"Among these friends of Andreae's were many whom we find later in other humanistic societies: Wilhelm von der Wense and Tobias Adami, pupils of Campanella, Johann Kepler, discoverer of the laws of planetary motion, , , Theodor Haak, Samuel Hartlib, , and Comenius. That these various societies had deeper motives than those generally ascribed to them is certain. The Italian academies, after the pattern of which the "Order of the Palm" was founded, must have been, to a certain extent at least, secret societies, since neither their organization, their symbolism, their forms, nor the list of membership was communicated to outsiders, and their real aims were concealed while publicity was given to purposes of a genuinely innocent and popular nature. That the German organizations were not the mere language societies they were generally considered is apparent when we look at the activities of their members. They emphasized the study of the mother-tongue, it is true, but there was hardly a writer among them who was not also interested in the study of natural philosophy, in religion, in mathematics or astronomy, so much so, in fact, that to most of them clung the suspicion of heresy—that they were Rosicrucians and as such members of a religious sect highly dangerous to the church and liable of course to persecution. Members of the seventeenth century academies were natural philosophers, reformers, theologians, educators, statesmen, poets, noblemen; such members there were, as Bacon, Giordano Bruno, Comenius, Robert Boyle, J. B. van Helmont, Campanella, Hugo Grotius, Leibniz, Oxenstierna, Valentin Andreae, Spanheim, Pufendorf, Opitz. Throughout the whole list of membership there runs a line of spiritual relationship in the fact of their tolerance for the beliefs of others, a tolerance remarkable for the seventeenth century. With this they united strict opposition to the scholastic method. They were seriously religious, even to the extent of being mystics, but they understood the essence of Christianity differently from the ruling dogma. They treat not only of the relation of man to God, but of man to nature and of men to each other. For them a knowledge incapable of helping mankind had no value; a science shut off from the people in its language is useless; hence their emphasis of the vernacular. To make all knowledge fruitful for the education of the human race and thus lead the race on to a higher stage of development was one of their great ideals. Their turn for the practical led them on in their striving for a general reformation of the whole world. With their keen sense of the significance of fraternal organization, they formed unions which were intended to benefit the whole man and his whole mode of thinking, to influence his whole life. Their activities were in no way directed, as has been claimed, toward "childish play with symbols and signs but toward inclusive spiritual, religious, philosophical, and scientific aims," the carrying out of which, in those times, could be accomplished only under secret organization. The difficulties under which they labored compelled them to proceed with extreme caution, concealing their real interests and exhibiting to the world only what they considered secondary. When the time and place is more propitious for a franker carrying out of their plans and purposes of reform, we shall find them in a country of larger opportunity; we shall find them in England."
January 1, 1970
https://en.wikiquote.org/wiki/Mathematics_and_mysticism