herid @herid@qoto.org

There's a superficial outer layer of number theory that's about hard puzzles like Fermat's Last Theorem and Goldbach's conjecture, but to me the interesting part of number theory has always been about general principles.

For example Galois theory is about how in a given language the only concepts you can express are those invariant under the symmetries of the interpretation of that language: this is why Galois invented groups and used them to decide when you can or cannot solve a polynomial equation using radicals.

Then Grothendieck generalized the concept of "space" to the point where even fields like the integers mod 5 can be seen as fields of functions on some sort of space (called a "scheme"). In this new outlook, Galois groups become symmetry groups of covering spaces, and many problems in number theory turn into problems of topology - but topology of a new generalized sort!

Pushing forward with this, people have found an amazing analogy between prime numbers and knots. My friend Minhyong Kim has applied ideas from gauge theory to number theory. And other people have shown there's a hugely generalized Galois group that's involved in renormalization.

So, number theory keeps expanding our concepts of number, space, logic and symmetry. And a lot of the resulting ideas are pretty simple and fundamental! - though you might never know unless you dig through piles of distractions.

If you ever want to learn more about this, about the most readable introduction is here:

• Pierre Cartier, A mad day's work: from Grothendieck to Connes and Kontsevich: the evolution of concepts of space and symmetry. https://www.ams.org/journals/bull/2001-38-04/S0273-0979-01-00913-2/S0273-0979-01-00913-2.pdf

It's not easy, but you can skim it and get a feel for it.

(2/2)

Talking to someone I said:

"By the way, I've been studying number theory. While it takes a long time to get to the really cool stuff, which is not about silly puzzles, when you finally do it's philosophically profound and quite amazing!"

They replied:

"How is it philosophically profound? Category theory has that feel. What about number theory?"

That's a great question, because when you first bump into number theory it may not feel that way!

So I thought I should share my answer.

(1/2)

😂 “ #Florida Gov. #DeSantis foiled by Disney once again.
The new board DeSantis appointed to oversee the company’s Orlando theme parks has discovered new wrinkle in its plans. The board’s chairman said that another “11th hour agreement” was signed before the board took over that allows #Disney to set its own utility rates for its resorts through 2032. By that time, DeSantis, who is term-limited and cannot run for reelection in 2026, will be long gone.”

https://apple.news/AXrPn7q8wTBCOB00E4s_BJA

RIP BuzzFeed News :(

Breaking News: Elon Musk has asked NASA for technical assistance following SpaceX's failed launch attempt. NASA immediately responded with a poop emoji.

So, Twitter decided to pull a DeviantArt move and change its Terms Of Services to include anything you post there on their AI dataset, to re-publish your art and benefit from it without your consent or compensation.

TIME TO DELETE YOUR ART PORTFOLIO ON TWITTER

I will only leave my contact information there, nothing else.

#Twitter #artistsonmastodon #TwitterAlert #AuthorsRights #AI #DeleteTwitter

😳Another day, another…

A #NorthCarolina man allegedly shot a 6-year-old girl, her parents and an additional neighbor after a basketball rolled into his yard #shooting

https://abcnews.go.com/US/6-year-parents-neighbor-shot-after-basketball-rolls/story?id=98717589&cid=social_twitter_abcn

1 in every 255 residents of #Indiana has died of #COVID-19. https://www.worldometers.info/coronavirus/country/us/

Fox News will likely try to recoup the $787 million settlement by negotiating higher carriage fees with cable providers.

Those providers will then pass the extra costs to you by increasing your monthly bill, even if you never watch Fox News

Fox News lies

You pay

8/ To confirm, Axios reports #Fox will not be required to give any apologies or retractions on its air as a part of the settlement deal.

Fox’s lies damaged (and continue to damage) all of us, but we didn’t all sue. We couldn’t.

Only Dominion sued. They got a gigantic amount of money, for a little company with 100 employees. They have every right to be happy.

We have every right to remain unsatisfied.

In light of the debate over Feinstein, a look at how the Senate has aged alongside the population — and the repercussions that aging has. https://www.washingtonpost.com/politics/2023/04/18/america-is-older-so-is-senate-that-has-repercussions/

Oh come on.

🚨 whoa. Big news for day 1 of Dominion v Fox.

After an extended 2-hour lunch break, the judge returned and dropped this bombshell. Not entirely unexpected considering we know they hid evidence… but still.