<p>I’m a numbers-wise solid candidate (albeit with the huge caveat that I’ve not yet taken the subject test) for a PhD program in Mathematics, but I’ve been several years away from school.</p>
<p>To keep my life story to a minimum, I’ve been working for an actuarial consulting firm that employs a lot of folks at Masters level and some at PhD the level (with the associated professional credentials of course). While there I’ve participated in in-house product development and research (reinsurance pricing software, etc.), but nothing quite like true mathematics research. I’m also just months away from my own brass ring of actuarial credentials (as if that matters if I go back to grad school).</p>
<p>I still have close contact with one previous professor that is familiar with my proofs and willing to write me a strong letter, but I’m not so confident that other professors remember me well enough to write any sort of decent letter. I’m wondering if rec’s from my mentor or managers at my previous employer would be a satisfactory stand in for professors?</p>
<p>Additionally, I may be able to swing a reference (again, not from someone who’s familiar with my mathematical work) from a fairly well known physicist. Is such a character reference (regardless of the weight of the name drop) as utterly useless as it probably ought to be? Should I pursue that avenue too?</p>
<p>In short, I’m thinking:
Professor familiar with my proofs
Professional with PhD or Masters who oversaw my research and development
Character reference with a known name (provided they are willing, of course)
Weak-ish professor reference (e.g. “oh, yeah, I think I remember you getting an A in some analysis course I taught…”)</p>
<p>It’s tricky to take a break from math and then go back to graduate school. I only know a single person who did that; he was an undergraduate math major at Princeton, worked as a software engineer for a couple of years, and when he wanted to go back to math, the most selective graduate program that accepted him was SUNY Binghampton - after he had taken classes as a non-degree-seeking student for a year. [He went on to get a post-doc position at Cornell, so it’s not like he was a weak mathematician. Just that being out of math for almost a decade was apparently held against him.]</p>
<p>You probably want at least one letter saying that you are <em>currently</em> up to speed on <em>at least</em> the undergraduate curriculum, if not parts of the graduate curriculum. The more selective graduate programs will give you absolutely no time to refresh your mind on the undergraduate curriculum before you have to start taking graduate courses to prepare for your qualifying exams.</p>
<p>That’s my 2 cents. The professor you are still in touch with can probably give you better advice than anyone on this board. Don’t be afraid to ask him about your letter-of-recommendation conundrum or application strategies!</p>
<p>Really, what I expected to hear… just hoping someone might have gone down a similar path. </p>
<p>Your mention of SUNY Binghamton throws up a bit of worry though. Most of the schools I’m looking at are UC Not-Berkeley caliber (was trying to be reasonable and aim for places I thought I’d be happy)… which are generally noted as of higher “rank”, whatever that means, than Bing according to the US News crystal ball. Hopefully I haven’t ended up shooting for the moon. I’d talked to my professor and aimed for schools I knew my fellow alums had had success at (though they’d entered just out of undergrad)… ugh.</p>