Ask HN: Advice on how to do B2B market research

I want to create a business that will allow me to do mathematics and software development. Now, I know that is too broad. It encompasses so much possibility that it is almost meaningless. So I want to identify a more specific area, e.g. machine learning or simulation, that gives a potential client a better idea of what the business can do.

But I am having difficulty in identifying which specific areas or terms to use. I think the problem is that I am putting the cart before the horse -- that I need to identify a need in a particular market in order to know what kinds of math and software businesses would find useful. But I'm not sure how to do that. How do you figure out what needs or wants a business has? I know this is pretty elementary marketing but I really have no idea what the first step in such a process would be.

Any help or advice is greatly appreciated.