Gilbert Strang Reflects on His Rich Academic Career and Lifelong Friendship with Linear Algebra and SIAM

By Lina Sorg

Longtime SIAM member Gilbert (Gil) Strang recently retired from his position as a professor of mathematics at the Massachusetts Institute of Technology (MIT), delivering his final lecture to a standing ovation on May 15, 2023. Strang—who spent a collective 66 years at MIT as a student, instructor, and faculty member—is especially well-known within the applied mathematics community for his popular undergraduate linear algebra course; since 2001, he has publicly hosted videos of each lecture on MIT’s OpenCourseWare platform. His lectures have been viewed more than 20 million times and are renowned among mathematicians and non-mathematicians alike for their engaging and clear delivery.

In addition to his robust career in academia, Strang has written 20 books — including six editions of the famed Introduction to Linear Algebra. Since 1986, he has self-published all of these texts through Wellesley-Cambridge Press. Strang has also remained an active member of SIAM over the years. He served as Vice President for Education from 1991 to 1996, was SIAM President in 1999 and 2000, and chaired the SIAM Committee on Science Policy from 2001 to 2002. Strang maintains a strong connection to SIAM’s Publications Department and has served as an editor for the SIAM Journal on Numerical Analysis, SIAM Journal on Matrix Analysis and Applications, and SIAM Review; much of his published research has appeared in these and other SIAM journals, as well as SIAM News. In 2003, Strang received the SIAM Prize for Distinguished Service to the Profession. 

Despite his recent retirement, the 88-year-old Strang shows no signs of slowing down. During a recent conversation with SIAM News, he discussed his lifelong career at MIT, passion for the subject of linear algebra, dedication to both teaching and writing, continued relationship with SIAM, and future plans for his next stage of life.

SIAM News: You were at MIT for 66 years as both a student and faculty member. What kept you there for so long? 

Gil Strang: I attended MIT as an undergraduate, was a Rhodes Scholar at the University of Oxford for two years, and then went to the University of California, Los Angeles for my Ph.D. After I graduated, MIT offered me a job as an instructor. I thought I might work in industry, but when the job offer came I naturally said “yes.” That was more than 60 years ago.

The Department of Mathematics at MIT is great. The students are good, the faculty is fun to work with, and we [my wife and I] like the Boston area — everything fit. It’s nice when that happens.

SN: What do you enjoy most about teaching and working with students?

GS: I enjoy figuring out how to present something clearly. My thoughts often go to the basic linear algebra course: how to start it and how to make it work. Everything in that linear algebra course is known, but presenting the ideas clearly is the challenge. So that was really an adventure. The students respond because they understand it, they know that it’s useful, and they’re ready to learn. They are good students to teach and much of my writing resulted from that course, which connected me with departments all over the country. It has been such a pleasure.

SN: You were one of the first faculty members to upload your lectures to MIT’s OpenCourseWare platform, a freely accessible online collection of MIT course content. How did that come about?

GS: It was a case of good luck and perfect timing. I had been thinking about making a recording of my classes for a while, and I actually recorded my linear algebra class a few months before I even heard of OpenCourseWare. When [then-MIT President Charles Vest] wanted courses, I already had material. The whole idea of MIT making courses available for public viewing was happening at the same time that I was videotaping my class. Most of the courses at MIT are not videotaped (it would be too expensive), but the larger classes do have a video component. My recordings were ready to go, so the timing was a fortunate accident. I get a lot of really nice messages from viewers. 

SN: What are the benefits of making this type of content freely accessible to a broader audience?

GS: Linear algebra is a beautiful subject, and by good luck it has also become necessary and super important. A lot of people now have a better idea of how linear algebra is used, why it’s significant, and how it develops. Linear algebra has always been a topic in pure math, but it needed applications as well. One such application is called least squares—everybody’s doing that nowadays—and there are many other applications, of course. It’s just the right subject at the right time.

It’s fun to think about where linear algebra is now; it has changed so much from when I took it as a sophomore. It is much more interesting and useful, and linear algebra classes are growing at all universities.

SN: Tell us about some of the current application areas of linear algebra.

GS: Well, certainly deep learning. Deep learning is an amazing system that just gradually evolved. It wasn’t a success in the beginning; it required new ideas and a lot of it was experimental. For each new set of data, you need to construct a matrix that weights the data. Constructing that matrix is the biggest consumer of computer time. In deep learning, you have to judge the importance of the data in order to weight it. It’s a mixture of optimizing matrix weights and designing the architecture of the whole system. Given the many features in the data, how do you fit those points in an efficient way? How do you pass a surface through the known data in a stable manner? This was previously an open problem, but eventually a nonlinear way was found.

Computer science departments usually handle deep learning and artificial intelligence (AI), but I wanted math to have a role. So I started a course at MIT called Matrix Methods in Data Analysis, Signal Processing, and Machine Learning and wrote Linear Algebra and Learning From Data, which published in 2019. The math of deep learning is really interesting and has a lot of open problems. It’s been fun and even appears in the sixth edition of Introduction to Linear Algebra, which published earlier this year.

SN: How do you keep new versions of Introduction to Linear Algebra unique and up to date? 

GS: Each new edition is a major job because I don’t just make tiny changes. The books sort of form themselves in my mind. As I begin to think about what the chapters should be, I get ideas about topics and phrasing. I can fortunately reuse some of the old exercises each time, since creating new problem sets for every section of Introduction to Linear Algebra would be a big project. I also have to think about which topics are the right ones at any given moment in time. In the most recent edition, I altered the introduction and changed the ending to be about deep learning and AI. 

SN: You self-publish all of your books though Wellesley-Cambridge Press. What inspired you to found your own publishing company? 

GS: I founded Wellesley-Cambridge Press in 1986, so that’s 37 years ago. I just thought I would have the adventure. I had already written two books, but my most active years of book writing came after Wellesley-Cambridge’s establishment. The easy thing is to send the manuscript off to a publisher and let them handle it, but I thought I would just stay with my books and see them through: choose the covers, select the paper, organize the printing, and so on. That really is my life’s adventure and I have enjoyed it all. People can contact me about everything, and they certainly do.

I still ask friends from SIAM for help with the covers, and SIAM keeps copies of all the books at its headquarters in Philadelphia. I’m in touch with SIAM so much — it really is a great society. 

SN: When did you first become involved with SIAM? 

GS: The first thing I did for SIAM was serve as Vice President for Education. Out of the blue, Ed Block asked me to take on that role and invited me to come to Philadelphia to talk about it. He met me at the airport, along with then-SIAM President Bob O’Malley, which was memorable. Ed was an unusual person: super active, always willing to do things, and exactly what SIAM needed. He truly was the founder of SIAM. And Jim Crowley was the best possible executive director for so many years.

SN: A few years later, you were elected SIAM President. What do you remember most from your tenure?

GS: Oh, I recall lots of things. It’s all been rewarding and was just fun to do with good people. My presidency was during a very active period in Washington, D.C., and we tried to boost funding for applied math. Mathematics had fallen behind, but Philippe Tondeur—the new director of the National Science Foundation’s Division of Mathematical Sciences at the time—came in with lots of energy. It was an exciting time to see the budget grow and watch mathematics take its rightful place.

The Annual Meetings were also particularly memorable. I was happy to be part of starting the SIAM Activity Group on Computational Science and Engineering — I remember initial conversations about that at the Annual Meeting in Toronto, Canada, in 1998. Some people felt that SIAM was already a society for computational science and therefore didn’t need an activity group on the topic. But I’m glad that we created one because it means that we have a big meeting at different times from the Annual Meeting.

SN: What makes SIAM so important to the research community? 

GS: SIAM is the right society for people who use mathematics in all kinds of ways, and I hope that we can keep making more connections with deep learning, AI, and statistics. Data science is just growing and growing, and it’s good that SIAM now has an activity group and a journal on this subject, and that it frequently appears in SIAM News. Interest in data science and statistics has now—quite correctly—moved front and center, which is a big change and a good change. 

As other societies like the American Statistical Association continue to grow, we’ll want to stay connected with them. We also need to focus on what students are learning and the jobs that they’re getting. 

SN: Do you have any specific plans for retirement? 

GS: I’ve been so busy that I don’t have any set plans, but I’m hoping to travel more now that COVID is ending. I don’t get to the theater as much as I should, so maybe I will now. I go for walks to the library and do plenty of reading, and of course there’s lots of email. I still receive and reply to many messages about my books and videos. I might even end up writing some more, who knows?

I’ll tell you a possibly crazy idea. I have been wondering whether high school algebra could use some new thinking. I’ll try to find out and make some connections with local teachers to see if there’s anything I can contribute. I might just call up the local high school and ask, but I haven’t done so yet. 

Of course, I have Wellesley-Cambridge Press and the textbooks, and I stay connected with distribution. And SIAM will still be a big part of everything! I have had a really happy friendship with SIAM for all of this time and I look forward to continuing it. I feel quite fortunate about everything; I’m very lucky.

Lina Sorg is the managing editor of SIAM News.