Hey Sonia,

How are you doing?

To answer your question (sorry for the late email, moving did not leave me much time to write), the math department is paying me to study KTu-L spaces.

You might have seen some references to them popping up in the past year, they have gained a lot of visibility as some mathematicians (mostly Providence’s research team which I will be joining this week) claim that they can be used to solve a number of interesting conjectures.

Sadly, the use of homemade notations makes them really hard to apprehend, and basically nobody but other experts in KTu-L is able to check their work. That’s a problem, we cannot build maths on blind belief in a small group of people. The goal with my postdoc is to bridge the gap between their work and the rest of the mathematical community to either debunk it (maybe they have been building on unsound foundations all this time… hopefully not) or help it spread if they fulfill their promises.

But at the moment it’s all super blurry for me (I am still unclear on the nature of things they call basic, like Y-S entities as defined in KTu-L). I will tell you how it goes in about a week :)

Best,
Philip

Hey Sonia,

Another long, rambling, email (but it would not be me if it were short :P).

Yeah, you are right, being rejected was definitely one of the things that motivated me to move to another country. It was… painful and the worst part is that I cannot just force my mind to do something else and stop thinking about it. I am hoping that, by letting my work consume all of my thoughts, I will be able to keep those messy feelings out and be productive in the meantime.

By the way, thank you for the copy of Stephen Pollock’s paper on the Kronecker product, it was really useful. I love the fact that the notation he introduces lets you see the problem in a very different way and that suddenly all the mathematical quirks of the Kronecker product become intuitive. I really like those rare papers that change your perspective in-depth, it is as if when you understand the proof it gets a grip on your mind and becomes a part of it. You don’t find those often but it is always a great feeling.

Speaking of papers, Howard (my lab supervisor) gave me some textbooks to get me started on the notations. That should let me decipher the easier theorems (gosh, I love being paid to learn new things but I feel like an undergrad right now). Hopefully next week I will be able to tell you a bit about KTu-L spaces!

Best,
Philip

Hey Sonia,

I didn’t expect to write so soon but I just found out something crazy! In my mind, KTu-L spaces came back no further than yellow&king[1895] but Robert Chambers (another postdoc here, he studies the history of maths and arrived a few weeks before me) showed me that they are much older. Some of their symbols are as old as Arabic numerals, appearing for the first time during the middle ages in the mathematical writings of Abdul Al-Hazred :o

And there is more! If you look around, you see that KTu-L spaces have been rediscovered several times by people who were not communicating together (sometimes with the same symbols). You find them in North Africa, the middle east but also Tibet and Japan!

Robert wonders whether that could be explained by a sort of common ancestor, theorems, and notations put together in Sumer and later propagated and rewritten by different cultures. But, that seems really unlikely to me: I can’t imagine Mesopotamian dabbling in highly abstract maths and I don’t see how their ideas would get to Japan… My feeling is that mathematics is not invented but discovered so it is not too surprising that different groups will discover the same thing as the thing that exists independently of its human transcriptor. A bit as if maths were things living on an actual, physical, continent that is “merely” on a different plane of existence…

Best,
Philip

Sonia,

It took me a long time but I am starting to see the light. I am now able to do some of the shortest proofs, they are surprisingly easy once you get a hang of the notation.

I thought that I could translate the KTu-L notation into more conventional symbols but now I am starting to think that it is not the proper way to go. Everything should be consumed, maybe replaced (?), by KTu-L. That would make the world a better place.

Rereading my own email, it seems a bit… much. But, it feels right. Howard proposed showing me a Y-S tomorrow, I will let you know how it goes.

Philip

Sonia,

You should see R’lyeh and its measureless beauty. Nothing can compare to the feeling of purpose, of unity, that you get when you realize that there is only one logical outcome and that the only meaningful thing to do is to work toward it.

Philip

Sonia,

Yes, you should definitely come. KTu-L needs you.

Philip

Annotated version.