well......it was the first case so they usually go easy anyway i'm sure that it will have more interesting and difficult to crack in the coming chapters
I dont want to say this, but you dont sound like someone whom has worked in a serious or professional environment. The female cop/MC might sound annoying but she is behaving rather normally in the given context. In fact, people like the math guy would usually be the first one to be fired in certain situations. A serious work environment where you can determine the life and death of someone isnt a place for frivolousness or childish behaviours. I would like to see anyone here tries the same stunt as this man baby in a professional environment. I dont think your "uncooperative" behaviours will keep you employed very long.
In the end, you sound incredibly childish. The first arc is just a establishment of the trope of Holmes and Watson. She has to play as the ignorant one so the professor can "enlighten" us of how awesome he is.

Is it weird that I already knew the culprit even without all that probabilities? I mean, it was obvious in my speculation.
Also, I don't like the woman. She's very, how to say this, annoying. She acts like any idiotic girl that agrees to anything if a person said that they did it that has enough evidence to be considered so, like a thoughtless person. I mean, isn't it reasonable to question whether they are saying the truth or not? Though the mathematician acts like a kid, she doesn't give him the respect that he should have, even though he is probably going to be the only reason as to why they discover whether they are telling the truth or not. I don't favor how most girls act like this within shoujo manga. She doesn't think rationally, but I suppose this is all some random critique from a person you don't even know, so who am I to judge. This is just my opinion, though, does anyone feel the same?