Have you ever been able to solve a problem at work that nobody else could, or solve it faster, or cleaner, or more robustly, by virtue of having learned previously about some random topic which you had no idea would one day be applicable to your work? I think most programmers have, and I'd hope that a good boss at a good organization would understand that - as long as you're accomplishing everything that's required of the job - independent learning is a great use of (a reasonable fraction of your) time that will benefit both you and the business.
I once "solved" a tricky issue with a random bug in an FPGA processing data from DDR. The issue was hardware "malfunction": DDR can flip some bits if accessed in some ways.
No one on the team did know about that, no one believed my fix could work (a one line for a bug we investigated on and off for months). It did. I had read a computer security article about how row hammer can be used to gain privilege or something and made the connection.
During my yearly evaluation, I mentionned it as the most impact that year. I was nearly laughed at. This bug precluded the product from functioning more than a few minutes, and we targeted at least several hours without any glitch. No one noticed that without me in the team, the product was dead for a few more month at least.
