The science of 'medicine' is the subject there and the use of commas at the beginning and end of the sentence talks about the type of the sentence which is known as a non-relative clause. This means the string between those two commas is merely for additional information removing which the sentence can stand all alone.
New York city, which is a very good place to visit, saw a great fall in tourism last year.
[mark two commas]
The science medicine, which progress has been rapid lately, is perhaps the most important of all sciences.
Here, the pronoun 'which' lacks in introducing the noun properly. 'Whose progress'? 'Progress in which field...?'
Adding a preposition or changing the pronoun work.
The science medicine, of which (the) progress has been rapid lately, is perhaps the most important of all sciences.
OR
The science medicine, whose progress has been rapid lately, is perhaps the most important of all sciences.
['whose' can be used for inanimate objects as well].