See also: 1823 in science, other events of 1824, 1825 in science, list of years in science.
Niels Henrik Abel partially proves that the general quintic or higher equations cannot be solved by a general formula involving only arithmetical operations and roots.
Augustin Louis Cauchy proves convergence of the Euler method. In this proof, Cauchy uses the implicit Euler method
Sadi Carnot scientifically analyzes the efficiency of steam engines.
Patent issued to Joseph Aspin for portland cement.
Copley Medal: John Brinkley
February 7 - William Huggins, astronomer
February 16 - Peter Kozler, cartographer, geographer.
March 12 - Gustav Kirchhoff, physicist
June 26 - William Thomson, Lord Kelvin, physicist