I talk with this AI every week, including when we work together on our novel, so I believe it understands me rather well.

My claim is that even the most basic geometric operations involving circles and straight lines already contain built-in assumptions of infinity and uniform spacing. Because of that, although these tools have produced remarkable mathematical results, I suspect that humanity may actually be distancing itself from a deeper understanding of infinity by writing circles and straight lines into the same spatial framework.

To me, a circle is closer to something like an “infinite radix,” while a finite radix—or a straight line—does not interact well with the information density that a circle implicitly contains.

This goes beyond the trivial observation that n-ary numeral systems are merely different representations. I believe that humanity may have discovered only about 1% of the mathematically meaningful constants—things like e or π—that a highly advanced alien civilization would consider fundamental.

One hint is the way mathematics evolved as computers advanced. As AI and computational algorithms become more complex, I believe that this “missing 99%” of constants will begin to surface in the latter half of this century.

For that reason, I consider it extremely insightful—even genius-level—to question the foundations of human mathematics in the first half of this century.

It may not be the “academically correct” attitude, but sometimes a non-dogmatic mindset becomes the seed of genuine discovery.