I believe symbolic algebra applications to be one of the greatest technological achievements of humanity.

My interest in symbolic algebra started during my PhD from 1989-1992 when I became interested in automating the tedious task of calculating symbolic differences for implicit gasdynamics solvers. I successfully used the REDUCE symbolic algebra system to generate FORTRAN code representing implicit integration methods, and used it to model supernova shock waves. Since then symbolic algebra has played a role in nearly all of my scientific activities, whether using the Maple, Mathematica, Mathcad, or Matlab symbolic application (thankfully the REDUCE command-line days are long gone).

I'm a symbolic evangelist: I introduce others to the incredible possiblities of symbolic algebra at every opportunity.

Example: a symbolic equation and its numerical evaluation (in the Maple symbolic algebra application). From work I performed in Maple as a research physicist at the DESY particle accelerator institute.

My applications of symbolic algebra have included:

• development of a symbolic algebra system for generating compilable code for implementing implicit 3D time-dependent PDE equation solvers. The system has been tested on an advanced gasdynamics solver using adaptive gridding.
• symbolic worksheets for modelling dust disruptions in electron particle accelerators
  (example: MapleV.3: symbolic analysis of trapped dust particles in HERA-e (.pdf))
• symbolic data analysis and visualisation of multi-dimensional datasets.
• animations for science, illustration and fun - driven by symbolic engines

For more examples of my applications of symbolic algebra please visit my Maple zone.