Cleve Moler was one of the big names in numerical methods, and participated in creation of canonical FORTRAN libraries for solving linear equations, and matrix algorithms more generally.

To teach this more conveniently to his students, he wrote the original version of MATrixLABoratory to allow interactive exploration of the library functions without having to compile FORTRAN code. The original version was about 2000 lines of code in FORTRAN.

Engineering students loved it so much that he decided to make a company around this product. His buddy expanded and rewrote the interpreter in C, for a PC, and the rest is history:

"In 1983 Jack Little suggested the creation of a commercial product based on MATLAB. I said I thought that was a good idea, but I didn't join him initially. The IBM PC had been introduced only two years earlier and was barely powerful enough to run something like MATLAB, but Little anticipated its evolution. He left his job, bought a Compaq PC clone at Sears, moved into the hills behind Stanford, and, with my encouragement, spent a year and a half creating a new and extended version of MATLAB written in C. A friend, Steve Bangert, joined the project and worked on the new MATLAB in his spare time."

User guide for the original version of MATLAB: https://blogs.mathworks.com/cleve/2018/02/05/the-historic-ma...

The source code of the very early (1982?) FORTRAN version of MATLAB: https://github.com/johnsonjh/matlab

The origins of the first PC version: https://blogs.mathworks.com/cleve/2018/03/09/matlab-history-...

Cleve Moler has died