=1105.= It was not alone the striving for universal culture which attracted the great masters of the Renaissance, such as Brunellesco, Leonardo de Vinci, Raphael, Michael Angelo and especially Albrecht Dürer, with irresistible power to the mathematical sciences. They were conscious that, with all the freedom of the individual phantasy, art is subject to necessary laws, and conversely, with all its rigor of logical structure, mathematics follows esthetic laws.--RUDIO, F. _Virchow-Holtzendorf: Sammlung gemeinverständliche wissenschaftliche Vorträge, Heft 142, p. 19._ =1106.= Surely the claim of mathematics to take a place among the liberal arts must now be admitted as fully made good. Whether we look at the advances made in modern geometry, in modern integral calculus, or in modern algebra, in each of these three a free handling of the material employed is now possible, and an almost unlimited scope is left to the regulated play of fancy. It seems to me that the whole of aesthetic (so far as at present revealed) may be regarded as a scheme having four centres, which may be treated as the four apices of a tetrahedron, namely Epic, Music, Plastic, and Mathematic. There will be found a _common_ plane to every three of these, _outside_ of which lies the fourth; and through every two may be drawn a common axis _opposite_ to the axis passing through the other two. So far is certain and demonstrable. I think it also possible that there is a centre of gravity to each set of three, and that the line joining each such centre with the outside apex will intersect in a common point--the centre of gravity of the whole body of aesthetic; but what that centre is or must be I have not had time to think out. --SYLVESTER, J. J. _Proof of the hitherto undemonstrated Fundamental Theorem of Invariants: Collected Mathematical Papers, Vol. 3, p. 123._ =1107.= It is with mathematics not otherwise than it is with music, painting or poetry. Anyone can become a lawyer, doctor or chemist, and as such may succeed well, provided he is clever and industrious, but not every one can become a painter, or a musician, or a mathematician: general cleverness and industry alone count here for nothing.--MOEBIUS, P. J. _Ueber die Anlage zur Mathematik (Leipzig, 1900), p. 5._ =1108.= The true mathematician is always a good deal of an artist, an architect, yes, of a poet. Beyond the real world, though perceptibly connected with it, mathematicians have intellectually created an ideal world, which they attempt to develop into the most perfect of all worlds, and which is being explored in every direction. None has the faintest conception of this world, except he who knows it.--PRINGSHEIM, A.