T he honoyr to be the creator pf the non – Euclidean geometry was belonging for a long time sometimes to the German Gauss, sometimes to the Russian (of the Polish origin) Lobacevski. The careful scrutinizing of the documents and their uinbiased interpretation gives an eloquent demonstration that author of this geometry, which has revolutionized the Mathematics and has masterly inmfluenced the Physics and zhe Astronomy, is the genius Ianoş Bolyai (1802-1860), a Romanian from Transilvania. To our consangvin belongs, as well, other epochal discoveries, for example, the Theory of Quaternions, anticipating with almost 20 years the great Irish mathematician W. Hamilton (1805-1865) to whom was initially atributed this paternity.