- Prizes will be awarded for published work of particular merit in pure mathematics, applied mathematics, mathematical statistics or mathematical physics.

- Normally one or more prizes of at least £50 will be awarded at four-yearly intervals, but an award may be withheld if no eligible work of sufficient merit has been published.

- A candidate for a prize

- must be 35 years of age or less at the time of the award,

- must either be a graduate of a Scottish University and/or have been engaged in postgraduate research in Scotland for at least three years.

- must be 35 years of age or less at the time of the award,
- No prizewinner shall be eligible thereafter.

The winners are listed below:

**1961**A G Mackie and A H Wallace

**1965**J B McLeod

**1970**D J S Robinson

**1973**A M Davie

**1977**G Brown and C A Stuart

**1981**J M Ball

**1985**J Howie

**1989**A A Lacey and M Röckner

**1993**M A Berger and A W Reid

**1997**A D Rendall

**2001**M L McQuillan and J A Sherratt

**2005**T Bridgeland

**2009**A Smoktunowicz

**2013**S White

**2016**A Bayer