I have no formal training in maths. A few years ago I became interested in numbers and how they behave. I lack knowledge of math symbols and vocabulary.
When I made a mechanism out of 3 pieces of cardboard which identifies exactly all the prime numbers less than 121 as I roll it along a numberline, I got hooked. I watched a lot of Numberphile, 3Blue1Brown, Mathologer videos, over and over. I found out that there are many unsolved mathematical questions.
I came to the conclusion that if a mathematician was capable of conjecturing something which most mathematicians agreed was probably true, but that no-one was able to prove or disprove the conjecture, there was a lack of understanding which occured some way along the path, a little way before the conjecture formed in his mind.
So I decided to study the behaviour of numbers from scratch, starting with zero and single digit numbers. In order to fully understand something, I try to make a mecanism or physical structure which illustrates it. Having no formal training may be an advantage because I have an external standpoint, so there is no beaten track in my mind. However, communicating with mathematicians is difficult, because I lack the vocabulary which they share.