Living between Code and Proof -- THE MACHINE AND THE BOOK --

As you know, I’m a student very interested in mathematics and computer science. You can check my About page above. I was thinking what connections between mathematics and computer science and finally I found it. To put it simply, it’s a world of gradation — gradation of mathematical world and computational world —.

To begin with, what kind of things do I actually like? How I find beauty in these fields? I love things that make me exclaim “Oh my god” in surprise, yet were already lurking within our own thoughts. To obtain that, we need to extend concepts.

Let Ω be OMG things. I mean, Ω is a surprising concept. The notation is also intentional. I chose the Greek letter Ω simply because its pronunciation reminds me of “Oh my God.” It is a personal notation rather than a conventional mathematical one.

Naturally, Ω depends on the observer. An idea that belongs to Ω for one person may be completely ordinary for another. Nevertheless, the elements of Ω often share a common property: they are not imported from outside our minds. They emerge from concepts we already possess, once those concepts are extended, generalized, or viewed from a different perspective.

That is the kind of beauty I admire. The greatest “Oh my God” moments are not those that introduce something alien, but those that reveal something that had been quietly hidden in plain sight all along.

We are entering an era shaped by AI and, perhaps soon, quantum computers. Yet I believe this makes human understanding more valuable, not less. Machines may discover patterns, generate proofs, or search vast spaces of possibilities, but the moment of genuine understanding—the moment an idea enters our own minds and becomes part of how we see the world—cannot be outsourced. The mystery of Ω therefore does not disappear. If anything, it becomes even more precious.

Then the natural question is:  how do we cultivate Ω? I believe there are two complementary approaches. One is through the natural world:  mathematics, physics, and the search for the fundamental principles that govern reality. The other is through the computational world:  computer science, where we study abstraction, algorithms, languages, computation, and intelligence. My interest lies not in choosing between these worlds, but in moving continuously across the gradation that connects them. It is somewhere along that spectrum that new elements of Ω are born.