# Mathematics is an obvious choice for Inger Sigstam

When she completed her doctorate at the start of the 1990s, she was the thirteenth woman who had defended a dissertation in mathematics in Sweden. But even though there have been few women in mathematics, Inger Sigstam has never doubted her choice.

“Mathematics was the most fun subject from the very beginning.  It was obvious to me that I wanted to learn mathematics. Since I had fabulous teachers and a father who is very much interested in mathematics, the result was that we talked about mathematics at home. I have never been afraid of mathematics in the way that some people sometimes are.”

After finishing at senior high school, Inger Sigstam began in the mathematics program as it then existed at Uppsala University and she soon became interested in mathematical logic, which later became her specialty.

“What is fun about mathematical logic is that it puts a framework around something which many mathematicians take for granted.  I discovered the same joy when I studied topology for the first time. I had already gotten several of the concepts in topology from earlier courses, but they didn't hang together. When I then took the first topology course I had an "aha" experience of about the same kind -- I could understand how it all hangs together.  It was like having a map drawn for me.”

Mathematics is of course built upon logical reasoning. But how can you depend upon something being true, that the system holds?

“It may not do that. We speak only about relative consistency. Thus we cannot prove that mathematics is consistent. There is a saying that it is not possible to prove within a system that the system is consistent. And then in some sense one simply has to rely upon it functioning. No one has thus far found a contradiction in relying upon the rules that we use. Certainly one sometimes encounters a contradiction, Russell's paradox for example, but then we have always succeeded in finding an error in reasoning and thus cleared up the whole thing. Regarding Russell's paradox, the concept quantity had been incorrectly defined. When it was correctly defined, the paradox did not appear.”

That gets me to thinking about the old question whether mathematics is a discovery or an invention. What do you think about that?

“I think it is a mixture of both.  If we take a theory, for example group theory, someone has invented it, that is, has thought through that certain axioms are appropriate. But when the group is fully invented, she then sits there in her room and tries to prove propositions and then I think that she is discovering.”

Since logic deals to a large extent with the foundations of mathematics, it is easy in a conversation with a logician to talk about questions relating to the philosophy of mathematics. But even if we touched briefly upon those questions, they do not constitute a large part of Inger Sigstam's daily life. Instead it is teaching which is her great passion.

“One of the most fun parts of my job is having contact with the students. For example, if I succeed in clarifying something which a student has gotten stuck on, it is very satisfying when it appears that the blockage has melted away.”

Inger Sigstam has taught a great many mathematics students and engineering students. One of the courses she teaches most is single variable calculus.

What is it like to teach an analysis course as a logician?

“It is really great fun. This is a fun course to teach since it all hangs together, it is a story that we tell. But it is also a great challenge, since quite a few academic programs include it. I think that I, as a logician, am perhaps more careful in explaining the logical steps in the proofs.”

How important is it, really, for an engineering student to learn the proofs?

“I think they derive benefit from it. If one needs to see why something is valid, it is easier to believe in the result and it is easier to remember the result if one has seen the proof. It is not necessary that one remembers the proof, but one must have followed along with the proof, followed on the pathway when I lead them through the woods. When I go through a proof on the blackboard the students can follow along and turn left and right as I turn. It is an exercise which they perform, and even if they don't learn the exercise by heart they have nonetheless walked it once with my help and they will be able to recognize it in the future.  That is the reason that I walk through theory. Mathematics is not just the result but also the way of getting to it.

Another part of Inger Sigstam's job which she very much appreciates is her assignment as the director of studies in the Department of Mathematics. In that assignment she obtains insight into how the Department and the university function, which she thinks is stimulating.

"It is fun to have contact with the teachers and the other people who work with education. It is exciting to be involved in the development of the educational programs and of the courses, but it can also be challenging when the different academic programs have different ideas about how the courses should look", Inger Sigstam says, and adds:

"Many teachers try new methods in their teaching, and I am convinced that as a result of their thinking about and being conscious of their teaching methods our courses are continually improved. The payoff for this is when I read the course evaluations of students who are very pleased, as I often have the pleasure of doing."

Alma Kirlic
10 January 2019

FACTS - INGER SIGSTAM

Where are you from?

I grew up in Herrängen in southern Stockholm. After senior high school at Norra Latin, I moved to Uppsala to begin studies in Mathematics. It was 1978 and the Department was newly-installed in Engelska parken [The English Park].

What do you like to do in your leisure time?

I like to do something together with my sons. Our family has a horse, so I spend a large part of my free time in the stables. It is a great way to relax, to get out and to think for a few hours about things completely different from my job.

What is your favorite kind of food?

I like to eat vegetarian food, but I also like fish very much.