I'm not new, but I don't know conditions and the like by heart. My priority is mostly to keep the game going.
To many the rules as written (RAW) is a balanced system that is fair when adhered to and can be unfair for players when not. So many gamers I know enjoy sticking to RAW and expanding our understanding of it as we play.
As the DM it is typically my responsibility to know the rules and to accurately convey them to my players. I too have another player in the group that is quite rules savy. Often he will bring up rules bits or rules questions during the middle of a combat or other relatively fast-paced part of the game. In my earlier days DMing it was quite a nuisance until I received some solid advice for dealing with such players and I'll pass it along to you now.
The best thing you can do is not to fight a player that enjoys playing the game in thsi way (besides being your brother). Instead utilize his knowledge and skill with the rules. Turn that irritating habit he has into an asset, something positive for the game!
I often set my rules-savy player on a rules fact-finding mission whenever a rules questions pops up mid-game, while I continue running the game! I rely on this player's referencing skills to quickly bring up the correct page and rule. After I reference the rule I make the call and then we run on it, with the understanding that rules debates and discussions occur away from the game table. Tough calls always go in favor of PCs because killing PCs over an incorrect rules call sucks.
Ultimately this accomplishes two things:
(1) It keeps the player busy and allows them to do what they enjoy doing anyways.
(2) You now have somebody that can zero in on rules while you can keep the game running at a fast pace.
The game will run faster and problem player isn't getting shot down but instead is turned into a contributor. The only caveat to doing this being that as DM you must remain the final rules arbiter. So you need to eventually know your stuff. I've seen where a very rules savy player used in this manner became the sole rules arbiter when the DM allowed them to do so. It is the DMs job to learn the rules as best as they can and to judge them fairly and with neutrality IMHO.
Best of luck!