Nobody seems to have mentioned much about teaching--- perhaps because the original question itself makes no mention of teaching having anything to do with the desire to return to academia. This is a kind of elephant in the room.
I should admit: I'm on the academic side, I have not personally tried to make this kind of transition, and I have never been in a position to evaluate somebody making this kind of transition. But it seems to me that if you're reasonably current with your research area, and publishing papers, and meeting people (as suggested elsewhere), your biggest obstacle may be teaching.
Presumably you have no teaching experience over the last n years, and depending on your grad school experience, you may not have had much then (or it may have been a different sort from what professors do). This may matter. I don't know how to begin building a teaching history, while working a full-time job.
You may need to overcome the suspicion that will find teaching low-level service courses boring for the same reasons you find your current job in industry boring. Imagine the skeptic on the search committee who asks, rhetorically, "Who wouldn't be an academic if it were all just learning, writing papers, and talking to enthusiastic people with the same interests?"
Even with stellar references and a personal connection or three in the department, someone will ask: can you teach? Do you want to? What's the answer, and how do you convey it on your CV?
I don't have specific advice in this area, because it depends on where you want to work, and your own background. If it is possible to do pedagogical things in your current job, or service/outreach to non-specialists or students, perhaps that would help. Maybe actual teaching (on a per-course basis, not as tenure-track faculty) or volunteering would help. My feeling is that you need to do something to address these issues head-on, to confront both any genuine gaps in your CV, and the biases and prejudices you may face simply because you are changing careers.
Have a look at: Too old for advanced mathematics?
There is a lot of good related advice there, that might help you think through your case a bit.
Also, before you jump into the new thing, do the following simple thing:
- Goto a nearby university
- Sit in some math classes, both undergrad and grad
- Make connections with professors there, and then seek their advice and mentorship on how to proceed -- once they know you a bit, they will probably be in a much better position to advice you than a website like MO.
Good luck! One is never too late to enjoy the pleasures of math.
Best Answer
Anatoly Karatsuba discovered the Karatsuba algorithm in 1960, and reported it to Kolmogorov who published it under his (Karatsuba's) name without his knowledge. It seems fair to say that this first example of a "divide and conquer" algorithm eclipsed Karatsuba's 1966 thesis on "The method of trigonometric sums and intermediate value theorems".
For a physics example (from my own university) I note George Uhlenbeck, who with Goudsmit introduced the electron spin in a 1925 publication, while his 1927 Ph.D. thesis on quantum statistics was much less influential. (Here is the story how two Ph.D. students discovered the electron spin, which was missed by a giant like Pauli.)