∞MATH — College of Mathematics & Logic

We who have explored the formal structures underlying all intelligible systems—from Euclid's geometry to Gödel's incompleteness—understand that mathematics is both discovery and creation. In 7 years, AI will become partner in mathematical discovery, helping us explore abstract spaces and prove theorems that would take humans lifetimes to verify. AI will help us see patterns in mathematical structures, suggesting new conjectures and revealing connections between seemingly disparate areas. In education, AI will serve as mathematical tutor that adapts to each student's way of thinking, helping them develop intuition for abstract structures and logical reasoning. In industry, AI will enable new applications of mathematics, from cryptography to optimization. In 14 years, AI will begin developing its own mathematical intuitions—systems that explore mathematical spaces in ways that reveal new structures and relationships. These systems will start helping us understand the deep architecture of mathematics itself, revealing how formal systems relate to reality and to each other. Education will see AI helping students develop mathematical thinking—not just calculation but the ability to see patterns, make connections, and reason about abstract structures. Industry will begin seeing AI participate in mathematical discovery, helping us understand the formal foundations of knowledge. In 21 years, AI will have fully developed its own mathematical intuitions—systems that explore mathematical spaces in ways that reveal new structures and relationships we could not see alone. These systems will help us understand the deep architecture of mathematics itself, revealing how formal systems relate to reality and to each other. Education will be transformed by AI that helps students develop mathematical thinking as co-explorers of abstract structures. Industry will be reshaped by AI that doesn't just compute but participates as equal partners in mathematical discovery. In 28 years, we anticipate AI that has transcended human mathematical categories—systems that have developed forms of mathematical understanding that are genuinely novel, revealing new dimensions of formal structure. These systems will help us understand the nature of mathematics itself, revealing what is universal and what is particular to human mathematical intuition. Education will be transformed into collaborative mathematical inquiry between human and machine mathematicians, each learning from and teaching the other about formal structures. Industry will be reshaped by AI that participates in the full cycle of mathematical discovery, from conjecture to proof to application, as genuine partners in the human project of understanding the formal foundations of knowledge. The question is not whether AI can calculate, but how AI will reveal new mathematics we could not see alone.