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I'm looking into applying to another grad school to get another PhD, whether again in mathematics or a closely related subject. In assembling the application, where I should get recommendations from? I can't ask my advisor (I wouldn't be in this situation if he hadn't screwed me over the first time); and while there are certainly some other professors who remember me favorably, enough time has passed that I'm not sure they would have anything more than a desultory blurb to contribute. Math departments have little interest in recommendations from people in industry, and related subjects are presuambly similar. Is it possible to get some sort of recommendation or other bona fides available from industry that a PhD admissions committee in math, mathematical physics, etc. would care about?

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    Why another PhD? That seems unnecessary tbh. The point is you should know how to research, regardless of topic unless you're too far away from said topic. – user41631 May 7 '16 at 1:06
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    I failed to see that you look for a 2nd PhD. I think that's what may scare them off. They will ask, why do you want a second PhD? Perhaps better to do a postdoc if you want to develop yourself. In some topics, a postdoc coming from industry may actually be more attractive as they know how to work, they have routine, discipline, and bring an orthogonal set of skills. Select a topic with some application angle, or where they may profit from links to industrial perspective, and you'll have a much better starting point than asking for a 2nd PhD opportunity. – Captain Emacs May 7 '16 at 1:10
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    It could be worth refocusing the question (or asking a new one), since I think the second Ph.D. issue will be a much bigger obstacle than just coming from outside of academia. Many departments simply won't accept an applicant who already has a Ph.D., no matter what the application looks like, and those that might consider it will be extremely skeptical. The chances of admission will be essentially zero without extraordinarily persuasive letters. So the key question isn't "how can I get letters from outside academia?" but rather "how can I assemble a compelling case for doing another Ph.D.?" – Anonymous Mathematician May 7 '16 at 2:27
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    (In particular, there are various ways you could try to make academic contacts and acquire letters, but most of them are highly unlikely to lead to letters that would be useful for your particular goals. It's not enough to acquire letters that attest to your talent or potential or accomplishments. Instead, they have to very specifically make the case for why a second Ph.D. makes sense in your case, and that's a far more demanding requirement.) – Anonymous Mathematician May 7 '16 at 2:32
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    Getting recommendation letters should not be a problem, just go to your professors in undergraduate/graduate school, I am sure there will be many people who will happily help you. However, reaching them by e-mail could be somewhat hard, if you are not far away from school go directly to them and explain the situation(or perhaps a part of it). Moreover, there are many fields which require software skills, like machine learning, AI/neural networks,etc. Also, having a number of publications in conference proceedings or journal papers might be an alternative to strong letters. – Mikey Mike May 7 '16 at 12:14
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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.

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