I recently posted a paper whose theoretical derivations got an enormous amount of help from GPT (even though 5.6 Sol wasn’t out yet at the time). My senior labmate and I took the proof outline GPT gave us, refined it, and distilled the insights. Over the summer, I talked with a lot of people, and one question kept coming up: what is the point of theory, and where is its future?
Let me start with something I heard from a professor in August: “What matters most in this era is how you define problems and develop a field, not finding well-defined tasks to solve. On mountains nobody really cares about, there’s no need to compete over who climbs faster or higher. The ultimate meaning left for humans is understanding, which at its core is a need for education. The human brain was never well suited to very complex math, so understanding should mean abstracting concepts out until things become intuitive. Theory has to return to its essential role, which is helping people understand, not solving open problems.”
For now, at least, I have an answer I’m satisfied with. Mathematics, or theory more broadly, should return to its essence: turning real-world problems into structure. That could mean helping people understand, or it could mean coming up with ways to solve real-world problems (here I’d say statistics is more about creating new tools to solve real problems). I hope future theoretical work can keep its own meaning and its own value, rather than just being treated as “literature.”
So where is the future of statistics? To borrow some views shared by friends and advisors: the essence of statistics is “Test,” that is, hypothesis testing, which can be further divided into “Inference” and “Prediction.” Rather than working out which inequality concentrates where, or how tight some bound can be made, I think what matters more is building a process that goes real-world problem → mathematical modeling → hypothesis testing → robustness. In other words, a rigorous chain of reasoning. When judging causality, you have to make the experiment as rigorous and clean as possible before you can draw conclusions. I think this logic is meaningful for any “real-world problem,” and it requires many statistical tools along the way. In short, statistics should return to its essential role as “a tool for solving problems”: when a new problem comes along, invent a new tool, instead of applying old tools to new problems and getting conclusions nobody quite understands.
Some say “mathematics” will gradually become “literature,” or even “theology.” I’m not that pessimistic yet. Perhaps in the not-too-distant future we’ll see a Renaissance of the theoretical disciplines.
These are just my shallow thoughts. Happy to hear other views and discuss.