Most of the ancient sources that you can get information on this are from Livy (Roman historian) and Polybius (Greek historian) - i think Livy based his information off Polybius or vice-versa however.

Basically looking at Hannibal's main battles - Lake Trasimene, Trebia, Cannae and Zama, its shown that Hannibal was able to utilise the various tools his army had (as it was made up of elements from Africa, Spain and Gaul) to their strengths (a good example is his use of the Numidian cavalry) to defeat the Romans in a variety of ways such as leading them into a trap, encircling them or developing a double envelopment.

Many of his subordinates wanted him to siege Rome to end the war but he didn't have the resources to (not going to go into detail here) and eventually his loss to Scipio Africanus at the Battle of Zama is usually attributed to 3 factors - Scipio learning how to counter the African elephants from when he was in Spain fighting, i think it was, Hasdrubal (Hannibal's brother who he left in Spain before he crossed the alps), the help of Masinissa (first king of Numidia who switched sides from the Carthiginians to the Romans), and Scipio having learnt from Hannibal at Cannae to be able to encircle the enemy using superior numbers of cavalry

In my opinion yes Hannibal was a military genius in his innovation in tactics, and his ability to take advantage of his opponents weaknesses was something that the Romans failed to deal with.

P.S. This is not including the Fabian strategy as, as soon as Fabius's dictatorship was over (6 months), the new consuls rushed into battle with Hannibal again.

While his three major battles in Italy (Trebia, Lake Trasimene, and Cannae) no doubt qualify him as a genius, Theodore A. Dodge holds that it's Hannibal's ability to move unimpeded throughout Italy with several Roman armies surrounding him in the years after Cannae as his greatest accomplishment. In doing so he employed numerous methods "Punic craft". Polybius mentions one particular instance of being hemmed in a valley with sizable detachments of Romans holding the passes out. In order to dislodge the Romans from one of the passes he tied bunches of wicker to the horns of cattle and set them ablaze, using the Numidians to drive them up a nearby mountain. Thinking the Carthiginians to be escaping a group of Romans dispatched from their position to take the Carthiginians in the flank. When they came closer they realized their error but by then the Carthiginians had already seized the pass and were able to retreat in an orderly fashion.

Also, another feather in his cap was his ability to pull out of battles in good order, and never with his army damaged beyond operational effectiveness, until Zama that is. This is best illustrated in the battle of Nola in which Marcellus was able to lure Hannibal close to the city gates thinking treachery by some dissatisfied citizens would be his key. Instead Marcellus sallied out with gusto from the main gate, and with smaller detachments coming out of two other side gates in flaking positions as the battle wore on. Hannibal's army was approaching Nola in lose order as they weren't expecting combat. When Marcellus' men rushed out of the main gate he quickly formed up a battle line to meet the incoming threat, and was able to meet the flankers as well when they joined the battle. After several hours of fighting in which the Romans apparently had the upper hand Hannibal was able to extract his troops from the field without much loss.

And I haven't even mentioned his crossing of the Alps, which is arguably the greatest march in military history. No army of his size had ever passed through the Alps at that point in time. Prior to even crossing he had to use diplomacy to win over the tribes on both sides to assure he would have guides and supplies to attempt the crossing. Along the way he encountered hostile mountain tribes which if luck had been different could have destroyed his army before setting foot in Italy. His march through the Arno marshes is equally brilliant, the Romans had thought them unpassable and left them unguarded. By traversing the swamps Hannibal was able to march behind the Romans and into the heart of Italy.

The only aspect of warfare that Hannibal was truly deficient in was siege. Although even this can not be held against him in many ways. He lacked siege materials and a proper supply line to keep an army victualed for the duration of a long siege. And there was the constant threat of being trapped between a city's walls and several Roman armies.

This post is based of the writing of Theodore A Dodge's 'Hannibal: A History of the Art of War...' and 'The Ghosts of Cannae' by Robert O'Connell.

To put it simply, it would require a heroic level of revisionism to come to the conclusion that Hannibal was anything less than a military genius. We would need to discount the primary sources dealing directly with him (Livy, Polybius, and later historians like Plutarch) as well as the more meta discussion of Romans mentioning Hannibal in passing.