Introduced the Taylor expansion - the main foundation of differential calculus - in words of
J. L. Lagrange
The Taylor Center
The software, the surrounding theory, and the community
The title of this site represents both a particular software, the theory surrounding it, and the community of interested researchers.
The software is an advanced ODE solver called
the Taylor Center. The solver is
an All-in-One GUI application for
Windows implementing the modern Taylor integration method (Automatic
Differentiation) in a multi-functional user friendly environment with
unique features such as graphing and real time animation of the
trajectories in 2D and 3D stereo, and with the highest number of
significant digits –
the Intel extended
10 byte format with 63-bit
mantissa (19 decimal digits).
The theory in the foundation of the method unifies the classical concept of elementary functions, Automatic Differentiation, the Taylor Method for integration of ODEs, analytic continuation, and the new type of the special points in holomorphic functions: The so called unremovable "removable" singularities. However there is an open question in this theory, the Conjecture remaining unsolved since 2004. Due to the nature of its claim, the Conjecture affects the ways of definition of general elementary functions and therefore the outline of the entire theory. Thus, as an organization, the Taylor Center seeks attention of the mathematical community in order to sooner close the gap in this otherwise comprehensive theory. This site therefore will provide a forum for discussing and advancing the solution of the Conjecture, as well as the updates and upgrades of the software.