Being able to program is not an "all-or-nothing" skill. It takes practice to program well. If you want to go into academia in physics you're going to need to be able to write basic computer programs. They don't need to be fully optimized programs that a comp-sci major would write, but you either need to be able to write a half-decent program or be absolutely
fantastic at doing things entirely analytically, and being "absolutely
fantastic" analytically is pretty damn hard. Lots of problems are just too hard to be done entirely by hand alone. Using a computer to solve or simulate problems, even if it's only to get an intuition for what your system is doing is common. And again, even if your ability to do things by hand is pretty good, pretty good isn't going to cut it if your prospective employer finds someone else who is pretty good
and can write a computer program.
That said, if you want to try, I would guess quantum gravity-esque fields are perhaps the most likely to be more mathy and not as program-y, but you might also find that they do programming too. I don't know any specifics about these fields, though.
Now, going into academia is a risky gamble on its own; trying to get into a field like quantum gravity is going to be very very hard unless you are
very, very good. It's a good idea to be able to program in the event academia doesn't work out, because then you at least have a marketable skill when looking for jobs.
Klockan3 said:
If you are talking academical then no, mathematical physicists are still needed and they can't be replaced by normal numerical ones. It is the same as how most who do pure maths don't need programming, one of our maths professors can barely use a computer! He handwrites his stuff and copies, and puts all of the info for his courses in a pile of paper outside his room instead of having homepages for the courses etc.
An exception that's increasingly rare these days. How old is this professor? If he got tenure when computers couldn't comfortably fit in one's backpack, then it's not so surprising that he can't use a computer very well. These days it's becoming rarer and rarer for a graduate student in science to not have any programming ability, so one is going to have to be very good doing things by hand in order for a complete inability to program to be overlooked.