johncarlosbaez

"I can not really imagine knowing what to say but not knowing how to write it."

I guess you're monolingual and have never tried operating in a new language.

Adelson-Velsky and Evgenii Landis were not the ones who named their tree the "AVL tree".

In my "crackpot index", item 20 says:

20 points for naming something after yourself. (E.g., talking about the "The Evans Field Equation" when your name happens to be Evans.)

Yes - by cooling it. See the problem?

You need to go more slowly and do lots of examples. Maybe start with

* Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen and William Traves, An Invitation to Algebraic Geometry, Springer, Berlin, 2004.

and then this:

* Igor R. Shafarevich, Basic Algebraic Geometry, two volumes, third edition, Springer, 2013.

This claimed proof is a bunch of baloney:

* First, it's written in the typical style of AI slop.

* Second, a mathematician I know and trust writes "I went straight to the technical part (Sect. 3) and randomly checked one of the results (Theorem 3.14), finding that it is obviously false. (The category Comp mentioned in the theorem is formally introduced and makes sense per se, but it is certainly not additive with the proposed definition, as claimed in the statement of the theorem)."

* Third, another mathematician I know and trust writes "I spent almost an hour poking through here carefully to see where the more central claims begin to fall apart. Theorems 3.24 and 4.1 brazenly contradict each other, proving respectively that problems in P are homologically trivial and that all NP-complete problems are homologically isomorphic to all problems in NP. Even more to the point, the proof of 3.24 really shows the lie where it says "The detailed argument uses the functoriality of the computational homology construction and the fact that homology isomorphisms preserve the 'computational topology' of problems." The last claim is, naturally, not mathematically defined. The computational chain complex also appears not to be genuinely defined, as far as I can tell. I haven't compared to see what the author chucked into the formalized definition."

I'm starting to make videos for the University of Edinburgh. My first one was about this paper saying that neutrino oscillations may increase the formation of gold and other heavy elements in neutron star mergers:

• Neutrino flavor transformation in neutron star mergers, https://arxiv.org/abs/2503.11758 Here it is:

Or if you believe the simulation hypothesis, the second-largest.

Quoting https://thenieveslawfirm.com/do-police-have-to-identify-them...:

You’re minding your own business when a police officer approaches you. They start asking questions, but something feels off. You ask for their name and badge number, but they refuse. What do you do?

As a citizen, you want to trust and cooperate with law enforcement, but you also have rights that must be protected. The question of whether police officers are legally required to identify themselves when asked is a complex one, with no easy answers.

In general, no, a police officer does not have to identify themselves even if you ask them—making it even more important to invoke your right to silence no matter who you think you’re talking to.

California Penal Code Section 830.10 states:

“Any uniformed peace officer shall wear a badge, nameplate, or other device which bears clearly on its face the identification number or name of the officer.”

However, there are a couple of key issues with this law that limit its effectiveness in ensuring police accountability:

    The law only applies to uniformed officers, meaning that plainclothes officers or those working undercover are not required to wear any identifying information.
    Even for uniformed officers, the law doesn’t explicitly require them to make their badge number or name easily visible or accessible to the public. An officer could potentially wear their identifying information in a manner that is obscured or difficult to read.

"Whatever the reason, the resistance to AC technology is making Europe a more impoverished civilization. It’s a major reason why Europe now feels shabbier and more hardscrabble than America..."

It feels shabbier and more hardscabble than America now? That's news to me.

It's a little late for a "wakeup call", no? More like "wake up, your house is on fire and behind your bedroom door it's a raging inferno out there".

> The economics profession should reflect on the fact that DOGE is proceeding without the input of economists because economists have downplayed the persistence and extent of government policy failures.

No, that's not the main reason why they're proceeding without the input of economists.

Fixed - thanks.

Never a good sign for a physics theory when the headline says it's "not dead".

My fifteen minutes of fame have finally arrived? :-)

Strange title, since we've known for a long time that Mars has an atmosphere unlike our own.

Why would anyone care what Rand Paul thinks?

Yes, we've really sunk to this: a rebel theoretical physicist feels the need to debate a guy who claims 1 × 1 = 2, presumably just to get some more publicity.

Howard's Wikipedia page hints at how he became this confused: "He has been married four times to three women". So one times one was two.

It's good to do if your life isn't boring enough and you need to avoid pleasure.

I know plenty of math, but having more ignorant victims will make it easier.

I hope they stop teaching people to calculate. Then I'll start up my career in fraud and embezzlement.

That explains having a 50% chance of seeing an electron somewhere, not seeing an entity of charge 1/2. It's like a weather report saying there's a 50% chance of rain doesn't mean you're going to see little raindrops cut in half.

Maybe, but getting fractional charges out of a system with charges that are integer multiples of the electron charge is no mean feat, and I want to understand the math behind this in detail. Someone knows, but I haven't found any clear explanations.

I've never seen a good clear explanation of "fractionalization" - the way that that systems can contain excitations that act like particles with charges that are a fraction of the electron charge. A typical non-explanation:

https://scitechdaily.com/quantum-revolution-redefining-physi...

Everything is always subliminally affecting you. It might as well do it in a helpful way.

It's too bad the top-rated answer on Reddit says "GR does not say Gravity is not a force (or if you do say it’s not a force, then none of the other forces are forces either)" rather than explaining what people mean when they say gravity is not a force (basically, it affects the geometry of spacetime in such a way that an unaccelerated particle can still move along a path that's not a straight line in the traditional sense) and why nonetheless we can treat gravity approximately (that is, perturbatively) as if it were a force, and why this perturbative description when quantized predicts a spin-2 boson, the graviton. Oh well.

I just looked into this story, and there was more to it than we usually hear.

I was saying that the temperature of the Universe in the far future will be about 0.000000000000000000000000000001 kelvin, if our current theories are correct. This is 10^(-30) kelvin.

I wrote "Gauge Fields, Knots and Gravity", but we were talking about my uncle, who wrote "The New College Physics: a Spiral Approach".

That book is great, but not mainly about algebraic geometry: it's more about differential geometry.

My favorite intros to algebraic geometry are these:

Igor R. Shafarevich, Basic Algebraic Geometry, two volumes, third edition, Springer, 2013.

Phillip Griffiths and Joseph Harris, Principles of Algebraic Geometry, 1994. (Especially nice if you like complex analysis, differential geometry and de Rham theory.)

David Eisenbud and Joseph Harris, The Geometry of Schemes, Springer, 2010. Currently at https://www.maths.ed.ac.uk/~v1ranick/papers/eisenbudharris.p...

But whenever I want to learn some new field of math I start with Wikipedia. This is a pretty good overview:

https://en.wikipedia.org/wiki/Algebraic_geometry

Cool! It sounds fun. Back then she used to sing at the so-called Nameless Coffeehouse in Harvard. Unfortunately I was 7 years old in 1968, so I missed all this.