I did it. Was working a software job and realized that I wasn't excited about the industry. I decided to apply to Ph.D. programs in math, got accepted to some, started a Ph.D. at 26, now work as a professor.

My years in industry weren't helpful in my Ph.D. applications, although from what I can tell they didn't hurt too much either. By the time I was applying for academic jobs I don't think anybody cared much what I had done before grad school.

Different academic fields have very different cultures, and there are some which may value your industry experience. Overall we academics have an annoying habit of not caring about anything that happens outside the walls of the ivory tower, but not all fields are the same, and not all individual departments are the same.

There are multiple definitions of a "successful academic career". If you want a tenure-track job at a research university, then yes, you absolutely need strong publications. If you want a tenure-track job at a more teaching-oriented university or college, then often you need strong publications there as well, but other factors are also very important.

As far as the "age" bit -- there is probably some age discrimination, but in practice "age" means "years since you finished your Ph.D."

There are also non-tenure-track positions. The pay varies from miserable (e.g. adjuncting) to mediocre but livable, and the job is primarily teaching with maybe a little bit of service. Can be a very enjoyable job, but it can be a little bit lonely, you're only a conditional member of the club. You'd probably need at least a Masters degree.

Also beware of the "demographic cliff": fewer students are expected to go to college in the coming years than in the previous ones, which is going to have a big impact on faculty hiring, and which will probably cause a lot of small colleges to go under. So, if you go for an academic career, make sure it's in a field that's expected to grow in popularity.

Bottom line -- difficult but maybe possible. Feel free to ask if you have any questions. Good luck!

That’s impressive! I have often been drawn to the diversity of techniques in analytic number theory. I have Apostol’s two books and have been meaning to give them proper attention.

My own background is in mathematical/computational biology and stochastic processes. I already have a PhD and Postdoc, but have had a five year stint in industry. I worry that this publishing gap has hurt my chances of a return to academia. My only plan is to try whole-heartedly to publish as much as possible to try and play catch-up.

I am very very sorry to say this, but I suspect that in your situation you would face extremely long odds looking for a traditional tenure-track job.

You might have better luck looking for "academia adjacent" jobs; for example, several number theorists I know are now working at the Center for Communications Research -- a government contractor that does classified research in crypto and the like. Overall they seem to love their jobs, and some of them still do number theory research and go to conferences and such.

What's your starting point? BSc or BEng?

If that's the case, you'd definitely get into grad school to do your masters, then your phd. You'd likely have an easy time getting a post doc, but you might have to move (may not be able to be picky on where). Then comes the tough part, getting a tenure-track position. Very tough. And all the way until that point, you're getting paid much less than what you likely make now.

I almost obtained a tenure track position after after 4 years in industry which followed my PhD. No postdoc. I was one of the final 3 candidates to do the whole 2 day interview on campus, pitch a research program, teach a mock class, etc. The first day was 14 hours and the second day was about 10. It was gruelling. Then I waited 4 weeks for the rejection. I was disappointed, but then relieved. I was beaten out by someone who had an existing research program they were brining with them from another institution and grant money that went along with it. It was impossible for me to compete on that front coming from industry.

My starting point is actually quite advanced. I already have a PhD and postdoc. I worry that the publishing gap caused by my five years in industry will bite me.

Fantastic to hear about your experience! Do you mind if I ask what you’re now?

How was your publication record during your PhD and Postdoc? What kind of related output did you have during your time in industry (patents, collaborations with any institutions, mentoring of junior devs or co-op students)? Will you want to springboard your research from your postdoc work or start anew? These questions are rhetorical mostly, but will be major parts of your application.

I ended up starting a startup based on the research program I had pitched for that tenure-track position. I didn't have a post-doc to springboard from and the university didn't have the equipment (MRI scanners) for me to continue from my PhD work. I welcomed the opportunity for a change anyhow.

I've had to wind down the startup last fall unfortunately. We had launched a pilot, which covid-19 killed. Ran out of money. Looking for my next opportunity right now actually.

How do you define academic? Do you mean teaching, research, or the likes of academic IT?

From personal experience, it's relatively easy to move from industry to academia in a support role(1), but hard to get Principal Investigator/tenured prof roles.

(1)as long as one can accept the salary tradeoffs