During this formative period of his work, Freud valued and came to rely on the intellectual and emotional support of his friend Wilhelm Fliess, a Berlin based ear, nose and throat specialist whom he had first met 1887. Both men saw themselves as isolated from the prevailing clinical and theoretical mainstream because of their ambitions to develop radical new theories of sexuality. Fliess developed highly eccentric theories of human biorhythms and a nasogenital connection which are today considered pseudoscientific. He shared Freud's views on the importance of certain aspects of sexuality -- masturbation, coitus interruptus, and the use of condoms -- in the etiology of what were then called the "actual neuroses," primarily neurasthenia and certain physically manifested anxiety symptoms. They maintained an extensive correspondence from which Freud drew on Fliess's speculations on infantile sexuality and bisexuality to elaborate and revise his own ideas. His first attempt at a systematic theory of the mind, his 'Project for a Scientific Psychology' was developed with Fliess as interlocutor.  Freud had Fliess repeatedly operate on his nose and sinuses to treat "nasal reflex neurosis", and subsequently referred his patient Emma Eckstein to him. According to Freud her history of symptoms included severe leg pains with consequent restricted mobility, and stomach and menstrual pains. These pains were, according to Fliess's theories, caused by habitual masturbation which, as the tissue of the nose and genitalia were linked, was curable by removal of part of the middle turbinate. Fliess's surgery proved disastrous, resulting in profuse, recurrent nasal bleeding - he had left a half-metre of gauze in Eckstein's nasal cavity the subsequent removal of which left her permanently disfigured. At first, though aware of Fliess's culpability - Freud fled from the remedial surgery in horror - he could only bring himself to delicately intimate in his correspondence to Fliess the nature of his disastrous role and in subsequent letters maintained a tactful silence on the matter or else returned to the face-saving topic of Eckstein's hysteria. Freud ultimately, in light of Eckstein's history of adolescecent self-cutting and irregular nasal and menstrual bleeding, concluded that Fliess was "completely without blame", as Eckstein's post-operative hemorrhages were hysterical "wish-bleedings" linked to "an old wish to be loved in her illness" and triggered as a means of "rearousing [Freud's] affection". Eckstein nonetheless continued her analysis with Freud. She was restored to full mobility and went on to practice psychoanalysis herself.  Freud, who had called Fliess "the Kepler of biology", later concluded that a combination of a homoerotic attachment and the residue of his "specifically Jewish mysticism" lay behind his loyalty to his Jewish friend and his consequent over-estimation of both his theoretical and clinical work. Their friendship came to an acrimonious end with Fliess angry at Freud's unwillingness to endorse his general theory of sexual periodicity and accusing him of collusion in the plagiarism of his work. After Fliess failed to respond to Freud's offer of collaboration over publication of his Three Essays on the Theory of Sexuality in 1906, their relationship came to an end.

Answer this question "What did they accomplish together?" by extracting the answer from the text above.
Their friendship came to an acrimonious end with Fliess angry at Freud's unwillingness to endorse his general theory of sexual periodicity