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I don't get it :-(
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I think it's just that Andrew Carnegie made his fortune in the steel industry, and the Mellons made their fortune in banking.
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Yes and

Carnegie Technical Schools was founded in 1900 based on a $1m donation from Andrew Carnegie,

Mellon Institute of Industrial Research was originally founded in 1913 by Andrew and Richard Mellon.

Carnegie Mellon was created by combining the two institutions in 1967.

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That's very fun and makes so much more sense than my half guess that it was from a defunct regional mid 20th century bank I had never heard of.
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