mathematics

From the Greek:   mathematikos ( maqhmatikws )

   fond of learning, eager to learn

    Among the Pythagoreans, advanced student

   In a scientific context, mathematician

From the Greek:  mathe ( maqh ) = mathesis ( maqhsis )

   learning, the getting of knowledge, desire of learning, education, instruction

From the Greek:  mathein ( maqaein )

   to learn, especially by study, practice, or heart

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So, in the general case, a mathematician was an a learned or educated person,

not just a person educated in mathematics.