It is about a "conjecture" I heard (when I was student). There would exist an algebraic structure on the homotopy groups of spheres such that this algebraic structure would be the free algebraic structure generated by one point. In the wikipedia page "Field with one element", it is written that the algebraic $K$-theory of the field with one element is related (can be identified ?) with the stable homotopy groups spheres. Is it the answer ?