Final answer:
The sentence in question is a run-on because it improperly joins two independent clauses. These clauses, 'However, young Einstein showed a talent for mathematics' and 'At the age of 12, he taught himself Euclidean geometry', should be separated by either a semicolon, or a period making them two sentences.
Step-by-step explanation:
The sentence in the question is a run-on sentence. A run-on sentence is when two or more independent clauses (complete sentences on their own) are joined together improperly without the right punctuation or conjunctions. The part before the comma, 'However, young Einstein showed a talent for mathematics' is a complete sentence, as is 'at age the age of 12, he taught himself Euclidean geometry', which is after the comma. Therefore, these two independent clauses must be separated correctly. One proper way to do so might be: 'However, young Einstein showed a talent for mathematics. At the age of 12, he taught himself Euclidean geometry.'
Learn more about Run-on sentences