If your math is wrong, one may assume it does not work, as it does not, but how do you know, if you don't DO anything with it with numbers?
Surprisingly you can find mathematical papers which never demonstrate with actual numbers, where in number theory that amazes me to no end.
What good is a math paper in number theory where at the end you cannot see with some number what was supposedly proven?
How is that even satisfying to anyone?
I find that when I look over math papers now (yes I do at times) I skim to the end, and see if they ever show anything with actual numbers.
Seeing mathematicians at their best as mathematical scientists puts the pressure on them to be correct, and numbers are brutally efficient at weeding out charlatans: the math of charlatans does not work!!!
The issue of certainty is one I'm aiming to put front and center across the academic world. That will make funding easy, as policymakers have the tools to tell when researchers are doing real work or not, regardless of the complexity of that research.
I covered that issue on one of my other blogs:
Simply forcing mathematicians to demonstrate what you can predict with their research about numbers and then see if that prediction is verified--where in mathematics 100% is usually required--removes human error in a functional way.
That does not replace mathematical proof. And since I defined mathematical proof I am very well aware of how it works.
However, mathematicians have the skills to evaluate proof. But even a college administrator with no math skills whatsoever can evaluate a predictive test.
If you said one thing would happen and it didn't, then your math is wrong.