There's been a lot of news recently about a major tomb discovery in Macedonia. In fact that tomb's been known of for years, but excavation is underway; the tomb has turned out to be massive and ornate, and it's just the right dating to be immediately post-Alexander the Great. This has almost inevitably caused people to announce that we've discovered the tomb of Alexander.
So could this be Alexander's grave?
No, not a hope in Hades.
After Alexander died, his Generals fought each other in a super-war for control of the empire. They were called the Successor Wars, and they weren't much fun. If you think Texas Chainsaw Massacre Meets Gladiator with a cast of tens of thousands then you wouldn't be far off. Throughout this brutal affair, whoever had possession of Alexander's dead body got extra victory points.
The major biographer of Alexander from the ancient world was a guy called Arrian. Arrian -- and every other ancient writer on the subject for that matter -- says that Ptolemy hijacked the body of Alexander while it was on its way elsewhere. (Yes, I know this is macabre.)
Ptolemy installed the body in Memphis, the capital of Egypt, while a temple and tomb was prepared in the newly-built city of Alexandria. (Alexandria was, of course, founded by Alexander.) Ptolemy's son, also called Ptolemy, oversaw the final installation of the corpse during the next generation.
Thus in the second century BC, Alexander is definitely in Alexandria, in a lovely temple in the middle of the city.
Cut to the birth of the Roman Empire. The history of Dio Cassius says that after Augustus conquered Marc Antony and Cleopatra in Egypt, he was taken to see the tomb of Alexander. The sarcophagus was opened and Augustus gazed upon Alexander's face.
Augustus, future first emperor of Rome, then got it into his head to kiss a 300 year old corpse. (Yes, this is kind of creepy.) Dio Cassius reports that in the process Augustus accidentally broke Alexander's nose.
It's possible that some time in the intervening years someone moved Alexander to Macedon, but if so, then who was Augustus pashing in 30BC? Furthermore, checking out Alexander's corpse became something of a de rigeur tourist attraction for high ranking Romans. Strabo and Caligula are both stated to have seen him, still in Alexandria. The tomb was eventually closed to tourists in the third century AD by Septimus Severus, who apparently had some sense of propiety.
Thus it's impossible that any grave in Macedonia could possibly hold Alexander. I'm thinking someone digging deep in Alexandria will eventually find it.