Physical world and mathematics

Jacob Lüroth

Jacob Lüroth (1844–1910) was a German mathematician and professor at Freiburg known for Lüroth's theorem, the Lüroth quartic, and the Lüroth problem on unirational varieties.

Jacob M. Taylor

Jacob M. Taylor is a theoretical quantum physicist at NIST, a NIST Fellow and co-founder of QuICS, who received the 2010 PECASE and helped implement the National Quantum Initiative.

Sep 20, 2026

Jacob N. Israelachvili

Jacob N. Israelachvili, also known as Jacob Israelachvili, was an Israeli-born chemical engineer and physicist at UC Santa Barbara who developed the Surface Forces Apparatus.

Jacob Palis

Jacob Palis (1940–2025) was a Brazilian mathematician at IMPA in Rio de Janeiro, known for work on dynamical systems, the Palis–Smale stability conjecture, and the 2010 Balzan Prize.

Jacob Sagiv

Jacob Sagiv is an Israeli chemist at the Weizmann Institute of Science, best known for founding the field of self-assembled monolayers between 1978 and 1980.

Jacob T. Schwartz (1930–2009) was an American mathematician and computer scientist at NYU's Courant Institute, known for the treatise Linear Operators, the Dunford–Schwartz theorem, and the SETL programming language.

Jacob Tsimerman

Jacob Tsimerman (born 1988) is a Canadian number theorist at the University of Toronto, known for proving the André–Oort conjecture and winning the 2026 Fields Medal.

Jacob Volhard

Jacob Volhard (1834–1910) was a German chemist at Halle known for the Volhard titration, the first synthesis of sarcosine, the synthesis of creatine, and the Hell-Volhard-Zelinsky reaction.

Jacobi elliptic functions

The Jacobi elliptic functions sn(z, k), cn(z, k), and dn(z, k) are doubly periodic meromorphic functions that invert the elliptic integral of the first kind, generalizing trigonometric functions.

Jacobi integral

The Jacobi integral, also called the Jacobi constant, is the only known conserved quantity of the circular restricted three-body problem, representing energy in the frame rotating with the two primaries.

Jacobi method

The Jacobi method, also known as Jacobi iteration, is an iterative algorithm of numerical linear algebra that solves systems of linear equations; Jacobi described it in 1845.

Jacobi polynomials

Jacobi polynomials, written P(α, β), are a family of classical orthogonal polynomials on (-1, 1), initiated by Carl Jacobi in 1826 and used in Gauss–Jacobi quadrature and spectral methods.

Jacobi's formula

Jacobi's formula is a theorem of matrix calculus stating that the differential of a square matrix's determinant equals the trace of its adjugate times the matrix differential.

Jacobian conjecture

The Jacobian conjecture, posed by Ott-Heinrich Keller in 1939, asks whether polynomial maps with constant nonzero Jacobian determinant must have polynomial inverses; it was refuted in dimension 3 in 2026.

Jacobian matrix and determinant

The Jacobian matrix of a vector-valued function is the matrix of its first-order partial derivatives; when square, its Jacobian determinant measures local volume scaling and appears in change of variables.

Jacobsen epoxidation

The Jacobsen epoxidation, also called the Jacobsen–Katsuki epoxidation, is a catalytic asymmetric reaction that turns unfunctionalized alkenes into chiral epoxides using a chiral manganese-salen catalyst with bleach.

Jacobsen's catalyst

Jacobsen's catalyst is a chiral manganese(III) salen complex introduced in 1990 by Eric Jacobsen and independently by Tsutomu Katsuki for asymmetric epoxidation of unfunctionalized alkenes.

Jacobsite

Jacobsite is a black, weakly magnetic manganese iron oxide mineral of the spinel group, occurring in metamorphosed manganese deposits and named in 1869 for Jakobsberg, Sweden.

Jacobson radical

The Jacobson radical of a ring R, written J(R), is the intersection of all maximal left ideals, equivalently of all maximal right ideals; it was introduced by Nathan Jacobson in 1945.

Jacobson ring

A Jacobson ring, also called a Hilbert ring, is a commutative ring in which every radical ideal is the intersection of the maximal ideals containing it.

Jacobsthal numbers

The Jacobsthal numbers are the sequence 0, 1, 1, 3, 5, 11, ... defined by the recurrence J(n) = J(n−1) + 2J(n−2), named for the German mathematician Ernst Erich Jacobsthal.

Jacobus H. van 't Hoff

Jacobus Henricus van 't Hoff was a Dutch physical chemist who received the first Nobel Prize in Chemistry in 1901 for chemical dynamics and osmotic pressure.

Jacobus Kapteyn

Jacobus Kapteyn (1851–1922) was a Dutch astronomer at the University of Groningen who used photography and star counts to found statistical astronomy, cataloging 454,875 southern stars and discovering the star streams.

Jacqueline Bloch

Jacqueline Bloch, born in 1967, is a French experimental physicist at CNRS who studies polaritons and quantum fluids of light, winning the 2026 CNRS Gold Medal.

Sep 20, 2026

Jacqueline K. Barton

Jacqueline K. Barton (born 1952) is an American inorganic chemist at Caltech who pioneered DNA-mediated charge transport, winning the National Medal of Science in 2011.

Jacques Blamont

Jacques-Émile Blamont (1926–2020) was a French astrophysicist who founded France's first space laboratory, the Service d'aéronomie, and became the first scientific and technical director of CNES.

Jacques Cousteau

Jacques-Yves Cousteau (1910–1997) was a French naval officer who co-invented the Aqua-Lung, explored the oceans aboard the Calypso, and won three Academy Awards for his films.

Jacques Curie

Jacques Curie (1856–1941) was a French physicist who, with his younger brother Pierre, co-discovered the piezoelectric effect in 1880 and later held a chair at Montpellier.

Jacques Dixmier

Jacques Dixmier, born 1924 in Saint-Étienne, is a French mathematician whose monographs on von Neumann and C-algebras defined operator algebra theory; he was a Bourbaki member and Alain Connes's teacher.