“I have so overwhelmingly much to write about my discovery that I know no other way of checking myself than taking a quarter of a sheet only to write on. I want an answer to my four-sheet letter. “I am unbroken in my determination to publish a work on Parallels, as soon as I have put my material in order and have the means. “At present I have not made any discovery, but the way I have followed almost certainly promises me the attainment of my object if any possibility of it exists. “I have not got my object yet, but I have produced such stupendous things that I was overwhelmed myself, and it would be an eternal shame if they were lost. When you see them you will find that it is so. Now I can only say that I have made a new world out of nothing. Everything that I have sent you before is a house of cards in comparison with a tower. I am convinced that it will be no less to my honour than if I had already discovered it.” The discovery of which Johann here speaks was published as an appendix to Wolfgang Bolyai’s _Tentamen_. Sending the book to Gauss, Wolfgang writes, after an interruption of eighteen years in his correspondence:— “My son is first lieutenant of Engineers and will soon be captain. He is a fine youth, a good violin player, a skilful fencer, and brave, but has had many duels, and is wild even for a soldier. Yet he is distinguished—light in darkness and darkness in light. He is an impassioned mathematician with extraordinary capacities.... He will think more of your judgment on his work than that of all Europe.” Wolfgang received no answer from Gauss to this letter, but sending a second copy of the book received the following reply:— “You have rejoiced me, my unforgotten friend, by your letters. I delayed answering the first because I wanted to wait for the arrival of the promised little book. “Now something about your son’s work. “If I begin with saying that ‘I ought not to praise it,’ you will be staggered for a moment. But I cannot say anything else. To praise it is to praise myself, for the path your son has broken in upon and the results to which he has been led are almost exactly the same as my own reflections, some of which date from thirty to thirty-five years ago. “In fact I am astonished to the uttermost. My intention was to let nothing be known in my lifetime about my own work, of which, for the rest, but little is committed to writing. Most people have but little perception of the problem, and I have found very few who took any interest in the views I expressed to them. To be able to do that one must first of all have had a real live feeling of what is wanting, and as to that most men are completely in the dark. “Still it was my intention to commit everything to writing in the course of time, so that at least it should not perish with me.