Question: The main character (male) is called to a lab built on the ocean floor that is atop some sort of vault that is in need of the main character's expertise in figuring out the password to unlock it. The calculations always come up with impossible numbers like 0/0. Does this ring any bells? I believe the main character appears in other novels by the same author. Published within the last 10-15 years.

Answer: 
Could it be [Sphere](https://en.wikipedia.org/wiki/Sphere_(novel)) by Michael Crichton, perhaps?

Journey to the ocean floor - check

Puzzle how to open a mysterious object - check.

Impossible things found - check. (Example - impossible sea creatures such as shrimp with no digestive organs. I don't recall if 0/0 was part of it.)

[Preview available](https://books.google.co.uk/books?id=t4b69z5hs58C&printsec=frontcover&dq=intitle:sphere%20inauthor:Michael%20inauthor:Crichton&hl=en&sa=X&ved=2ahUKEwjC_dnHgZTsAhW1URUIHYsYArYQuwUwAHoECAEQBw#v=onepage&q&f=false) on Google Books. See if it looks at all familiar.
At least a partial match to Peter Watts' [Rifters](https://us.macmillan.com/series/rifterstrilogy/) series, which is about a group of genetically modified humans working in a deep-ocean lab/power plant that accidentally release a pandemic causing microorganism. The main character is Lenie Clarke who is blamed for the release and her name is subsequently taken by AIs as a name for a bunch of cyber attacks/viruses.

IIRC at one point in the series (I think in book 3 or 4). One or more of the main characters returns to the lab after being on the surface for some time to find that there has been a coup of sorts and that they are locked out/excluded and they need to hack their way back in.

Note that these books are freely available from Watts' site [rifters.com](https://www.rifters.com/real/shorts.htm) and a number of other sites too without DRM.