“possesses an intuitive faculty for the higher analysis, and possesses it to such a wonderful degree that all of us here stand before him in genuine amazement. He knows apparently but little about our systems of formulation, though every day rapidly advancing in technical knowledge. And yet, by processes not in the books, processes apparently original with himself, and which he is not able to explain, he has worked out with ease results such as have most violently exercised the highest order of mathematical minds. In a word, this extraordinary youth may be said to think in figures and symbols—the ordinary career of his reason is along the pathway of scientific formulae. More than all this, his mind seems to have grasped at processes and solved problems which we cannot compass with all our skill, and which, with his present deficient powers of expression, he is incapable of interpreting to us.”

“he could not seem less than one of our own people had been dropped upon this earth, a full-grown stranger, accidentally snatched from some other sphere where the customary interchange of thought is through the medium of mathematical formulas.”

“for I need not tell you, men like this Letoile are of too fragile and delicate a constitution to endure rough usage. We can send our earthenware to the well, but we must keep our finer porcelains indoors. And if any mental or moral hurt should come to the young man, we could not fail to be deeply grieved. Our Faculty look upon him as the professors of a musical academy are said to look upon a child possessed of one of those rare voices which do not appear more than once in a century—something to be treasured more zealously than the Sibyl’s books.”

“It has been well observed by one of the deepest thinkers of our century, that there is nothing in the nature of mathematical science which prescribes any boundaries to its infinite progress. There is no limit to the applicability of mathematics, for there is no inquiry which may not finally be reduced to a mere question of numbers, as notative functions of quantities and their relations. The limitation that does exist is in ourselves, in the imperfections of our intelligence, and the absence of power in our minds to go beyond certain processes and degrees of comparison and abstraction. It is only by the discovery of new and simpler methods that the human intellect is able to grapple with the overpowering multitude of new relations and conditions which come up as knowledge advances. And this rank growth of strange weeds in the garden of Science will always run beyond our capacity to eradicate them; for it is part of our unhappy constitution that we are more apt at imagining than we are at reasoning. Hence, we do right to look abroad for new methods and better processes of high analysis; for, while these subtler processes will of course open up to us a vast new field of questions beyond our grasp, they will at the same time give us power to solve many problems already presented, but as yet impracticable to our imperfect algebra. I need not tell you that the present advanced condition of mathematical science, as compared with other sciences, has not resulted from a methodical progression, but has been reached per salturn. It is not coordinate with the advancement of the race, but due to the sublime flights of individual genius. Our science has not crept along with common men on the face of the earth, but has leaped from point to point up the giddy heights, under the impulses given to it by the minds of such uncommon men as Euclid, Archimedes, Apollonius, Pappus, Diophantns, Vieta, Descartes, Kepler, Newton, Leibnitz, Napier, Laplace, and the many other illustrious names which we delight to honor. A new genius, therefore, in giving us new methods, may virtually enrich the world with a new mathematics. Hence the sense of responsibility which we feel toward this young man, who seems to have at his control, could we contrive to develop them, new processes in our science of as great utility to us now as were those of Diophantus to the geometers of his day.”

“I might indeed have pulled down the altar, but I could not have destroyed the idol, for that was engraven upon a woman’s heart, and so was indelible forever.”

“I have Spoken of Raimond’s mathematical studies—but indeed that is scarcely the proper word. What he did in this way seemed done not by process of reasoning, but by pure evolution of consciousness. [...] Raimond Latoile’s lips seemed to be counting off fugues from and variations upon the grand harmonies of the spheres, tern of apportioning the stars into various constellations. He gave them names and number, in their widest and most transcendent generalizations. Now and then, as he advanced in knowledge of our common symbols, he would, by way of exercise as it were, set down fragments from these essentially rhythmical reveries —abstruse developments of the properties of recondite curves, unguessed corollaries and scholia from the general laws of the stellar spaces, and speculations within the profoundest twilight of the Calculus - demonstrations always complete and exemplary so far as I could understand them but often, when most carefully written out, as much too difficult for me, as the propositions of The Principia or the Mecanique Celeste would be to an ordinary schoolboy.”

“ There!” he cried, “there is my home, in the cycles of yonder bright wilderness of spheres which you call Arcturus! There is my home; and since I was sent from thence I have had no word from home, until Cherry’s voice uttered it just now, with such a familiar accent. Surely you are one of our denizens, Cherry, wandering, like me, a little while from home.”

“ Cherry’s whole life is a poem, Raimond,” I answered for her; “ and a very sweet one. But it is only set to earthly music, after all, and I do not imagine she understands the language of the spheres.”

“ Yet she speaks to me in that language,” responded Raimond, musingly.”

“to his great surprise, instead of having a photographic image of the comet, his plate contained the representation of a series of strange characters or symbols, arranged in order, in a circumscribed lozenge, very much like the ideographic writing of the ancient Egyptians. How it came there he could not imagine, nor what it meant. The characters are not those of any known language, nor have the works of Champollion or Young or Rawlinson afforded any key to them - if, indeed, they be characters at all, which I am inclined to doubt. But Doctor Cometenbahnen not only claims that they are demonstrably characters, but also that they are mathematical symbols, and that they contain a problem of importance to the world, if a solution can only be found. And, he truly says, the human ingenuity that has deciphered the strange monuments of Egypt and the cuneiform inscriptions of Assyria, need not be staggered before the text of any language, even though it embody the songs of the very stars.”