Humanum est

But Mihály Babits – and after him Wang Wei – was not the only one who, enraptured by the “new world created out of nothing” by János Bolyai, wrote a hymn to the author of the Appendix. The same was done by the philosopher Branislav Petronijević, the Serbian translator of the Appendix, about whom Bertrand Russell wrote in volume 11 of his collected works:

A man who impressed me, not so much by his ability as by his resolute absorption in philosophy even under the most arduous circumstances, was the only Yugoslav philosopher of our time, whose name was Branislav Petroniević. I met him only once, in the year 1917. The only language we both knew was German and so we had to use it, although it caused people in the streets to look at us with suspicion. The Serbs had recently carried out their heroic retreat before the German invaders, and I was anxious to get a first-hand account of this retreat from him, but he only wanted to expound his doctrine that the number of points in space is finite and can be estimated by considerations derived from the theory of numbers. The consequence of this difference in our interests was a somewhat curious conversation. I said, “Were you in the great retreat?” and he replied, “Yes, but you see the way to calculate the number of points in space is…” I said, “Were you on foot?” and he said, “Yes, you see the number must be a prime.” I said, “Did you not try to get a horse?” and he said, “I started on a horse, but I fell off, and it should not be difficult to find out what prime.” In spite of all my efforts, I could get nothing further from him about anything so trivial as the Great War. I admired his capacity for intellectual detachment from the accidents of his corporeal existence, in which I felt that few ancient Stoics could have rivalled him. After the First War he was employed by the Yugoslav Government to bring out a magnificent edition of the eighteenth-century Yugoslav philosopher Boscovic, but what happened to him after that I do not know. (Some philosophical contacts, 1955)

A copy of Petronijević’s 1928 translation of the Appendix was found by us in the library of the Hungarian Academy of Sciences. This copy was dedicated to the Academy by the translator himself, who also transcribed the most important titlepage informations from Cyrillic to French. His translation – in a way quite unusual in a book on mathematics – starts with a poem of the translator dedicated to the author of the book. Below we include with the English translation also the Latinized transcription of the poem for an easier reading.

Veliko ime, a mali spis, Ostavio si samo Apendiks. Genije mladi, bujan si bio, I Gausa si njime nadmašio. Gaus te istina hvaliti stade, Ali ti priznanje ne odade. Malodušnost je njega voditi spala, I na pismima ga zadržala. Okolina te ceniti nic znala, Ona te ružila, ismevala. Grob ti se zadugo nije znao, Ni znak ga nije obeležav'o. I rođenjem si nesrećan bio, U malom si se narodu pojavio. Do tebe Mađar mali je bio, Velikim ti si ga učinio.

A great name and a small writing: you’ve only left behind the Appendix. You were a young and great genius who surpassed even Gauss himself. Gauss, true, praised you but he gave you no recognition. He was led by jealousy which kept him back in his letters. Your environment could not appreciate you, they despised and did not acknowledge you. Your tomb was long unknown to all, and nobody adorned it with a sign. Your birth was also unlucky: you were born to a small nation. Hungary was small to you: it was you who made it great.

The poem culminates in the ancient philosophical topos of “not the place makes the man, but man makes the place”, which probably was of some consolation also to the Serbian philosopher. It is further illustrated by the stories of Gauss’s jealousy and the unmarked tomb of Bolyai.

The story of the unmarked tomb is true. When János Bolyai died in 1860, he was accompanied to the cemetery by only four people, including his servant Julianna Szőcs. In 1894 it was her to show the tomb, which by that time became unrecognizable, to architect Ferenc Schmidt who had rediscovered the work of Bolyai and made it an integral part of international scholarship. This was followed in 1911 by the solemn reburial of the two Bolyais, father and son, which was also remembered by two of the greatest poets of the age, Endre Ady and Mihály Babits whose poem was just translated by us.

But what about this story with Gauss?

A rare portrait of Gauss on the terrace of the Göttingen observatory, with the “heliometer” invented by him. Lithography of Eduard Ritmüller, after 1814 (the year when this heliometer was produced)

Farkas Bolyai – the father of János – and Carl Friedrich Gauss were fellow students and very close friends in Göttingen. After Farkas returned to Transylvania in 1799, they continued to change letters, but by the time these got less frequent. Farkas wrote to Gauss for the last time in 1816. In a warm and intimate tone he asked Gauss, at that time already “the prince of mathematicians”, to accept his son János as a pupil, and to even accomodate him in his own house (which was not unusual in the period). However, he was indiscreet enough – or perhaps he overestimated the strength of their friendship of twenty years ago – to finish his letter like this:

In view of this plan, please tell me frankly whether: 1. you have a daughter who could be dangerous to him (and vice versa), for it is natural that young people have to fight this battle, and we can thank to our reason only to a minor extent if we do not wake from our Elysian dreams as an invalid hit by a cannon ball. – 2. Are you healthy, and not poor? Satisfied, and not grumbling? And mainly: is your wife an exception among women? Is she not more inconstant than the weather-cock? Not more incalculable than the changes of the barometer?

Gauss never replied to this letter.

Sixteen years later, after the publication of the Appendix in 1832, Farkas Bolyai wrote once again to Gauss, sending him the work of his son. To this letter Gauss replied immediately:

And now something more on the work of your son. If I began by saying that I must not praise it, you will be certainly shocked at the first moment. But I cannot do differently, for if I praise him, I praise myself. In fact, the whole content of the work, the way your son is following and the results he got are almost completely identical to my considerations in the last 30-35 years.

Nevertheless, in a letter written some days earlier to Gerling, professor of mathematics at the Marburg university, Gauss did not keep himself back:

In these days I received from Hungary a small opus on non-Euclidean geometry. I have found in it all my ideas and results exposed with great elegance… I regard this young geometer, Bolyai, a first-class genius.

However, to János Bolyai only got through so much that Gauss – although he had not published anything on the subject – vindicated to himself the priority of this discovery and that he did not want to support with his authority the international recognition of the Appendix. The refusal ruined him. Four weeks after Gauss’ letter he asked permission for three years of absence for the purpose of scholarly research, but he never reached the level of the Appendix any more. He died as a bitter, ill-tempered, misanthropic odd person.

Today we already know – as Gauss also recognized it in his letter to Gerling – that Gauss’ hypotheses were far less developed than the derivations of the Appendix, and that Bolyai in fact created a “new world” in geometry. However, this fact has still not really spread in the educated public opinion. Daniel Kehlmann in the fictive biography of Gauss, the Measuring the world of 2005 about which we have recently written, gives this meditation into the mouth of Gauss:

Just recently a Russian mathematician has sent him a treatise in which he exposed the hypothesis that the Euclidean geometry is not the true one, and that parallels do meet. Since when he replied that these ideas were not new to him, he has been considered a swaggerer in Russia. The idea that someone else could publish what he had known since a long time, caused him an unusual stabbing pain.

The Russian mathematician is most probably Nikolai Lobachevsky, who obtained similar results to Bolyai’s in more or less the same period. However, Gauss never corresponded with Lobachevsky. Kehlmann here has confused this latter with Bolyai. The Measuring the world, which in 2006 was the second best selling book of the world and will obviously determine the image of Gauss for several years, covers again with the mist of forgetfulness the name of Bolyai. The poem of Petronijević is now more timely than ever.

Marginal scribbles of János Bolyai on the draft of his application for absence submitted to Archduke Johann in 1832