# 2017 CHM Fellow Cleve Moler: Mozart of the Matrix

The Book of Nature is written in the language of Mathematics. Galileo Galilei

Though thousands of years old, mathematics underwent dramatic changes in the 20th century with the development of the electronic computer. New techniques and approaches to solving mathematical problems, as well as the re-imagining of older methods for use on computers, have been the underpinnings for the technical progress defining our age: atomic bombs, hearing aids, television, jet travel, bridge design, genetics, stock market prices, space travel — all underpinned by modern mathematics.

Across dozens of such scientific and technical fields, wherever we are measuring change over time it’s possible to arrange the resulting numerical quantities in matrix form. (A matrix is just a rectangular array of numbers or symbols arranged in rows and columns). It turns out that using matrices is an excellent way of solving all sorts of scientific and engineering problems.

This year CHM honors American mathematician and inventor of the MATLAB numerical computing environment, Cleve Moler. Moler created the original MATLAB program, short for “Matrix Laboratory,” while at the University of New Mexico as a quick calculator for his students doing basic matrix operations.

Today MATLAB is no longer a single program but a platform and an ecosystem used by millions of scientists and engineers around the world. Its maker, MathWorks, has 4,000 employees in two dozen cities and Moler serves as Founder and Chief Mathematician at the company.

Cleve B. Moler was born in Salt Lake City, Utah, in 1939 and was a precocious student.

I was always one of the geeks. So there were a handful of us that were interested in technical pursuits. We all ended up leaving Utah to go away to school to Harvard or Stanford or Caltech. I was in the statewide math contest in Utah, and I came in second in the contest. In junior high school, a teacher by the name of Albert Persh had me in his class and he gave me a book and sent me down to the library to study on my own. And it was a textbook for a quick course in college mathematics that was used in the Air Force in the Second World War. So I was doing college mathematics on my own, thanks to Mr. Persh, when I was in junior high school even.

When it came time to attend university, Moler chose Caltech over MIT (he was accepted at both) due its small size and mathematics because it offered the most electives.

Caltech is a tiny place. They only admit 180 freshmen every year. So no, most people don’t realize that. Good weather. Southern California versus winters in Boston. It was an easy decision.

Due to his success in John Todd’s courses in numerical analsysis, he chose that area in which to specliize and Moler began to write simple programs for solving his homework on Caltech’s Burroughs 205 Datatron computer, in 1959.

Upon graduating with a BA in mathematics in 1961, went to Stanford University to study under George Forsythe, a legendary figure there and founder of its computer science department. Forsythe and Todd had worked together earlier at UCLA’s Institute for Numerical Analysis at which the groundbreaking SWAC computer was installed. So Moler was studying with two of the leading figures in the field.

At Stanford, Moler wrote his 1965 dissertation on “Finite difference methods for the eigenvalues of Laplace’s operator” and so began his lifelong interest in matrices. After a postdoc year at the ETH in Zurich, Moler joined the faculty of mathematics at the University of Michigan in 1966. This began a 20-year academic career at Michigan, at the University of New Mexico, and with a couple of visits back to Stanford.

In the 1970s, Moler was a co-author of LINPACK and EISPACK, Fortran subroutine libraries for matrix computation. He wanted students to be able to access these packages without writing Fortran programs, so he wrote the first version of MATLAB as a simple, interactive matrix calculator. The system, both the mathematics and the array syntax, turned out to be useful in other fields of science and engineering that he had not anticipated. Moler made MATLAB freely available.

In 1984, with Moler’s permission Jack Little and Stev Bangert re-wrote and enhanced MATLAB, making it available on the new IBM PC, and Little and Moler founded MathWorks to commercialize the result.

In 1983, I think it was, there was a conference in Boulder, Colorado, organized by Lloyd Fosdick on mathematical software for small machines. The PC had just come out and people were trying to use the PC for technical computing, it was hard because the PC was small and slow, and didn’t have much memory. I went to Boulder with a couple of my graduate students from New Mexico. We hauled a couple of IBM PC/XT’s with us to show off MATLAB at this conference. John Little came from California to the conference specifically to see me and to ask me about commercializing MATLAB. He appreciated the possibility of the PC as a serious technical tool, he wanted to start a company based on MATLAB. [p.71, Haigh]

Little has remained with the company as CEO all this time, a rare occurrence, and Mathworks is now celebrating its 33rd anniversary. The dazzling variety of applications technical community has created using MATLAB – from space craft dynamics to derivatives trading — has made it a kind of universal moldeinng and calculation tool ideally suited to science and engineering problems. To paraphrase Galileo, today “The Book of Nature is written in MATLAB.”

## Further reading

- Haigh, T., Interview with Cleve Moler, SIAM, CHM 102746804