Paul Abbott has used Mathematica extensively since 1988. His research is in the areas of wavelets, quantum physics and special functions, and he has general interests in problems in computational and mathematical physics. All of his publications have used Mathematica in some way. From 1989 to 1991 he worked for Wolfram Research as a member of the Applications department. He was a contributing editor of The Mathematica Journal from 1990 to 2005 and has been a consultant to Wolfram Research since 1997. With Chikara Miyaji he coauthored the book MathLink: Network Programming with Mathematica. In 2002 he was a winner in the SIAM 100-Dollar, 100-Digit Challenge, and in 2015 he received a Wolfram Innovator Award.
Paul was a faculty member of the School of Physics at The University of Western Australia (UWA) from 1992 to 2016. He taught courses on a wide range of topics, including electromagnetism, relativity, data analysis, group theory, special functions and wavelets, and received a number of teaching awards, including a Computational Science Award in 1995 and an Australian University Teaching Award in 2016. Abbott has lectured on Mathematica in the United States, Japan, Singapore, Thailand, Malaysia, Taiwan and India and has given Mathematica courses at several Australian universities. His courses have been attended by professionals and students from a wide range of backgrounds, including people from government departments and financial institutions, scientists, engineers, academics and medical researchers.
- Visualizing atomic orbitals
- Ground State Energy of Helium via Perturbation
- The Routh-Hurwitz stability criterion
- Orthogonal polynomials computed via matrix determinants
- A curious mass ratio
- Unique father problem: Conway conjecture settled
- Area of the Mandelbrot set
- The rotational dynamics of space station Mir
- Matrix quantum mechanics
- Self-verifying papers as computational notebooks, e.g. Eckart potential
- A "Closed-Form" Solution to the Geometric Goat Problem
- Inscribed Square Problem