One half, the irreducible fraction resulting from dividing one by two (½), or any number by its double
The Green-function technique, termed the irreducible Green function method is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions.
One necessary condition for -peridoicity is that , where is monic irreducible over.
the two vibrational states of a molecule transform according to the same irreducible representation of the molecular point group.
Hilbert's irreducibility theorem, in number theory, concerning irreducible polynomials
Robert Rosen, founder of "Relational Biology" provided a comprehensive mathematical and category-theoretic treatment of irreducible causal relations he believed to be responsible for life.
Nevertheless, particles can indeed be neatly divided into groups that form irreducible representations of the Lie algebra SU(3), as first noted by Murray Gell-Mann and independently by Yuval Ne'eman (see the eightfold way).
Three-dimensional Euclidean space is irreducible: all smooth 2-spheres in it bound balls.