Greek India

This may have been done earlier.
Is it plausible that Alexander the Great pushed his invasion all the way to India, and ended up building a Hellenistic empire in that region and beyond (SE Asia)? How would this be done?
What would the culture of this hybrid Indian culture be like that? How this India affected world history?
Lastly, how long would it lasted?
Not just the Alexandrian Empire, but the Greek language and culture there.
Could it stand to modern age?

Thanks in advance!
 
Indo-Greek culture resisted to 1st century AD OTL, without conquest. It had gone heavily native in the process, however.
So, the impact on India would be massive, both politcally and culturally, and chances are that this would survive into modern era in some way (as it did in OTL Middle East or Europe, for example).
However, I seriously doubt it was possible for Alexander to conquer India. At best, he could manage to take and hold the Indus valley, and this alone would mean a whole lot of consequences. The challenges for the Macedonians to conquer and keep a hold beyond that are painstaking. Totally alien environment and cliamte, with new fucking diseases, unfamiliar food, flora, fauna, people, languages, customs, massive numerical inferiority. Their enemy would have comparable tech, alla the advantages of defense in a familiar landscape, and numbers, on its side, even without considering that we are speaking about the Mauryan empire in its rising star phase, under the leadership of Candragupta, whose skill as a military commander and personal charisma could have been easily a match for Alexander's. And, on top of all this, Macedonian troops could not care less about conquering India. Persia had been enough to them. They were on the verge of mutiny OTL. Would Alex conquer India alone? :D
OTOH, the Mauryan Empire is a single entity. Once defeated in an adequately conclusive manner (a very, very unlikely outcome for the Macedonians) Northern India is taken, at least for a while. I can easily imagine a completely different Indian civilization (in its top manifestation, at least; grassroots level of lore and popular religion are going to be far less affected) emerging from such kind of protracted contact.
 
Top