Can You Hear the Algebra

I was on a long flight from Shenzhen to LA, and like many travelers, I decided to catch up on some movies. Among the selections was Oppenheimer. One particular line in the movie struck me:

“Algebra is like a score. The question is not ‘can you read the music?’ but ‘can you hear it?’”

Oppenheimer’s response was quick and simple:

“Yes. I can hear it.”

In that moment, I couldn’t help but reflect on the comparison between algebra and music. Oppenheimer’s point was clear: reading the symbols and structures of algebra isn’t the crux; seeing the picture, the physical motion, is the more important thing.

But as soon as that thought passed through my mind, I was reminded of Beethoven. Famously, Beethoven composed some of his greatest works after he became deaf. He couldn’t physically hear the music anymore, but that didn’t stop him from creating symphonies that have lasted through centuries. Beethoven didn’t need to hear the notes to “feel” and understand the music. He knew how it worked at such an intimate level that the sounds lived in his mind without needing to be externalized.

Mathematicians can do the same.

For musicians like Beethoven and some mathematicians, it’s not about what they see or hear—it’s about what they can internalize and feel at a deeper, abstract level. The Bourbaki group was like that too. They built vast abstractions, working with pure concepts without needing any visual images.

But I’m no Beethoven. I need to hear the music to play an instrument, and I need to see images to guide me in doing proofs. Algebra, for me and at least for now, is too abstract without those tangible representations. And that’s okay—I might not be able to fully “hear” algebra in the way others do, but that doesn’t mean I can’t appreciate or work with it in my own way.