My question to you all is how can I have the new math I create checked without worry of someone stealing the ideas or finishing ones that aren't finished?

Hi,
Call the US Government Patent Office, and get more information.
I am 64 yrs old, and was a high school math teacher for 13 yrs, before changing careers. "New Math" has started over and over, during the last 35 yrs!
I do wish you the best, and good luck.

I think you have to trust someone.

Mathematics is a collaborative activity and in my experience (as a phd student with published mathematical papers) I have never encountered a corrupt mathematician who would deliberately steal someone else's ideas and not give them appropriate credit. Really I think only maybe 0.000001 per cent of mathematicians would do such a thing.

When I do mathematics, I appreciate the time of anyone willing to read through my work and let me know if they find errors or have ideas for how it could be improved. I'm much more afraid of publishing something incorrect than having my ideas stolen. The danger is a lot greater.

The case of Andrew Wiles was a bit unusual. Any number theorist might be able to help you.

The thing to remember though is that in mathematics, creating ideas is really the easy part. The hard bit is pursuing them to completion. Most mathematicians have a long list of their own ideas that they would wish to pursue, if only they could live long enough. So it is common-place for them to give them away freely. Conference presentations often end with "future research directions" and "open questions". Professors are often keen to have their students work through ideas that they have. So there is really no danger of anyone stealing your ideas - they are too busy with their own.