Janos Bolyai

Janos Bolyai was a Hungarian army officer and the son of respected mathematician. From an early age, Janos was exposed to the world of mathematics. Janos's father, Wolfgang, had studied with Gauss at Gottingen, and their sporadic correspondence lasted a lifetime. In fact, in their correspondence, Gauss had pointed out the fallay in the elder Bolyai's 'proof' of the Parallel Postulate.

In 1817, Janos entered the Imperial Engineering Academy in Vienna at the age of fifteen. After completing his studies in 1823, he embarked upon a military career. An expert fencer with numerous successful duels to his credit, Bolyai was also accomplished violinist.



The early teaching of his father prompted Bolyai to continue his study of mathematics. However, when Janos informed his father of his interest in the study of parallels, the elder Bolyai wrote: "Do not waste hour's time on that problem. It does not lead to any result; instead it will come to poison all your life." Ignoring his father's decree, the younger Bolyai pursued he elusive Parallel Postulate.

After several failed attempts to prove the Parallel Postulate, Bolyai, too, proceeded down the path of denying Euclid's assumption of the existence of a unique parallel. In a manner not unlike that of Gauss, even though he was unaware of Gauss's work. Bolyai assumed that more than one parallel existed through a point not on a line. He developed several theorems in this new, consistent geometry. He was so excited over his discovery that he wrote, "Out of nothing I have created a strange new world."

Hastening to publish his work, the younger Bolyai published his theory as a 24-page appendix to the elder Bolyai's two volume Tentamen Juventutem Studiosam in Elementa Matheseos Purae (An Attempt to Introduce Studious Youth to the Elements of Pure Mathematics). Although the book is dated 1829, it was actually printed 1832.

When Wolfgang Bolyai sent a copy to his old friend Carl Gauss, the reply than heartening to Janos, Gauss responded, "If I begin by saying that I dare not praise this work, you will of course be surprised for a moment; but I cannot do otherwise. To praise it would amount to praising my self. For the entire content of the work, the approach which your son has taken, and the result to which he is led, coincide almost exactly with my own meditation which have occupied my mind for the past thirty or thirty-five years. It was my plan to put it all down on a paper eventually, so that at least it would not perish with me. So I am greatly surprised to be spared this effort, and i am overjoyed that it happens to be the son of my old friend who outstrips me in such remarkable way."

Not seeing the true compliment that the great Gauss had bestowed upon him, Bolyai feared that his work was being stolen. His feelings were compounded by the total lack of interest on the part of other mathematicians, and deep periods of depression set in. Janos Bolyai never published again.

---------------------------------------------------------
wiki : http://en.wikipedia.org/wiki/Janos_Bolyai