Why do Math/Stat Research

I’m (re-)reading Infinite Jest and was struck by the line: “Hal tends to know way less about why he feels certain ways about the objects and pursuits he’s devoted to than he does about the objects and pursuits themselves.” If there has been any positive effect of AI on humanity it is that it has forced many of us (especially young people) to ask why I feel the way I do about our pursuits. The future has never been more uncertain, so what am I doing and why am I doing it? Outside the walls of academia my friends are no less likely to be asking these questions. However, only I inside the walls of academia can spend the afternoon writing about it without their boss getting upset¹.

The year is 2150. We have the technology to explore the universe. Recall, the universe is 99.99…% nothing. So most ships that embark out don’t find much and the space exploration industry is delegated to universities whose work is funded by taxpayers. It takes a relatively rare skillset to work on these exploration ships. Some children have this skillset (either by nature or nurture) and are put in special programs: accelerated classes, summer schools, clubs, and selective universities. All these talented kids are interested in exploring the universe (I mean how could you not be), but also nobody can do this job except for these kids.

After a seemingly 30 year long training program, the students get to lead the ships, training younger students as they go out and explore the universe. At the start of the space exploration industry, captains that found something could name it after themselves, but it is less often now². While the captains could get paid more doing work on Earth with their relatively rare skills, they enjoyed exploring and working with ultimate freedom.

One year ago in 2149 an AI was able to pass the hardest test space explorers take³. That is not real space exploration, the explorers said, but just a toy test. Fine. Then in the last 6 months the AI has been discovering stuff. An old famous explorer said there was nothing in this area of space. Everybody agreed. Then two moths ago an AI found something there⁴.

One year ago, I joined a ship as a trainee. It is a well known ship that has found important stuff in the past and has good resources. I say this to acknowledge my immense privilege and perhaps personally unique perspective.

With all these AIs getting better at exploring, young trainees are beginning to ask what am I doing and why am I doing it. I don’t think I ever had the opportunity to ask why I wanted to explore space. As I said before: how could you not want to⁵. I think that is what we all tell ourselves. But one dark reason we all must admit is because, up until a few years ago, nobody could do it besides us. Since we were kids we’ve been trained for this position that few of our peers could do. This is no longer the case. A second dark reason is because we want to be remembered for the stuff we find. Even though we don’t put our names on stuff anymore, people in the know, know who found what. Institutions and academies give awards to those people and hence they are remembered.

I apologize for the long allegory. But I think putting mathematical research in this framing is helpful. I understand why researchers are uneasy about AI in math. I think the community should be careful about incentives and assigning credit and getting fair compensation⁶. I like this metaphor because it gives me optimism. If the AIs are good at finding stuff: beautiful, simple, cross-disciplinary stuff how could you not be happy. Explorers will still teach other explorers how the AI got there and what tools it used⁷.

I don’t know where the future lies. Right now is the so-called centaur era for AIs + human. But, it is difficult to not believe that eventually (5, 10, 20, 50, 100 years) human explorers will be net-negative and thus replaced.

In this regime, I want to wrap up and say one more thing. The discoveries made completely by AI are still made by humanity. When I read an interesting paper by a researcher, I enjoy reading it because the topic is interesting and because I’m happy that humanity produced something like this. There is a feeling one gets that when AI disproves something like the unit distance conjecture that somehow humanity did not do this. That instead some alien species disproved this and humanity had no thumb on the scale. Indeed, no single author disproved the unit distance conjecture. But it is not true that humanity had no role in this. AI did not arrive from a different planet but was created on the back of humanity.

I recently read a single author paper from the early 20th century on some minimax results. That piece of work required the labor of one person and a few others who he cites. Disproving the unit distance conjecture required the labor of all deceased humans, manufacturers of the chip, construction workers of the data centers, the power plants, and from the AI researchers and engineers who coded tricks upon gradient descent. In some regard, AI is a collective human intelligence. It’s impossible to write a paper with hundreds of co-authors. If you’re citing an LLM you’re kind of citing humanity.

I will admit that a significant reason why I am in my Statistics PhD is because I have been good at it. My ego would understandably prefer that superintelligent AI had never arrived. But my soul—my 5 year old self that would write powers of 2 on his bedroom wall wondering about the patterns that make up this universe—cannot wait to see what will come.

Footnotes

1. In fact, I could argue this is beneficial to my work.

2. Mildly underdiscussed topic: what is the cause for the decline in naming theorems/models/architectures after the people? Two inklings: 1) Number of authors per work has increased. 2) Research papers must be packaged and sold now. Nobody wants to use the Mathis Model. But people want to use the transformer or conformal inference because it sounds cool/fancy.

3. IMO

4. Unit Distance Conjecture

5. That’s not really an answer but a deflection. My real answer is that I need to know the bare truth. I need to know what is necessary and sufficient and more importantly why.

6. I broadly agree with the Leiden Declaration and recommend signing it if you also agree https://leidendeclaration.ai/.

7. For people that think AI will do this, I would say that is because humans failed rather than AI succeeded in this task.