I recently attended a DOE Office of Science-funded workshop in Minnesota and was inspired by many excellent presentations.
One moment, however, surprised me. A student apologized for including “so many equations” in his presentation. I found myself wondering: since when do we need to apologize for writing equations? Aren’t we supposed to use the languages of mathematics, physics, chemistry, and biology to test hypotheses, discover new things, and answer difficult questions?
Another moment also stayed with me. I gave a university seminar on geologic hydrogen, where I shared my passion, vision, and the broader opportunities in this emerging field. Given the audience and time constraints, I simplified many of the technical details. Afterward, a senior professor asked me, “Can you write any equations?” Clearly, he did not mean the chemical equations for hydrogen generation, which are central to this research. I was surprised again. Since when has the ability to write equations become the measure of whether one can advance a new field or technology?
Since I was a PhD student, I have written countless equations, formulated them into code from scratch, tested the code, debugged it, and started over many times. For a long time, I had almost nothing to show except equations, algorithms, and code. But I never felt that I had to apologize for that.
At the same time, I also learned that equations alone are not enough. For example, when I worked on contact problems in computational mechanics and geometry, I realized that a few simple algebraic equations could represent the concept of complex geometry and contact potential. Writing a few new equations may take ten steps. But translating those simple algebraic equations into robust, working code can take ten million steps-- especially in computational geometry. That is why the most challenging computational problems are often problems of computational geometry: contact mechanics and moving interfaces.
So I do not know exactly what is wrong with the scientific world today. But I do know this: in the new AI era, the people who will make a real difference are not those who avoid equations, nor those who worship equations as the only measure of intelligence. They are the people who can write equations, understand their limits, translate them into computation, and think creatively about the algebraic, geometric, topological, physical, chemical, and biological structures of molecules, materials, Earth systems, and the universe.