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.
“I am deeply surprised that this task can be spared me, and I am most of all pleased in this that it is the son of my old friend who has in so remarkable a manner preceded me.”
The impression which we receive from Gauss’s inexplicable silence towards his old friend is swept away by this letter. Hence we breathe the clear air of the mountain tops. Gauss would not have failed to perceive the vast significance of his thoughts, sure to be all the greater in their effect on future ages from the want of comprehension of the present. Yet there is not a word or a sign in his writing to claim the thought for himself. He published no single line on the subject. By the measure of what he thus silently relinquishes, by such a measure of a world-transforming thought, we can appreciate his greatness.
It is a long step from Gauss’s serenity to the disturbed and passionate life of Johann Bolyai—he and Galois, the two most interesting figures in the history of mathematics. For Bolyai, the wild soldier, the duellist, fell at odds with the world. It is related of him that he was challenged by thirteen officers of his garrison, a thing not unlikely to happen considering how differently he thought from every one else. He fought them all in succession—making it his only condition that he should be allowed to play on his violin for an interval between meeting each opponent. He disarmed or wounded all his antagonists. It can be easily imagined that a temperament such as his was one not congenial to his military superiors. He was retired in 1833.
His epoch-making discovery awoke no attention. He seems to have conceived the idea that his father had betrayed him in some inexplicable way by his communications with Gauss, and he challenged the excellent Wolfgang to a duel. He passed his life in poverty, many a time, says his biographer, seeking to snatch himself from dissipation and apply himself again to mathematics. But his efforts had no result. He died January 27th, 1860, fallen out with the world and with himself.