[2] Raoul Bott was also at the Institute at that time; he recounted his mathematical contacts in an AMS-MAA invited address August 9, 1988, in Providence Rhode Island: In 2000 Allyn Jackson interviewed Bott, who then revealed Shapiro's part in the Periodicity Theorem.
In 1960 Shapiro contributed to the Bourbaki Seminar his "Algèbres de Clifford et periodicité des groupes πK(BO))".
This oral communication was later recalled in the Mathematical Intelligencer article "Arnold Shapiro's eversion of the sphere".
Arnold Shapiro died in 1962 in Newton, Massachusetts where he was a tenured professor at Brandeis University.
Each year an undergraduate student of mathematics at Brandeis University is awarded a Shapiro Prize in memory of Arnold.