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The best known philosophical statement by René Descartes is "Cogito ergo sum" (French: Je pense, donc je suis; English: I think, therefore I am).

  COGITO = ERGO * SUM

Which digit does each letter represent? (Please present the full analysis how these digits can be determined. Every letter stands for a digit in base-10 representation, different letters stand for different digits, and leading digits are always non-zero.)

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908520 = 6780*134
(I love these things :P)

Reasoning:

First I realized that there were 9 different letters, so every digit must be used. The likelihood that O would be a 0 was high so I took a gamble on that...
But I'm afraid apart from that, for multiplication alphametics I haven't heard of a full proof way of solving one. The best solution is trial and error.

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