There is no Nobel Prize in Mathematics, which has led to considerable speculation about why Alfred Nobel omitted it. Some recipients of the Nobel Prize in other fields also have notable achievements in and/or have made outstanding contributions to mathematics; for example, Bertrand Russell was awarded the Nobel Prize in Literature (1950) and Max Born and Walther Bothe shared the Nobel Prize in Physics (1954). Some others with advanced credentials in mathematics and/or who are known primarily as mathematicians have been awarded the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel: Kenneth Arrow (1972), Leonid Kantorovich (1975), John Forbes Nash (1994), Clive W. J. Granger (2003), Robert J. Aumann (who shared the 2005 Prize with Thomas C. Schelling), and Roger Myerson and Eric Maskin (2007).
Several prizes in mathematics have some similarities to the Nobel Prize. The Fields Medal is often described as the "Nobel Prize of mathematics", but it differs in being awarded only once every four years to people younger than forty years old. Other prestigious prizes in mathematics are the Crafoord Prize, awarded by the Royal Swedish Academy of Sciences since 1982; the Abel Prize, awarded by the Norwegian government beginning in 2001; the Wolf Prize awarded once a year by the Wolf Foundation; the Shaw Prize in mathematical sciences awarded since 2004; and the Gauss Prize, granted jointly by the International Mathematical Union and the German Mathematical Society for "outstanding mathematical contributions that have found significant applications outside of mathematics," and introduced at the International Congress of Mathematicians in 2006. The Clay Mathematics Institute has devised seven "Millennium Problems," whose solution results in a significant cash award: since it has a clear, predetermined objective for its award and since it can be awarded whenever a problem is solved, this prize also differs from the Nobel Prizes.

Emphasis on Discoveries over Inventions
Alfred Nobel left a fortune to finance annual prizes to be awarded "to those who, during the preceding year, shall have conferred the greatest benefit on mankind". One part, he stated, should be given "to the person who shall have made the most important discovery or invention within the field of physics". Nobel did not emphasize discoveries. But these are much more respected by the scientific community than are inventions: 77% of Nobel prizes in physics have been given to discoveries, compared with only 23% to inventions. This emphasis on discoveries has moved the Nobel prize away from its original intention of rewarding the greatest contribution to society in the preceding year.