In a recent historical overview, Cristian S. Calude, Elena Calude, and Solomon Marcus identify eight stages in the development of the concept of a mathematical proof in support of an ambitious conjecture: we can express classical mathematical concepts adequately only in a mathematical language...

Let denote an algebraically closed eld with characteristic 0. Let denote a vector space over with nite positive dimension and let denote a tridiagonal pair on . We make an assumption about this pair. Let denote a nonzero scalar in which is not arootofunity. Weassume and satisfy the -Serre...

Whatever other beliefs there may remain for considering Cantor's diagonal argument as mathematically legitimate, there are three that, prima facie, lend it an illusory legitimacy; they need to be explicitly discounted appropriately. The first, Cantor's diagonal argument defines a non-countable...

This work presents the results of assessing the accuracy of statistical routines as implemented in the IDL 5.6 platform. This is “a complete computing environment for the interactive analysis and visualization of data. IDL integrates a powerful, array-oriented language with numerous...

By the topological imitation theory, we construct, from a given colored link, a new colored link with the same Dehn surgery manifold. In particular, we construct a link with a distinguished coloring whose Dehn surgery manifold is a given closed connected oriented 3-manifold except the 3-sphere....

We give precise definitions of primitive and formal mathematical objects, and show: there is an elementary, recursive, number-theoretic relation that is not a formal mathematical object in Gödel's formal system P, since it is not the standard interpretation of any of its representations in P;...