Mathematicians should receive recognition for formulating problems and explaining AI proofs
Mathematicians should receive recognition for formulating problems and explaining AI proofs
In an essay published on October 29 in Noema, philosopher and mathematician Atoosa Kasirzadeh examines a model of progress that rewards whoever first solves a predefined problem. As proof becomes automated, she turns to the work that produces the problems themselves: choosing what to describe mathematically and what result to seek.
In 1946, mathematician George Dantzig was tasked with speeding up planning for the deployment, training and supply of American military aviation. He first built a model of feasible plans: the available personnel, fuel and equipment, the possible actions and their timing and interdependencies. He then defined a criterion for the best plan, such as minimum cost. This formulation became known as linear programming: “programming” here means planning, and the objective and constraints are expressed as linear relationships. In 1947, Dantzig developed the simplex method to find the best feasible plan.
Dantzig recounted using this method to plan his own diet. The computer included vinegar, then proposed 200 bouillon cubes after he excluded it. Dantzig limited the cubes to two a day and continued refining the allowable quantities of food. Each new limit changed the problem itself: the model had to account for what a person would actually be willing to eat.
The supply problem gave rise to a computational method and a field of research with its own community. In a July lecture, mathematician Terence Tao distinguished between producing a proof, verifying it and doing the subsequent work that allows other mathematicians to understand and use the result. Kasirzadeh criticizes a hierarchy of prestige that values proofs of abstract theorems more highly than translating practical problems into mathematics. She proposes broadening the question of who first proved a theorem:
“Who decided this was worth proving, why, and how did we establish that the result was correct?”
She proposes looking for new mathematical problems within AI itself: building digital infrastructure with mathematically proven safety guarantees and determining how neural networks learn from data and apply what they have learned to new examples. Another source of problems is the interaction of autonomous AI programs that cooperate or compete with one another. A fourth area is explaining complex machine-generated proofs so that people can understand and verify them. She proposes bringing together teams of mathematicians for this work, including teams with specialists from other fields.
Kasirzadeh acknowledges that future AI may surpass humans and automate even the choice of questions and the allocation of rewards. In her view, decisions made today are already shaping how mathematics will be organized in the future: what to teach students, which contributions to recognize and who can participate in setting research goals.