What were the decisive victories in antiquity attributable to elephants? I feel like I’ve read countless tales of them running away or rampaging amongst their own troops but relatively few of them carrying the day.
Most Ancient Indian battlefield depictions featured war elephants. Of course, it wasn't called India then and they were multiple warring princely states under dynastic rule.
The Tamil phrase ரத, கஜ, துரக, பதாதிகள் refers to Chariots, Elephants, Cavalry, Infantry respectively and is used in several fictional descriptions of antique battlefields. The historical fiction novel, Ponniyin Selvan by Kalki (written in mid 20th century) about the Chola dynasty (circa 3rd century BCE to 13th century CE) has this exact phrase appearing in Volume 1, Chapter 19.
> காத தூரத்துக்குக் காததூரம் ரணகளம் பரவியிருந்தது. ரத, கஜ, துரக, பதாதிகள் என்னும் நாலுவகைப் படைகளும் போரில் ஈடுபட்டிருந்தன
(trans: The bloody battlefield was spread out over four square miles. Chariots, Elephants, Cavalry, Infantry--all four forces were fighting the battle)
In Tamil classical literature, there is a verse form called பரணி (Parani). The literal meaning of this verse form is:
> ஆனை ஆயிரம் அமரிடை வென்ற மானவனுக்கு வகுப்பது பரணி.(இலக்.வி. 839)
i.e., A song in praise of a warrior who fought and won a thousand elephants in battle.
There is a 12th century poem titled கலிங்கத்துப்பரணி (Kalinga's Parani/Verse) written by செயங்கொண்டார் (Jeyamkondaar). It was customary to give the name of the defeated as the title of the verse. This one was the defeat of the Kalinga ruler Anantavarman by the Chola king Kulothunka Chola. Hence the name.
> At Bagradas (255 B.C. – a rare Carthaginian victory on land in the First Punic War) [...] the elephants disorder the Roman line. In the spaces between the elephants, the Romans slipped through, but encountered a Carthaginian phalanx still in good order advancing a safe distance behind the elephants and were cut down by the infantry, while those caught in front of the elephants were encircled and routed by the Carthaginian cavalry. What the elephants accomplished was throwing out the Roman fighting formation, leaving the Roman infantry confused and vulnerable to the other arms of the Carthaginian army.
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> Elephants could also be used as area denial weapons. One reading of the (admittedly somewhat poor) evidence suggests that this is how Pyrrhus of Epirus used his elephants – to great effect – against the Romans. It is sometimes argued that Pyrrhus essentially created an ‘articulated phalanx’ using lighter infantry and elephants to cover gaps – effectively joints – in his main heavy pike phalanx line. This allowed his phalanx – normally a relatively inflexible formation – to pivot.
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> Thus the war elephant wasn’t a ‘battle winner’ so much as a dangerous complication thrown in the way of the enemy’s plan of attack. And at that, they were awesome.
The stereotypes about Hannibal include that he used elephants effectively against the Romans. But in his last battle, the Romans had already figured out how to scare and kill the elephants.
Every good classicist has heard the story why unlike every other Greek tribe the Makedonians did not erect tropaia on the battlefield. They used to, but after a major battle a lion came down from the hills, found the new scratching post, knocked it over, and left. They considered that a message from Zeus and stopped.
Lions are mentioned in the Odyssey, implying that Greek listeners would have been familiar with them. I'd always assumed these were some sort of mountain cat, but that map suggests no, actual lions!
if you scroll all the way East on the Tabula Peutengeriana (a medieval copy of an ancient Roman road map) you get to India where "in his locis elephanti nascuntur" meaning "in this place Elephants are born" and a little West of that the same thing for scorpions. Some detail pics in this blog post including the Elephants one, and you can find full size scans of it but I don't want to deep link to them because they're huge.
If this kind of thing is of interest to you I'd recommend reading Philip Freemans Biography of Alexander the Great. He also has solid biographies on Caesar and Hannibal (if you need more for your war elephant fix)