Gauss was not the son of a mathematician; Handel’s father was a surgeon, of whose musical powers nothing is known; Titian was the son and also the nephew of a lawyer, while he and his brother, Francesco Vecellio, were the first painters in a family which produced a succession of seven other artists with diminishing talents. These facts do not, however, prove that the condition of the nerve-tracts and centres of the brain, which determine the specific talent, appeared for the first time in these men: the appropriate condition surely existed previously in their parents, although it did not achieve expression. They prove, as it seems to me, that a high degree of endowment in a special direction, which we call talent, cannot have arisen from the experience of previous generations, that is, by the exercise of the brain in the same specific direction.--WEISMANN, AUGUST. _Essays upon Heredity [A. E. Shipley], (Oxford, 1891), Vol. 1, p. 97._ CHAPTER XII MATHEMATICS AS A LANGUAGE =1201.= The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world wide states that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and to write. --WELLS, H. G. _Mankind in the Making (London, 1904), pp. 191-192._ =1202.= Mathematical language is not only the simplest and most easily understood of any, but the shortest also.--BROUGHAM, H. L. _Works (Edinburgh, 1872), Vol. 7, p. 317._ =1203.= Mathematics is the science of definiteness, the necessary vocabulary of those who know.--WHITE, W. F. _A Scrap-book of Elementary Mathematics (Chicago, 1908), p. 7._ =1204.= Mathematics, too, is a language, and as concerns its structure and content it is the most perfect language which exists, superior to any vernacular; indeed, since it is understood by every people, mathematics may be called the language of languages. Through it, as it were, nature herself speaks; through it the Creator of the world has spoken, and through it the Preserver of the world continues to speak. --DILLMANN, C.