[3] The Society was founded in 1936 by J. H. C. Whitehead together with two of his students at Balliol College, Graham Higman[4] and Jack de Wet.

[5] The name of the society was chosen at random by Higman from the titles of the books on Whitehead's shelf;[6] in this case, Oswald Veblen's Invariants of Quadratic Differential Forms.

The opening lecture was given by G. H. Hardy in Hilary Term 1936, with the title 'Round Numbers'.

[7][8] Though many members joined the armed forces during the war, meetings continued, including lectures by Douglas Hartree and Max Newman, as well as debates - 'Is Mathematics an end in itself?'

[9] The society has hosted hundreds of prominent mathematicians,[10] including lectures by Benoit Mandelbrot,[11] Sir Roger Penrose,[12] and Simon Singh.