Wilhelm Winter
Professor of Theoretical Mathematics
On AI [a working mathematician's perspective]
The way mathematics is being developed has now
changed for good. We mathematicians find ourselves
at a new forefront, with the noble mission to help defending
humankind's intellectual independence.
We also have to find ways of putting technology to good use,
and to do so in ethically responsible ways. This includes
revising our manners to produce, communicate, and evaluate
mathematical results.
Most urgently, we have to find new ways of defining and
shaping careers, and take responsibility especially for those
at the beginning of their journeys.
I advocate for a human-centred approach to these tasks.
By this I mean that we should insist that mathematics
keeps being produced and written down in a such a way
that humans can understand it, and that we use human
attention as a lead currency to evaluate and appreciate
mathematical advancement. (Here, by `human attention'
I do not mean mere citation or click numbers, but the
willingness of individual people to engage and spend
their time and energy on something.)
So...
..should we still do mathematics?
Yes!
Mathematics is a universal science, and we humans
need it to understand the world around us. Which we
want to do, since we are curious.
..should we still train mathematicians?
Yes!
Mathematics remains both beautiful and difficult, and
if we as humans accept that we need it, we need people
specialising in understanding, explaining and applying it.
..but how many, and will they have jobs?
That's tricky, and impossible to predict. Mathematics is
in no better position than any other research field or industry
today. We might need fewer, or maybe more mathematicians
in the future, and surely their jobs will be very different from
what they are today. They will keep doing mathematics, though!
..should I use AI for my research?
Up to you. You can make conscious decisions on this, and they
can vary from project to project. Document what you are doing,
and include carefully written methodology sections in your work.
Also, make sure you understand what you are writing, write
it so that others can understand it, give proper credits, and
generally take author's responsibility.
..should I use AI to study mathematics?
Same - it's up to you. And again, make conscious decisions,
which may vary across projects and topics. AI can
be an excellent private tutor, but in the end you have to
and want to understand things yourself.
..will doing mathematics still be fun?
Yes, I think so. It will be different, and we need to get used to this, but it will still be fun.