Editing Mathematical physics (section)

=== Quantum ===
Another revolutionary development of the 20th century was [[Quantum mechanics|quantum theory]], which emerged from the seminal contributions of [[Max Planck]] (1856–1947) (on [[Planck's law|black-body radiation]]) and Einstein's work on the [[photoelectric effect]].  In 1912, a mathematician [[Henri Poincare]] published ''Sur la théorie des quanta''.<ref name=McCormmach>
{{cite journal
  | last =McCormmach
  | first =Russell
  | title = Henri Poincaré and the Quantum Theory
  | journal = Isis
  | volume = 58
  | issue = 1
  | pages = 37–55
  | date = Spring 1967
  | doi =10.1086/350182
| s2cid =120934561
 }}</ref><ref name=Irons>
{{cite journal
  | last =Irons
  | first =F. E.
  | title = Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms
  | journal =  American Journal of Physics
  | volume = 69
  | issue = 8
  | pages = 879–84
  | date = August 2001
  | doi =10.1119/1.1356056
|bibcode = 2001AmJPh..69..879I }}</ref> He introduced the first non-naïve definition of quantization in this paper. The development of early quantum physics followed by a heuristic framework devised by [[Arnold Sommerfeld]] (1868–1951) and [[Niels Bohr]] (1885–1962), but this was soon replaced by the [[quantum mechanics]] developed by [[Max Born]] (1882–1970), [[Louis de Broglie]] (1892–1987), [[Werner Heisenberg]] (1901–1976),  [[Paul Dirac]] (1902–1984), [[Erwin Schrödinger]] (1887–1961), [[Satyendra Nath Bose]] (1894–1974), and [[Wolfgang Pauli]] (1900–1958). This revolutionary theoretical framework is based on a probabilistic interpretation of states, and evolution and measurements in terms of [[self-adjoint operator]]s on an infinite-dimensional vector space. That is called [[Hilbert space]] (introduced by mathematicians [[David Hilbert]] (1862–1943), [[Erhard Schmidt]] (1876–1959) and [[Frigyes Riesz]] (1880–1956) in search of generalization of Euclidean space and study of integral equations), and rigorously defined within the axiomatic modern version by [[John von Neumann]] in his celebrated book ''[[Mathematical Foundations of Quantum Mechanics]]'', where he built up a relevant part of modern functional analysis on Hilbert spaces, the [[spectral theory]] (introduced by [[David Hilbert]] who investigated [[quadratic forms]] with infinitely many variables. Many years later, it had been revealed that his spectral theory is associated with the spectrum of the hydrogen atom. He was surprised by this application.) in particular. Paul Dirac used algebraic constructions to produce a relativistic model for the [[electron]], predicting its [[magnetic moment]] and the existence of its antiparticle, the [[positron]].