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Severo Ochoa shared the Nobel Prize in Physiology or Medicine with Arthur Kornberg in 1959. They were recognized for their work on the synthesis of nucleic acids, specifically Ochoa's discovery of the enzyme polynucleotide phosphorylase, which synthesizes RNA, and Kornberg's discovery of DNA polymerase, which synthesizes DNA. These discoveries laid the foundation for understanding the fundamental processes of genetic information transfer and replication.