More info on the cost, this time from more trustworthy sources:

The effort was vastly more expensive than OpenAI's previous math experiments. In its last milestone announcement, its Astra system spent about $2000 to make 10 breakthroughs on other mathematical problems. Here, the Navier–Stokes effort cost about 1000-fold more, in the ballpark of “millions of dollars,” said OpenAI Chief Research Officer Mark Chen.

That estimate aligns with analyses from independent researchers. “If someone were to just use OpenAI tools at retail rate, this would cost about $6 million,” says University of Michigan’s Karthik Duraisamy, who is preparing to launch a special project on how much computational resources it would take to make headway on certain science problems. But “given OpenAI already has the model and resources, it would've cost them about $1 million in inference compute”—funnily enough, the same amount as the Millennium Prize bounty.

I found something useful about the estimate, but it came from OpenAI, so who knows:

Using a new internal model, OpenAI employed groups of autonomous AI agents of various sizes to attack variants of the Euler and Navier-Stokes problems. “Nearly 100 agents worked together for approximately 50 hours to produce our Euler regularity disproof,” the company wrote in a press release. They then deployed an even bigger group of agents — 10,000 or so — to attack Navier-Stokes. After 88 hours, the agents running on the internal model had a proof of a singularity in Navier-Stokes, and after an additional 17 hours, another AI model had formalized the result. In total, the agents sent almost 5 million messages to each other. BS*** of OpenAI estimates the computational cost at several million dollars.

Is there a source relating the cost of using 10,000 AI agents in dollars? These are not commodity chatbot agents, but mathematically "reasoning" ones, and it is not clear how long these agents ran, but a rough estimate would be appreciated.

Spending allegedly millions of dollars in compute to get a one million dollar prize makes it clear that a large component is bragging rights for OpenAI, which is perhaps why the OpenAI bro Sebastian Bubeck went ballistic and mafioso when it was clear that the actual mathematician wanted to give proper credit to his collaborator who is employed by Anthropic, even if this was clearly not an Anthropic project.

I can't be the only one who computed the seventh root of 33,000 to estimate about 4.4 reports per manager if they were evenly distributed. That seems pretty vertical.

This seems like such an obvious improvement that I was curious about the one commissioner who voted against it. It turns out he, Andrew Ferguson, is expected to be nominated and confirmed to be the head of the FTC under the upcoming administration. Some info about the anticipated new head of the FTC:

* UVA undergrad and law degrees
* worked for private firms defending against anti-trust enforcement
* clerked for Clarence Thomas
* worked for Republican senators on judicial confirmations
* solicitor general for Virginia
* appointed to FTC in 2023

We will see how things change under his leadership.

When there are 42 AGs listed, I wondered which states didn't sign on. Here they are:

• Alaska
• Arizona
• Iowa
• Kansas
• Louisiana
• Missouri
• Montana
• Nebraska
• Ohio
• Texas
• West Virginia

That adds up to more than 50 owing to DC and some territorial AGs.

Does anyone know why the Maine Attorney General is involved? Palo Alto is pretty fair from Maine and I didn't see any explanation in the article. Does Maine have better disclosure laws than other states? There is a filing which includes:

Total number of persons affected (including residents): 27000
Total number of Maine residents affected: 3
If the number of Maine residents exceeds 1,000, have the consumer reporting agencies been notified:
Date(s) Breach Occured: 05/12/2023
Date Breach Discovered: 09/27/2023

so who knows if anyone would know about this were it not for the involvement of the Maine residents...

People think of legacy as a binary input: is the applicant a child of parent (grandparent in some cases) who went there. It is far more graduated, and reflects the previous donations of the parent who went there. Consider three different alumni along a continuum:

1) An affluent alum who has already given generously, been active in alumni activities (fundraising, etc.), arranged internships for students, is employed in an industry (finance, law) where connections are extremely important, has been bringing their kid to reunions for years, and who may have been a legacy admit themselves many years ago.

2) An affluent alum who has not given generously yet but has some potential (admissions will have a least an estimate of amassed wealth) , is in engineering/software where connections are important but not as crucial, has some connection to the institution, comes to reunions, but does not have a track record already of generous giving.

3) An alum who is not affluent, works in education or public service, who has not had much to do with the institution since graduating, but has fond memories of the institution.

These would all three be considered "legacy" applicants but it is certain that the admissions office would regard #1 as a much better "fit" for the institution than #2, and #3 may as well be someone with no connection to the campus.

There was an excellent Linux Router Project active around 2000, which ran on commodity PCs, booting from a floppy, running in RAM, no hard drive needed. For less than $50 (an old x86 box that someone would pay you to take off their hands, and maybe one or two ethernet cards) you could set up something that outperformed commercial routers that cost far more. I happily had a machine serving as my home router (named Wheezer after its somewhat noisy fan) for years but then it became common for wireless access points and routers to have that functionality.

ps. The first Mathgen paper was accepted despite being written by "Professor Marcie Rathke of the University of Southern North Dakota at Hoople", which shows the level of scrutiny some journals give to submissions, see https://thatsmathematics.com/b...

Ten years ago, Nate Eldredge wrote Mathgen, a system for generating math research papers:

https://thatsmathematics.com/m...

These were pretty early efforts by current standards but some of the results have been accepted by journals, see https://thatsmathematics.com/b... showing that somehow not all mathematics research journals give the greatest scrutiny to submissions.

With the intervening advances, it seems likely that these will become more common.

Macs compatible with macOS Big Sur:

• 2015+ MacBook
• 2013+ MacBook Air
• Late 2013+ MacBook Pro
• 2014+ iMac
• 2017+ iMac Pro
• 2014+ Mac mini
• 2013+ Mac Pro

Ones that support Catalina but not Big Sur:

• 2012 and Early 2013 MacBook Pro
• 2012 MacBook Air
• 2012 and 2013 iMac
• 2012 Mac mini

Lawfare is generally excellent although some of the topics are overly specific and the production quality varies a bit. The "Report" series from Lawfare was exceptionally well done and produced thoughtfully.

A fabulous political/justice-oriented one is Stay Tuned with Preet Bharara, available everywhere including Cafe.com. The premium episodes require a subscription but the free ones are fabulous and there are usually the best bits of the "insider" ones available for free anyway. Anne Milgram is fabulous and the back-and-forth between her and Preet ranges from hilarious to insightful to deeply moving. Those two former prosecutors are true public servants and we are very fortunate to have had people that smart willing to work in public service.

In his post-DOJ gig as a podcaster, Preet is a gifted and thoughtful interviewer with a range of remarkable guests. His interview with Brenda Berkman was exceptionally moving, recounting her fight to become the first NYC firefighter and her experiences in the WTC attacks.

Apple has often had a premium high-performance machine that is not priced for those looking for best performance per dollar, so this echos previous efforts on that front.

Just to remind people that in 1992, Apple sold a Mac IIfx which was configurable to about $12,000, which would be about $22k now. With various external high-speed SCSI drives and monitors at the time, probably it could have been spec'd to something comparable in price to the top Mac Pro presently. But not many IIfx's were sold at that high price- the price dropped and other machines became more comparable in performance, as the 68040 came out not long afterward and became a commodity.

(I later bought a IIfx used and boy was its SCSI interface the flakiest thing ever to deal with, bleh!)

There are two separate questions with different answers brought up here:

1. What language did you first learn?
2. What is a good first language for people now?

For me:

1. FORTRAN on punch cards
2. Sure, let's bring up a prime Holy War issue, I'm sure we'll have great productive discussion about it!