Mathematics is the art of seeing the same thing in more than one way. A complex number is a field element and also a vector. A matrix is a ring element and also a linear function. A topological space, if reasonably well-behaved, can also be thought of as a ring of continuous functions, and so on. One of the skills we learn early on is when to change our glasses and look at what we’re studying from another viewpoint.
In Canadian universities, the faculty members are salaried professionals. For much of the week, we write our own schedules. We have a satisfyingly large amount of control over our research. If we need to work in the evening or on a weekend, we do it because it’s part of our job, not because we get paid overtime for doing it. But our positions, too, are ambiguous. Most of us are unionized – and, every few years, if contract negotiations don’t go well, we may find ourselves on strike.
My union’s facing that situation now: we haven’t reached the last stage of negotiation yet, but a strike could be only weeks away as I write – and possibly taking place as you read this. If that happens, suddenly our regular lecturing schedules will be interrupted. Instead of going the extra mile to make sure that our students keep up with the course, we’ll be in the uncomfortable position of not being able to help them. Instead of delivering carefully-crafted lectures, we’ll be walking around the perimeter of the university campus, expressing ourselves via messages of a few words, printed on sheets of corrugated plastic – a surreal change.
But, when you look at it from one angle, we _are_ just employees, in an organization that could do other things more easily if it paid us less. This adversarial system is how society establishes the value of our services: we reach our collective agreements in the same way that miners or steelworkers do because of the aspects of our employment that we have in common. It sometimes seems like an odd way to do things, but it’s the system we’ve got.
In some countries faculty are civil servants, with salaries set by legislation. In other countries everybody has to negotiate their own salary individually, and those who don’t push hard enough fall behind. Our system has its flaws, but so, I think, do the others. Whatever the system, we have to make it work – even if it means walking the picket line.