The DE MORGAN MEDAL, the Society's premier award, is awarded every third year (in years numbered by a multiple of 3), in memory of Professor A. De Morgan, the Society's first President. The De Morgan Medal for year X can only be awarded to a mathematician who is normally resident in the United Kingdom on 1st January of year X. The only grounds for the award of the Medal are the candidate's contributions to mathematics.

The POLYA PRIZE is awarded in those years, not numbered by a multiple of 3, in which the De Morgan Medal is not available for award. The Prize is in memory of Professor G. Polya, who was a Member (and later Honorary Member) of the Society for about 60 years. The Polya Prize is awarded in recognition of outstanding creativity in, imaginative exposition of, or distinguished contribution to, mathematics within the United Kingdom; it may not be awarded to any person who has previously received the De Morgan Medal.

The SENIOR BERWICK PRIZE is named after Professor W. E. H. Berwick, a former Vice-President of the Society, and is awarded in even-numbered years. The Senior Berwick Prize for year X can only be awarded to a mathematician who is a member of the Society on 1st January of year X; it is awarded in recognition of an outstanding piece of mathematical research actually published by the Society during the eight years ending on 31st December of year X-1; and it may not be awarded to any person who has previously received the De Morgan Medal, Polya Prize, Senior Whitehead Prize or Naylor Prize.

The SENIOR WHITEHEAD PRIZE is awarded in odd-numbered years, in memory of Professor J. H. C. Whitehead, a former President of the Society. The Senior Whitehead Prize for year X can only be awarded to a mathematician who is normally resident in the United Kingdom on 1st January of year X. The grounds for the award may include work in, influence on or service to mathematics, or recognition of lecturing gifts in the field of mathematics; the Senior Whitehead prize may not be awarded to any person who has previously received the De Morgan Medal, Polya Prize, Senior Berwick Prize or the Naylor Prize.

The BERWICK PRIZE, also named after Professor W. E. H. Berwick, is awarded in odd-numbered years. The Berwick Prize for year X can only be awarded to a mathematician who, on 1st January of year X, is a member of the Society, is under the age of forty years (except that this age restriction may be relaxed when it appears desirable to do so in order to take fair account of broken career patterns), and is not already a Fellow of the Royal Society; it is awarded in recognition of an outstanding piece of mathematical research actually published by the Society during the eight years ending on 31st December of year X-1; and it may not be awarded to any person who has previously received the De Morgan Medal, the Senior Berwick Prize, the Senior Whitehead Prize, the Naylor Prize or a Whitehead Prize.

The WHITEHEAD PRIZES are also in memory of Professor J. H. C. Whitehead and are awarded each year. Whitehead Prizes for year X can only be awarded to mathematicians who, on 1st January of year X, are normally resident in the United Kingdom or members of the Society mainly educated in the United Kingdom, who are not already Fellows of the Royal Society, and who are under the age of forty years (except that this age restriction may be relaxed when it appears desirable to do so in order to take fair account of broken career patterns). Grounds for the award of a Whitehead Prize may include work in and influence on mathematics. From 1999 the maximum number of Whitehead Prizes awarded in any one year increased from two to four to allow for the award of prizes across the whole of mathematics, including applied mathematics, mathematical physics, and mathematical aspects of computer science. Such a prize may not be awarded to any person who has previously received any other LMS Prize.

The NAYLOR PRIZE AND LECTURESHIP IN APPLIED MATHEMATICS is awarded in even-numbered years, in memory of Dr V. D. Naylor. The Naylor Prize for year X can only be awarded to a mathematician who is normally resident in the United Kingdom on 1st January of year X. The grounds for the award may include work in, and influence on, and contributions to applied mathematics and/or the applications of mathematics, and lecturing gifts. The Naylor Prize may not be awarded to any person who has previously received the De Morgan Medal, the Polya Prize, the Senior Berwick Prize or the Senior Whitehead Prize. The winner of the Naylor Prize for year X is normally invited to give the Naylor Lecture at a Society meeting in the year X+1.

The FRÖHLICH PRIZE is awarded in odd numbered years in memory of Professor Albrecht Fröhlich (De Morgan Medallist 1992). The Fröhlich Fund for this purpose was based on a generous donation from Mrs Fröhlich, reflecting Professor Fröhlich's great enthusiasm for, and gratitude to, the London Mathematical Society. No person shall be awarded a Fröhlich Prize more than once. A Fröhlich Prize may not be awarded to any person who has received the De Morgan Medal or the Polya Prize. The Prize shall be restricted to mathematicians who, on 1st January of the year of the award, are either (i) normally resident in the United Kingdom of Great Britain and Northern Ireland, or (ii) members of the Society mainly educated in the United Kingdom. The Prize shall only be awarded to a mathematician who on the 1st January of the year of its award is under 40 years old except that this age restriction may be relaxed when it appears desirable to do so in order to take fair account of a broken career pattern. The Prize shall be awarded for original and extremely innovative work in any branch of mathematics.

Finally, no person is eligible to receive a given Society prize more than once.

Current Prizewinners
Previous Prizewinners