The Maï-Taï cocktail was created in 1944 in Oakland, California by Victor Jules Bergeron Jr, alias "Trader Vic". He is the founder of the Trader Vic's restaurant chain.
If the recipes diverge more or less from one source to another, it is partly because the creator himself has modified the Mai-Tai recipe over the years, and partly part because the cocktail is a little too strong for the taste of some bartenders who therefore tend to add new ingredients without alcohol. But a Maï-Taï should always be made with fresh mint, rum, lemon, curaçao and orgeat.
The night he created this cocktail, Trader Vic had a visit from 2 Tahitian friends, Ham and Carrie Guild. Trader Vic says that when Carrie took a sip she exclaimed "Maï-Taï - Roa Ae" which could be translated into French as extraordinarily good. In short, that's why the cocktail was called "Mai-Tai".
Be that as it may, the Mai Tai is a cocktail very rich in flavors, as long as we don't forget the lemon zest and especially the mint as decoration, otherwise a Mai-Tai wouldn't really be one one.