in a proof are inferred from other steps that are either given or already inferred. Sometimes though, in previous lectures, a professor would begin proving a certain theorem or equation (such as in calculus and statistics) and then at some point that may as well have been arbitrary to me, declared it proven. What decides the last step in a proof and what about it is so special that it “proves” the subject?
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Math is simply a few concepts we have observed to be true, and we combine those simple concepts to make complex conclusions.
Imagine you found a function, where for every X you plug in, it produces a Y value that is divisible by 3.
What steps do you think you can take to say 100% for certain that all numbers it produces are divisible by 3? Sure, you might be reasonably certain but if you aren’t 100% certain, people could die if we used your formula for something like flight-navigation. That is VERY serious.
While we can’t assume all of your functions numbers are divisible by 3, we are reasonably certain that any number times 3 is divisible by 3.
We can be certain that your function multiplies x by 3, and therefore can be certain your function works bc if it isn’t then it means these rules that we as a race have observed for thousands of years to be true aren’t true.
So, instead of taking YOUR word for it, we instead take the word of every human before us and go off what they all agreed upon. If you can prove that your idea is true because if it’s false it means our understanding of math is wrong, then you have proven that either humanity is wrong or you are correct.
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