Ernst Pascual Jordan (German: [ˈɛʁnst pasˈku̯al ˈjɔʁdan]; 18 October 1902 – 31 July 1980) was a German theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matrix mechanics, and developed canonical anticommutation relations for fermions. He introduced Jordan algebras in an effort to formalize quantum field theory; the algebras have since found numerous applications within mathematics.

Jordan joined the Nazi Party in 1933, but did not follow the Deutsche Physik movement, which at the time rejected quantum physics developed by Albert Einstein and other Jewish physicists. After the Second World War, he entered politics for the conservative party CDU and served as a member of parliament from 1957 to 1961.

Jordan was born to Ernst Pasqual Jordan (1858–1924) and Eva Fischer. Ernst Jordan was a painter renowned for his portraits and landscapes. He was an associate professor of art at Hannover Technical University when his son was born. The family name was originally Jorda and it was of Spanish origin. The first born sons were all given the name Pasqual or the version Pascual. The family settled in Hannover after Napoleon's defeat at the Battle of Waterloo in 1815 and at some stage changed their name from Jorda to Jordan. Ernst Jordan married Eva Fischer in 1892.

An ancestor of Pascual Jordan named Pascual Jordan was a Spanish nobleman and cavalry officer who served with the British during and after the Napoleonic Wars. Jordan eventually settled in Hannover. In those days the House of Hanover ruled the United Kingdom. The family name was eventually changed to Jordan (pronounced in the German manner, [ˈjɔʁdaːn]). A family tradition held that the first-born son in each generation be named Pascual. Jordan was raised with a traditional religious upbringing. At age 12 he attempted to reconcile a literal interpretation of the Bible with Darwinian evolution; his teacher of religion convinced him there was no contradiction between science and religion (Jordan would write numerous articles on the relationship between the two throughout his life).

Jordan enrolled in the Technical University of Hannover in 1921 where he studied zoology, mathematics, and physics. As was typical for a German university student of the time, he shifted his studies to another university before obtaining a degree. The University of Göttingen, his destination in 1923, was then at the very zenith of its powers in mathematics and the physical sciences, such as under the guidance of mathematician David Hilbert and the physicist Arnold Sommerfeld. At Göttingen, Jordan became an assistant to the mathematician Richard Courant for a time, and then he studied physics under Max Born and heredity under geneticist and race scientist Alfred Kühn for his doctorate.

Jordan suffered a speech impairment throughout his life, often stuttering badly when giving unprepared remarks. In 1926, Niels Bohr offered to pay to treat it, and on the advice of Wilhelm Lenz, Jordan sought treatment at Alfred Adler's clinic in Vienna.

Together with Max Born and Werner Heisenberg, Jordan was a coauthor of an important series of papers on quantum mechanics. He went on to pioneer early quantum field theory before largely switching his focus to cosmology before World War II.

Jordan devised a type of nonassociative algebras, now named Jordan algebras, in an attempt to create an algebra of observables for quantum mechanics and quantum field theory. While the algebras proved not to be useful for that purpose, they have since found numerous applications within mathematics. Jordan algebras have been applied in projective geometry, number theory, complex analysis, optimization, and many other fields of pure and applied mathematics.