OE
The word “although” indicates that what the professor is doing is unusual or not required of a retired person. “Takes pains” also indicates that what she is doing is difficult. To keep “abreast of” a topic is to remain current and is therefore the correct answer. “Akimbo” means in a hands-on-hips stance, which would probably be a pain but isn’t something the professor could do “to the latest developments in her field.” “Obtuse” (slow-witted) does not fit the desired meaning. There’s no reason to believe that the professor is “subservient to” the developments in her field. And finally, “askance” means with a look of disapproval, which also doesn’t fit in this sentence.
Answer: B