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I am seeking some general advice from applied mathematicians at American universities. In my statement of purpose, would my stating that I want to pursue a PhD in applied mathematics primarily for the purpose of working in industry be a bad idea, in general?

This would be sort of "keeping it real" and being honest, when knowing that the vast majority of phds will end up in industry and not in academia, where jobs are extremely scarce.

Or is it still better to tell them what they want to hear? I am assuming that what they want to hear is that I want to be an academic and make contributions to teaching and publish in academic journals, etc.

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I have done graduate admissions for my math department. I am a "pure mathematician" but my department is just the math department: there is no formal separation between pure and applied.

Others can speak for themselves, but I always find honesty refreshing, and the idea that a prospective PhD student does not want to pursue an academic career does not horrify me: rather, in some ways it relieves me. Moreover, if you know this "all along" and don't disclose it right at the outset, when will you disclose it? There is no natural time until you are graduating / going on the job market, and then it will be way too late for your programmatic experiences to be tailored to your true goals.

The worry here, I suppose, is that you risk looking "less serious" than other applicants. In my opinion you can completely counteract this by including, a plausible, specific post-PhD career plan in which having a PhD plays a natural role. That is, don't say "I don't plan on pursuing an academic career" or even "I plan on pursuing an industrial career", say which industrial career you are aiming for and why the PhD will be helpful and/or necessary. Math PhD programs would like to have students with specific, realistic future plans that they can work towards steadily during their time in the program. We don't see many such students, but we would like to have them anyway.

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    @ff524: What I had in mind is that there is no natural time to reveal that you were not honest about your intentions until the point when the dishonesty would be revealed anyway. But since you ask: yes, it is pretty common for math students to change their mind about academia versus industry and, very unfortunately, if so it is very common to keep that to themselves until the last possible moment so as not to "disappoint their advisor". If you've started up the process of keeping this to yourself before you even arrive, what event will make you change your mind? – Pete L. Clark Dec 8 '15 at 4:24
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    +1. There are certainly some faculty who still view students who opt for careers in industry as failures, but from my experience, I'd be happy to work with a talented student who was well aware of the realities of the post PhD job market and has realistic career plans that don't begin with "Plan A. Tenured faculty at an R1 university. Plan B: there is no plan B." – Brian Borchers Dec 8 '15 at 4:25
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    One reason mathematics is different is that (even for applied mathematics), there are very few jobs in industry for which a PhD is actually relevant. Hence, unless a student is very close to finishing, if they decide they do not want an academic career, it is usually in their best interests to drop out of their graduate program as quickly as they can do so gracefully (usually at the end of the semester after they have lined up a job). – Alexander Woo Dec 8 '15 at 4:30
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    @Ooker - If by "applied sciences" you mean engineering and medicine, then on average (but not in every instance), applied mathematics is much farther from industry. "Applied mathematics" frequently means the uses of mathematics in the theoretical aspects of other academic subjects, usually science or engineering. So, as an extreme case, some applied mathematicians work on mathematical aspects of string theory. If you are comparing instead to "applied physics", then I would guess the mean is about the same but the distribution much wider. – Alexander Woo Dec 8 '15 at 19:21
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    @AlexanderWoo A few years ago, I had a student deciding between dropping out in year 4, or getting a Ph. D in year 5 and then heading to industry. I wrote some of my friends in software and finance jobs to get their take. Several of them thought that the Ph. D was more hireable, despite the lack of any relevance of his research to their companies, because it demonstrated ability to see a project through and because it would otherwise not be clear that he had done anything in those 4 years. So it might not always be best to drop out as quickly as possible. – David E Speyer Dec 10 '15 at 4:53
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If you mean by a job in industry working at a research lab sponsored by a company (or the government) that is like being at a university minus the teaching, then you can ignore the rest of this answer. Those positions are practically like being in academia, minus the teaching. They are also almost non-existent these days.

If you don't mean a quasi-academic job, then you need a realistic reason why you will need a PhD to work in industry.

There are very few jobs in industry that actually require a PhD in Mathematics. For almost all jobs, a Masters degree or a solid Bachelors degree is more than adequate. The jobs that require a PhD have some specific, unique reason why they require someone with research abilities. Unless you can articulate what some of these jobs are, why you want such a job, and how earning a PhD helps in such a job, I am going to be quite worried that either you will waste your time getting a PhD for no reason, or you will drop out after a year when you realize you don't need a PhD. Neither is optimal.

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    Edited first paragraph to state rarity of such jobs (it was actually in my draft version). – Alexander Woo Dec 8 '15 at 7:38
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    Do you have evidence to support the assertion There are very few jobs in industry that actually require a PhD? As a new PhD student I've been told the opposite by pretty much everyone at my university. Maybe they're biased and are trying to make the new PhD students feel better about their choice / not drop out, but when I look at my friends who have graduated already and went into the industry, their time spent as a PhD student doesn't seem to be useless. – user9646 Dec 8 '15 at 9:56
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    @NajibIdrissi check out economist.com/node/17723223 - which makes the case that doing a PhD is often a waste of time. Of course, if you had to choose between 2 identical candidates except one has a PhD and the other doesn't, then you will choose the one with the PhD. But if you had to choose between 2 identical candidates except one has a PhD and the other has 4 years of industry experience, wouldn't you choose the one with experience? Maybe in your industry you need a PhD, but I wouldn't just take your university's word for it. – emory Dec 8 '15 at 12:38
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    @emory The only relevant fact I could find in that article is that the premium for a PhD is only slightly bigger (or sometimes equal to) the one for a master. Sure, that's one metric, but it says nothing about the type of jobs these people get except that the pay is equal. (Maybe it wasn't clear in my previous comment, but the university is telling us, people already enrolled in a PhD program, what kind of jobs a PhD can lead to, inside and outside academia -- it's not to convince us to enroll, we're already here). – user9646 Dec 8 '15 at 12:43
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    @emory You're making this about me even though I'm asking in general, but nevertheless: I want to work in academia, so a PhD is 100% required. And regardless, you're assuming that if after my PhD I get a job that I could possibly have gotten after (as you suggested, for example) a master's and 4 years of experience in industry, then I have wasted my time in my PhD. I don't think that's necessarily the case, and I also don't know why you don't equally regard the 4 years spent in industry as equally wasted: after all, you could have gotten the job with "just" a PhD... – user9646 Dec 8 '15 at 13:09
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With applied math, the sky's the limit. The variety of areas math can be applied to is more than one person can conceive of.

Yes, you can go out and get a real job with a PhD in applied math. Here's a small example for you: Carl de Boor, whom I think of as Mr. Spline, did a lot of work for the automotive industry in Detroit, using splines to help design auto bodies.

I would not expect an applied math department to hold its nose when considering an applicant who's intending to get a job outside academia after graduating.

If you already have some ideas about what sort of math and applications you'd like to do in industry, share your ideas in your essay.

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You might get several possible reactions.

  • That's great, industry needs more people with solid academic training and it's our role to provide the educated workforce that's needed in our competitive industrial economy.

  • You're being naive. Do you really think you will be more employable in industry if you have a PhD? They would much prefer to take you three years earlier and train you in relevant skills on the job.

  • This is a university, not an apprenticeship scheme. We're here to pursue scholarship and the pursuit of knowledge, not to help our students earn a living. If you don't share those ideals, find somewhere else.

So by all means put forward your motivation, but be prepared to handle such objections.

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