but we didn't know how many

[azz]

a. Tony was the biologist who had published a number of important research papers, but we didn't know how many. John was the biologist who had published a number of important research papers and we knew how many.

b. The biologist who had published a number of important research papers, but we don't know exactly how many, started to talk.

Are the above sentences grammatically correct?
Do they make sense?

My problem is that the phrase 'but we didn't know how many' seems to be the most important part and it seems to be part of the defining clause.

Many thanks

[Alan]

I would suggest replacing 'but' with 'although' (and within parentheses rather than commas).
Otherwise, fine.