How to get recommendations for PhD program when outside academia
Who did write you the recommendation letters for the first PhD? Maybe you could use them again. I think there is nothing wrong in using recommendation letters from industry, in any case. I was in the industry when I started my PhD and I showed my boss' recommendation letter, but my field is not math but physics. 
On the other hand, I agree with people that recommend you to try a post-doc instead of a second PhD.