Personally I tend to rely as little as possible on Wikipedia ever since a colleague made me note that whole articles have been shamelessly copied from scientific handbooks and that, in those cases, seems like Wikipedia "no copyrighted material without permission!" principle doesn't seem to apply.
Anyway back to unicorns now.
The most commonly accepted source of ispiration for both the Western and Eastern traditions regarding the unicorn is no fossil but a living animal, the Indian Rhino (Rhinoceros unicornis).
Ctesias, the first known written source on Unicorns in Western tradition, didn't see rhinos firsthand but somehow (and don't ask how) got it mixed with the kulan (Equus hemionus), the Asian wild ass: ironically rhinos and asses are close parents (both belong to the order Perissodactyla).
Ctesias has often been believed to be a Greek-language physician who worked for a few years at the Persian king's court before returning home and writing a couple of (known) books: one dealing with Persia itself and the other dealing with India (ie the rest of Asia). While Ctesias may well have been a physician I personally believe (just like Marco Polo) that all he did was retelling previous travellers' tales, which went increasingly wilder with each retelling, and that if he ever went to Persia, language was a main issue, leading to a LOT of mistakes.
Talk about witnesses reliability...
The Western world took a great liking to the classic Unicorn: let's not forget just how important the horse became in most of Europe after the barbaric invasions. Just look at the Lombard codes to see how many chapters deal with horse-related crimes.
Over the centuries the Unicorn became progressively mythical and acquired many incredible powers: his horn could mak poison harmless, he could only be tamed by a virgin etc. Chivalrous artists took a particular liking into the Unicorn and used it as a basis for many exquisite works.
...and when a Norseman came from beyond the Artic Circle with Walrus tusks or Narwhal teeth to sell he always found a willing public to buy his merchandise.
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Fas: Ite, Maledicti, In Ignem Aeternum.