When proof rules emotion

One benefit appreciate now more than could in the past was the questioning of certainty. Before did have situations where thought that proof was about a certainty of having checked everything. And could go over mathematical equations over and over again, thinking were correct. But thankfully had that collapse more than once.

People can talk mathematical proof, yet how do you know something is a mathematical proof? Answering that question for me became much about identities.

But still there is that fear of being a person who can look at something believing is true, and mind can play tricks on you. Which I think is how the mathematical discipline has turned to other eyes and checking by others. But human fallibility remains possible. Especially with complex arguments where I DO think computers will handle all proof checking, eventually.

For me though practical reality after looked into computerized proof checking, years ago, even contacting an expert in the area and getting nowhere, pushed me first with functional ideas, and then to number authority.

So defined mathematical proof functionally. But also now like to look at things like:

(46² + 48² + 72²)(172² + 258² + 430² + 602² + 1762²) = 

            615² + 3075² + 14145² + 15990²  + 188497²   =  77⁴*2¹⁰

Which is my favorite one lately. It was found using the BQD Iterator. Where was easy to figure out, but the cool thing is the numerical perfection. Once calculated you know must be perfect. Checking is easy enough with modern systems.

Compare though with:

(x² + 2y²)(u² + 3v²)(x'² + 4y'²)(u'² + 5v'²) = p² + 359q²

And finding integer solutions for all the variables is easy.

x = 1, y = 2, u = 2, v = 2, x' = 3, y' = 2, u' = 4, v' = 2, p = 358, q = 2

First iteration is easiest.

Both examples also should say demonstrate modular in that am using BQD Iterator with basic form u² + Dv² = F.

So that module is used twice for first, where expanded with a technique for having as many squares as wanted, and four times for second. So went less fancy with second example and left in variables versus putting in solutions like with prior one.

But feels so different to me regardless. There is logic and there is the feeling around looking at things. Now a step backwards to symbols, and is not so easy for me at least to feel certainty. Though mathematical proof IS there. And is interesting I think the emotion can feel despite the proof. Which in my experience?

Is great! The proof does not care about my emotion. When I do the math, it works.

Contrast with emotion the other way, where for instance trusting humans, you find that trust disappointed. Would rather be skeptical and find my skepticism overturned than go that route, as have done before.

I prefer to talk to the math.

The math will never make a mistake. The math will never be wrong.

The math is always right.

To me, when proof rules emotion you know as you go upside down. Trusting not your faith in your ability to look over the mathematics. Which is weird, huh?

So I go through the checks. Like use my definition of mathematical proof to check, every aspect from beginning to end. So I know have a proof, intellectually. Logically it is perfect. Yet part of me still is hesitant, until the relief, when run some numbers.

That burst of positive have found works vastly better to continue, than the other ever did.

Numbers rule.


James Harris