Although not explicitly stated, it’s generally accepted that the Klingons acquired warp drive, and presumably the basis for most of their advanced technology, from the Hur’q, who occupied and enslaved the Klingons for some time. However, even if we accept that as canon, there still would’ve had to have been Klingons who were like “yes, yes, we will hunt our oppressors to extinction, drink blood wine from their skulls, etc., but have you taken a look at how these engines work?!”

i used to assume the klingons had gone through various cultural trends and the whole viking thing was less then 200 years old by TNG. maybe it's like "neo-warriorism" like some kind of reactionary cultural movement

There's an episode about a klingon who became a doctor.

My headcanon is that Klingon Scientists are just as toxically competitive as their warriors

So basically imagine our Stemlords on steroids who occasionally challenge each other to duels to the death

Like that one DS9 episode had a Klingon Lawyer who was basically that

Klingon culture changed over time. After the Klingons invented/adapted warp in the aftermath of the Hur'q, it became far easier for low status clan houses to move up the social hierarchy by venturing forth and plundering or conquering the less advanced planets around them. Why dedicate your life to academic research, when it's way easier to just spend a few years pillaging? Established clan houses with resources and reputations do have scientists. A couple of siblings might be warriors who are out there preserving the houses honor, but a couple of siblings might be academics or administrators.