Born in London, Reuben Louis Goodstein (1912-1985) completed his secondary education at St Paul's School and in 1931 proceeded to Magdalene College, Cambridge, with a Major Open Scholarship to read mathematics. He graduated in 1933 having taken firsts in Parts I and II of the Mathematical Tripos. From 1933 to 1935 his research on transfinite numbers was supervised by Professor J. E. Littlewood. He took a MSc and left Cambridge in 1935 to take up an appointment as lecturer in pure and applied mathematics at Reading University, a position he held until late 1947. While undertaking a strenuous teaching load at Reading his research interests were developing and for this work he received a PhD from the University of London in 1946, which was supervised by the philosopher Ludwig Wittgenstein.