For what it's worth, I have a B.S. in biochemistry which I would expect indicates some level of intelligence to potential employers. However, I have had a lot of difficulty even getting to the interview stage when I apply for programming positions. I've spent a lot of time learning on my own and studying the CS side of programming (i.e. algorithms/data structures) which expect is neglected by many late converts and even when I say this in my cover letters I rarely more any further in the interviewing process.
A math PhD may have better luck but my experience has been negative so far.
It's not so much a matter of intelligence (although that is important), but a matter of ability. Companies are much more interested in a demonstrated ability to program, and one of the easiest ways is to actually build something that you can show off. So if you really want to get yourself noticed you should put up some personal projects on something like github or contribute to open source projects. And considering you are a biochemist, there are lots of interesting open source projects in your language of choice that are being used for sequence analysis, phylogeny, cell simulation, etc. :)