It's been many years since I read this story, so some of the details that follow may not be 100% accurate. I remember the story pretty vividly, but unfortunately I can't remember anything that might actually help me track it down...
Two boys were born simultaneously - different mothers, completely unrelated biologically, they just happened to be born at the exact same time, or very close to it.
One was born into a wealthy, supportive, and functional family. He grows up to be your standard All-American boy - tall, blond, and good at everything - except math. Math is the one area that he can never quite get his head around. In high school his parents hire him a tutor due to his problems with math (he might have lost his virginity to his math tutor? The tutor was female and there was some sexual tension in their relationship). Despite the tutor he only barely passes his math courses, but still graduates with an impressive academic record. I'm pretty sure that he played sports as well, probably maybe football?
The other boy was pretty much the opposite. He grew up poor, with little to no support, and the only thing that he was good at was math - but he was very, very good at it. He barely graduates high school despite his high aptitude for mathematics.
Both end up drafted in the Vietnam War. The first one gets promoted fairly quickly and ends up leading a group of soldiers. The second stays a grunt, working artillery (due to his skill with math).
There's a big deal made of how artillery strikes work in the story:
- A strike is called in with an estimate of the location that should be hit
- Based off of the initial strike, an adjustment is called in - e.g. 15 degrees further North
The first one (bad at math guy) is known among the artillery for being overly conservative for his adjustments - he'll call for several adjustments of a couple of degrees each, instead of a single adjustment of 10 degrees. So he calls for an artillery strike and an ensuing adjustment. But the second one (good at math guy), who is providing the artillery, knows that the other one is overly cautious when requesting strike adjustments, and compensates for that. Instead of adjusting the strike the requested few degrees, he adjusts it by a lot more than was requested and fires away.
It just so happens that the requested adjustment was actually perfect - the over compensation results in an artillery round being dropped almost on top of the requesting party. A piece of shrapnel (I want to say that it was a shard of bamboo?) ends up lodged in the brain of the first one (bad at math guy). He ends up in a coma (in a VA hospital?)
The ending gets a little bit fuzzier in my brain - the big take away is that the guy in a coma eventually dies, and his temporal "brother" dies at the same moment, despite the fact that he was perfectly healthy.
Other information that might be helpful: when I originally read it, it was in a collection of short stories all by the same author, whose name I cannot remember for the life of me. I want to say that he (it was definitely a male author) had a sort of generic first name - Joe, maybe? It was a hardback book with a blue cloth cover. I want to say that largely the stories were unimpressive, because this is the only one that stuck with me.