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"It is well known that..."
xconfuzzledonex
"... a closed orbit of a hamiltonian system is preserved under small perturbations of the hamiltonian function, provided that the orbit is nondegenerate in a certain sense.

"...a contact manifold admits a Riemannian metric compatible with the contact structure."

"...the maximal abelian extension of Q is generated by all roots of unity."

"...every Laurent polynomial f(t) in Lambda=Z[t,t^{-1}] with f(1)=1 is the Alexander polynomial of some ribbon 2-knot."

"...the manifold of a Lie group can be furnished, in a natural way, with a symmetric affine connexion, called the 0-connexion, and that the manifold is Cartan-symmetric with respect to this connexion."

"...the ring D=D(A) of k-linear differential operators on an affine k-algebra A is not Noetherian in general."

"...if Sigma is a domain of holomorphy in C^n, then it is a Cousin I domain; it is also a Cousin II domain if and only if H^2(Sigma,Z)=0."

"...the Hubbard tree of a postcritically finite complex polynomial contains all the combinatorial information on the polynomial."


these are all opening sentences of papers published in mathematical research journals. (google for so many more than there should be.)

whiskey. tango. foxtrot. IT IS NOT WELL KNOWN. >_<

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It is well known that published mathematicians are full of shit and like to say things to make themselves feel smarter than the rest of the world . . .

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