making mathematical conjectures If a non-mathematician wanted to conjecture something and had strong numerical evidence to support the conjecture, how would he/she go about doing so? Would the mathematical community
(a) take it seriously?
(b) even look at it?
 A: As with any serious field, there are those in the math community who might take it seriously, and others who wouldn’t. There is also a huge swath of the community for whom it would make little or no difference, and those in that swath might not even ever come across it.
If it's significant — and that can probably best be measured by either having a large potential impact on a small portion of mathematics, or an impact (of any size, really) on a large portion of mathematics — then enough mathematicians will look at it within a reasonable time after its "release" (e.g., publication) to either validate its merit(s) or debunk it. Either way, progress is made.
As for how to go about it, you could "publish" it here on MSE for others to poke at, you could write up a paper yourself and either submit it to a journal or just post to the arXiv, or you could contact another mathematician (preferably one with a knowledge of the specific area of mathematics in question) and see if you can pursue a collaboration.
