The conjecture was made in 1904 by the French mathematician Henri Poincaré, who was working on classifying manifolds when he noted that three-dimensional manifolds posed some special problems.
Note that Simon's and Kato's papers discussed in the historical part of Sect. 9 were both preprinted in early 1972 after this conjecture, so the original conjecture was made for a local Stummel space rather than (L^2_{loc}) but eventually, it was updated to (L^2_{loc}).
Scientific method begins with abduction or hypothesis: because of some perhaps surprising or puzzling phenomenon, a conjecture or hypothesis is made about what actually is going on.
On this base, conjectures were made and a general theory produced, first by Poincaré and then by the American engineer-turned-mathematician Solomon Lefschetz, concerning the nature of manifolds of arbitrary dimension.
In addition, some conjectures are made from our numerical observations.
Several conjectures are made as to how all of the resonance horns generically evolve between these two extremes for forced oscillations in oscillatory systems that are near a Hopf bifurcation.
It is the environment where tools are developed, observations and conjectures are made, hypotheses are formulated and tested, multiple scenarios are run, and discoveries are made for the betterment of science or patients.
The conjecture has been made that every form of degree d (in the same sense as degrees of ordinary polynomials) over Qp, in which the number of variables exceeds d2, has a nontrivial zero in Qp.
The following conjecture can be made from the previous relationships.
