"Now one final remark on the term spectrum. In physics each type of atom or molecule possesses a characteristic spectrum formed by its emission or absorption lines. Quantum mechanics interprets these as the characteristic values of an operator, the Hamiltonian, acting on a certain Hilbert space. It is thus natural to speak of the discrete spectrum of the Hamiltonian. The emission or absorption bands correspond to a continuous spectrum. In the early 1930s von Neumann succeeded brilliantly in defining the concept of a self-adjoint (unbounded) operator H on a Hilbert space 𝔥 and its spectrums. The contribution of Gelfand in 1940 was in associating a commutative Banach algebra A with the operator H and an isomorphism of A onto C0(S;\mathbb{C}). From that point on the evolution of the meaning of the word spectrum can be understood. For Grothendieck the spectrum of a commutative ring consists of its prime ideals (as in the case of Dedekind)."
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Pierre Cartier (mathematician)
Pierre Émile Cartier (born 10 June 1932) is a French mathematician. An associate of the Bourbaki group and at one time a colleague of Alexander Grothendieck, his interests have ranged over algebraic geometry, representation theory, mathematical physics, and category theory. He was an Invited Speaker at the International Congress of Mathematicians in Nice in 1970.
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