Lev Landaus mother had trained in medicine and she had undertaken work in physiology while his father was a petroleum engineer who worked at the oil fields in Baku on the Caspian Sea Lev was a prodigy in mathematics when he was a child

Could you correct the punctuation please?
Lev Landau's mother had trained in medicine and she had undertaken work in physiology, while his father was a petroleum engineer who worked at the oil fields in Baku on the Caspian Sea. Lev was a prodigy in mathematics when he was a child.