There is an odd thing to being puzzled at how your fellow human beings react to some mathematical object. To me these are things. A mathematical object is a bit of logic or a lot with some numbers, and usually some abstract symbols mixed in there which can DO things or express things done.
What decides how we react as human beings to a mathematical object?
That question is more interesting to me now, while have pondered it before, when was more interested in validating mathematics as have been gifted with a trying situation. So I defined mathematical proof because did not get reaction from people I thought expert who thought could check mathematical approaches that was expected.
Ok, so in general, human beings designated as experts will not consider something, does that mean is incorrect, or unimportant, or what?
You can end up kind of stuck, as how can you get them to do something when they do not so wish? And why would you try? But then how are you supposed to know with your own math research?
One thing I could eliminate on my own though was question of correctness, if I had a perfect method to check. So I discovered a functional way, and found an easy definition. So yeah, went looking because of a need and ended up MUCH better off that way as well.
mathematical proof (noun): a mathematical argument that begins with a truth and proceeds by logical steps to a conclusion which then must be true.
From my reference post for my definition of mathematical proof.
It is remarkable that NOT getting what I thought I needed, led to an advance for the human species. Where for a lot of years have wondered why that was for me to explicate, though wonder less lately.
So yeah, you have something like that and wonder around it and about it for years, but also most importantly I'd use it. It WAS functional for me. So then I could eliminate questions of correctness, and realized mathematics was embodied in logic, but logic is bigger. So logic is bigger than mathematics, and I had to handle questions of logic for a bit, but was fun. And yeah why a post on logic is on this blog, way back to blog beginning year 2005. So yes, logic is bigger than mathematics, but is also, easier in many ways.
Our reactions as human beings are so much about emotion. And through years of hammering at problems, and hammering at problems and getting nowhere, simply felt better when switched to using my imagination and pretending at times like was asking a powerful entity I called the math. And the math became my constant companion and getting answers, I wondered what value emotion in math? When asking the math a question, emotion has no value. The math does not care. Yet, if you ask in the right way, with the right question the math will just tell you, as my imagination made it feel real.
To me success with numbers IS emotional though. And the math does not care, but does not block or punish that emotion.
Like look at something like:
60*2551100302 + 2551100292 = 19924730292
For me looking at it, I have mixed emotions. Why can you square 255110029, and add result of adding one to it and squaring multiplied by 60, to have another square? I know the mathematical answer. Still feels remarkable. So I remark.
That is simply a mathematical object. It cares not.
But also feel like is mine in some sense as I am the discoverer. YOU are seeing that as a result of my thoughts and my questioning. Without which, human beings..who knows. Someone else might have discovered, eventually.
Success in mathematics to me is in contemplation, of mathematical objects previously unknown, now known. Maybe for each of us, is a question to answer, what is success?
Which is a question to try to answer for those who care, of course.