This chapter returns to our narrative, explaining how all the projects of the young Descartes—physico-mathematics, universal mathematics and universal method—came to a climax and inflection point in the late 1620s. Working in the shadow of Marin Mersenne's cultural battle against both radical scepticism and religiously heterodox natural philosophies, Descartes launched out, trying to realize his earlier dream of a methodologically sound "universal mathematics". Riding on his physico-mathematical and more purely analytical mathematical results, and the confidence they fed into his dream of method, he worked himself into an intellectual dead end. This project, inscribed in the latter portions of his unfinished Rules for the Direction of the Mind, did not blossom into a magisterial work of method and universal mathematics. Rather, it collapsed in 1628, under its own weight of self-generating problems. From this point on, Descartes did not believe in his method, although he continued to exploit it for public presentation of his work. Descartes now entered upon a process of rapid change of direction of his intellectual agenda, and correlatively, his self-understanding and identity.