So who is the one with no future now, professor?
I am not going to be that person. I am going to defend mathematicians’ work, because I think there is a great deal of hype, falsehood, and fear surrounding artificial intelligence. I acknowledge that it is an efficient tool for many things, but I still do not see the impressive capacity for intellection that people talk about so much.
It seems to me that we are confusing certain operations of intelligence with intelligence itself. Relating concepts or developing a line of reasoning are operations we associate with it, but performing them does not settle what the system performing them understands. That confusion leads us to declare entire careers finished based on what we see a tool can do.
Something happened to me recently that made me think about this. I am legally blind, although I retain a small percentage of sight in one eye. It is not much help, but I can still use it for some things. One of them is identifying areas on a simple sketch map.
I cannot consult a map full of information because my vision cannot process it. A simple sketch map, like the one you receive to get to a cousin’s wedding in some small town, can be useful instead. When I go to a university, I sometimes get one and invert its colors for more contrast. I already use artificial intelligence for that part.
This time I thought of asking for something more. Along with inverting the colors, I asked it to mark the main entrance with a red X, the route to a classroom with a yellow line, and the route to the restroom with a blue line. Those are the places I most need to identify when I arrive at a university.
The first result took me to the classroom through buildings. All that was missing was a lesson in walking through walls.
I tried again and kept changing the instructions. I went through about thirty prompts before finally getting a result that seemed good. Then I noticed it had moved the main entrance. The one I had originally marked was now somewhere else on the sketch.
In terms of reliability, that leaves me with a problem. I need to know to what extent I am justified in accepting that result and using it to find my way. It does not help much that the route looks right if it starts in the wrong place.
Because I tutor children, I asked one of them to do the same activity. I gave him the sketch and two colors to mark the routes. I only had to give him one instruction. I did not need a whole prompt-engineering process for him to understand what I was asking.
He is the same child I am teaching to do operations on the number line.
Artificial intelligence can solve mathematical problems that this child is still far from understanding, yet he could carry out an activity with which the tool had difficulty even after many instructions. That makes me think that we are gathering very different capacities under one word and assuming that extraordinary performance in one means the same thing in all the others.
Much of the advantage I see in these systems lies in their ability to execute enormous numbers of operations and identify patterns at a speed we do not possess. If a person could perform thousands of operations per second, they too could try more paths, find errors faster, and recognize regularities in their attempts. That difference in capacity matters, but it does not seem enough to me to declare the work of a scientist or mathematician over.
I am not a mathematician, though I would have loved to be one. I think one of the most enjoyable parts must be sitting before a problem and looking for creative ways to solve it—spending a long time trying to understand it, like when you have a riddle whose solution you cannot find.
I understand that this part of the work may change if an artificial intelligence explores far more paths in less time. But the understanding of what has been obtained, and its application to other problems, remain.
When I began learning data analysis, one of the first things we were told was that we had to know the business. You could learn extraction, transformation, and loading processes, conduct exploratory analysis, and apply statistics, probability, and programming. If you did not know the business, its interests, and its goals, all that work could end up serving little purpose.
You can analyze data correctly without understanding what you need to obtain from it. I think the same of a mathematical operation. Understanding its nature and the conditions in which it works makes it possible to find applications beyond the case you were solving.
That is where I think there will continue to be work for mathematicians: in understanding the operations they perform and finding ways to use them.
The child whose math teacher saw no future for him used to ask what all of that would be good for. I think that question now also belongs to mathematicians at major universities. Having a tool that makes obtaining results easier makes it even more important to know what to do with them.
I think about this often because of the problems I face as a blind person. An obstacle-identification system in a car might contain useful elements to help me move through the street. When I raise that possibility with an artificial intelligence, I usually get answers such as “yes, but” or “yes, although we must consider.”
I understand there are limitations. That is precisely why I am looking for ways to adapt it. I am interested in identifying which elements could be transferred from one application to another and what would need to be solved for them to work.
Sometimes I end up arguing with the tool so that it will help me find those relationships. I have to add context, insist on certain possibilities, and explain why a limitation does not necessarily cancel the idea. On many occasions I end up solving the part of the problem for which I had begun by consulting it.
That leads me to ask who should be credited with the idea and the process of intellection. Artificial intelligence intervened, but I was the one who identified a need and tried to transfer a solution from one area to another.
Here a discussion that interests me, by Adams and Aizawa, enters: the difference between a causal and a constitutive relationship. There is also Clark’s proposal of the extended mind. Using a notebook to support my memory raises questions about the role that tool plays in my cognitive activity. With artificial intelligence, those questions become more complicated.
From my perspective, in the cases I am describing the cognitive operation remains with the human who uses the tool. That person understands the problem, seeks an application, and evaluates whether what was obtained works for what they need. Artificial intelligence’s participation does not seem sufficient to me to attribute that operation to it on its own.
That is why I think mathematicians still have an advantage in understanding problems and in the ways they apply results. Tools can make many operations easier, but someone still has to find what to do with them and understand the circumstances in which they could be useful.
Competing with artificial intelligence in processing speed is a bad bet. It can execute large volumes of operations and identify patterns much faster than we can. If all competition is reduced to that, we are unlikely to win.
I would look for the advantage in other human capacities: analyzing, reflecting, empathizing, finding solutions, and persisting in the face of a problem. Also in the experience of whoever needs to solve it, because that is where possibilities arise that do not always appear in a tool’s answer.
That is what I mean by being more human. In my case, the need to move through a university led me to look for an application of artificial intelligence, recognize its errors, and keep trying to solve them. The result I need depends on understanding that situation, and I think there is still much to do from there in work such as that of mathematicians.