ok, that's better, having some investment and you both being programmers will be easier to sell your idea to potential cofounders. I would say best is to find another co-founder that is willing to take only shares more than 10%, up to 25% would be reasonable if he's good. A sign that he is good would be that he will have good ideas on how to go on from where you are, that is how to best spend your 10k, until the next round of investment. So go out interview potential cofounders with one of the question being this one.
Anyone who's basing their business model on cheap programmers is doomed to fail. The reason is that he/she does not understand the inherent nature of programmers. The quality therefore productiveness of programmers follows the power law distribution, meaning that a single good programmer can not be matched by 100 average coders. So if not possible to pay him a stellar salary, try with equity options. However your idea must be worth something, and the cofounders need to be worth something, which I seriously doubt.
Absolutely! Many tend to give up on the math part too early, because they can't immediately see how it relates to real world applications. Sometimes you need to let your mind loose and dive deep into theory before starting to think of the applications. But in the end of the day you need to enjoy it for what it really is, not just because of the big pay off.
Skills that have been scarce and always will be are good math skills. Coupled with decent programming skills and you can do magic. There are many coders/engineers that lack a decent background in math, so they are severely limited to what they can do. Besides the technologically cheap ideas are quickly being scooped up. I am not saying that there will be less space for such ideas in the future, it's really hard to say that. But nevertheless having larger scope can give you a competitive advantage.
The technologically intensive ideas right now and especially when you graduate in 5 years will be machine learning, AI, robotics, image processing, computer graphics computer vision and they all require decent math background and intuition.
Besides having good training in applied math can help you on both fronts, the business as well the engineering part.