In a brand new article published yesterday on Medium, Kasper Müller writes about The Riemann Sphere: A world where you can divide by zero in a manner which weaves in some insights that have been the endpoints of several private thought experiments. So as I'm reading the article, not only do I immediately see it's a "variation on the theme" of an article I wrote on this site a couple years ago, but I'm delighted to see that the new insights (which apparently others have known for years) fit well into the larger theory I'm working on.

I honestly had a moment while reading Müller's article where I thought: "The coincidence of so many details is too great. Surely he has read my articles in this area" and I scrolled to the bottom of his article to see if perhaps he mentioned one of my previous weblog posts in a footnote or something. Nope. As I continued reading, I humbly realized this is not likely. He's simply independently putting together elements which coincidentally correspond with things I'm independently discovering. I'm okay with that for three reasons:

- My own theory is obviously pretty far out there with an approach and elements that most mathematicians will likely reject right away, although much of the general theme is solid, being exposed competently by other mathematicians within Wheel Theory. However, that theory is so obscure and new that few mathematicians know about it yet.
- His article is one of a long stream of articles by him talking about similar themes. There is a rich history of him circling these ideas independently. And, to his credit, his material is better informed within traditional mathematical approaches, so it might be easily argued (but false) that I'm copying from him. I'm not. It's not about that. Instead, I'm simply sure we would have a fun and long conversation if we got to talking about such things.
- He says at the beginning of the article: "Something is going on with infinity that we don’t fully understand." Yes. Not only do I fully agree, but I've been working on a coherent understanding of it for years. I'm pretty sure I've worked out something others
*can*understand -- which the rest of his article confirms.

When Charles Darwin received a letter from someone proposing a theory of evolution, he was already famous for his voyages on the Beagle. All of Europe knew him as a brilliant scientist, which is why he received that letter. However, there is a little-known fact: Darwin immediately recognized that his manuscript version of the *Origin of the Species* was about to get trumped by someone else. He quickly finished his manuscript and published it.

More famously, Leibniz and Newton independently discovered calculus at the same time. The methods they used were so different from each other that it is obvious they did so independently, but this was not clear within their lifetimes.

Likewise, Fermat and Descartes had similar rivalry in areas where they were independently working on the same things. There are others; this is a common theme throughout history.

But why am I talking about Darwin, Newton, Descartes, who are famous for seismic-sized discoveries which changed history? It's not only because they're commonly-known references, but because I humbly believe the Riemann Sphere insights touched on in this article have the potential to be at that level of profundity. Not everyone sees this aspect, but it is getting clearer by the day. I go into this in another recent essay so I'll leave off saying more than that here.

Instead, I'm writing this brief note as the fourth in a sequence of periodic weblog posts about discovering *others are working on the same ideas* which, for a decade, I thought I was developing alone. Seeing others working on these themes is exhilirating to me, not competitive. For example, I really rejoiced when I encountered the very cool 1dividedby0.com website soon after it came out. My recent essay in this area spends time talking about the curious idea that *humility may be a necessary element* of these discoveries. Humility is not competitive; it's very much not a zero sum game, it's quite the opposite.

There are many thousands working on the related Riemann Hypothesis. But RH is mostly about prime numbers. What I'm talking about here is more about Riemann's Sphere and how it intersects with infinity, the complex plane and other areas of math in a beautiful, elegant way that fits every possible mathematical standard of rigor. And it's brand new. And it's big. This is what's exciting for me.