P.A. MacMahon: Ramanujan’s Distinguished Contemporary

Abstract

P.A. MacMahon, a noted combinatorialist, wrote a famous treatise on Combinatory Analysis in which he included a discussion of the combinatorial significance of the Rogers–Ramanujan identities that neither Rogers nor Ramanujan emphasized. This article describes MacMahon’s life as a Major in the British Army stationed in India and later as an assistant to G.H. Hardy of Cambridge University. MacMahon’s mathematical connections with Ramanujan are not just due to the Rogers–Ramanujan identities, but also due the table of partitions he compiled in order to verify the famous Hardy–Ramanujan asymptotic formula for the partition function. The story of how Ramanujan discovered his famous partition congruences upon seeing this table is also described.

This article appeared in The Hindu, India’s National Newspaper, in December 1993 for Ramanujan’s 106th birth anniversary.