green496.bsky.social

Not that the average American cares, but this is a high crime and misdemeanor and Blanche should be impeached and tried.

Aaron Rupar@atrupar.com

Blanche on CBS says his suit against Alaska is "asking the court to step in where the Alaska Supreme Court didn't, which is to look at federal law and if necessary to allow a process for Alaska to decide who should be certified as the winner." (So, the voters won't get to decide. Got it.)

This is the language of domestic abuse. “If you don’t give me the power, you don’t get any money.”

Aaron Rupar@atrupar.com

Trump on Camp Lejeune water contamination claims: "If we win the House and Senate, I am directing the Department of Justice to settle all remaining legitimate claims as soon as possible ... if we don't win, there's no money."

Since the Trump admin can’t give a straight answer to this vital question of national security, it’s going to be up to Congressional Dems to subpoena everyone involved to get to the bottom of this.

Hoodlum 🇺🇸@nothoodlum.bsky.social

A stuttering Marco Rubio: “Nobody ordered that Starlink speed to be slowed down. It sorta happened.”

nytimes.comA Billionaire Wanted a Trump Pardon. His Family Gave Alina Habba a $50 Million Deal. (Gift Article)Julio Herrera Velutini, a prominent Venezuelan, was seeking clemency. He got it not long after his daughter gave Ms. Habba, a lawyer close to President Trump, an extraordinarily lucrative job.

As much of a joke as Alina Hanna is, clearly she knows how to play the graft game and get her bag. The next Democratic president needs to prosecute all of these corrupt Trump admin officials to the full extent of the law.

Don Moynihan@donmoyn.bsky.social

My brain cannot process this level of corruption. She was being paid $50 million to engineer a pardon from Trump *while working at the Justice Department* as a "Special Government Employee." And it worked. He got the pardon, and she got the money. www.nytimes.com/2026/10/20/u...

on.wsj.comExclusive | Musk Ordered Starlink Slowdown That Blindsided UkraineThe SpaceX founder authorized the move and has been discussing Ukraine with Trump, but the president has denied ordering the restrictions.

Has a single private individual ever had so much power in geopolitics before? Clearly private individuals can’t be trusted with it, so Democrats should think hard about how to stop this from happening again.

The Wall Street Journal@wsj.com

Breaking: Elon Musk ordered the Starlink slowdown that blindsided Ukraine on.wsj.com/4sgcxkt

mediaite.com‘Not an Appealing Quality!’ Democrats on CNN Panel Rip Abdul El-Sayed Over ‘Cockiness’"He gives this vibe that he just has to be right. He drives and drives, and he has this... some might call it confidence, some might call it cockiness"

David Axlerod is Exhibit 1A in somebody attaching themselves to a generational talent and then thinking that they themselves were the genius.

Dean Obeidallah@deanobeidallah.bsky.social

‘Not an Appealing Quality!’ Democrats on CNN Panel Rip Abdul El-Sayed Over ‘Cockiness’ The same pundits who tell female candidates to "smile more" now tell the Muslim Senate candidate to be more respectful to the white bigot who smears them with lies. #STFU www.mediaite.com/media/news/n...

youtube.comViral heckler’s GOP ties EXPOSED after El-Sayed clashYouTube video by MS NOW

Just one small point about this exchange: for a long time, Republican operatives and politicians have gotten away with trolling Democratic politicians who didn't know how to respond. But the younger generation of Ds know exactly how to punch back (AES, Ossoff, etc.).

All In with Chris Hayes@allinwithchris.bsky.social

WATCH: After the viral exchange between Abdul El-Sayed and a heckler named “Tommy,” independent reporter @marisakabas.bsky.social uncovered the man’s ties to Republican politics.

This exchange is also indicative of how the Republican operative class is getting dumber and dumber... they think calling out AES about the Muslim Brotherhood is going to be some slam dunk gotcha. Trump truly is remaking the GOP in his own image.

To be clear: this is almost certainly a new tax avoidance and stock price inflation scheme made possible by new rules on Trump accounts that permit donations of individual stocks that cannot be sold for 5 years or declined.

CNN@cnn.com

Elon Musk has said he will give every child in America a stake in SpaceX, his $2 trillion aerospace and artificial intelligence company, as tech firms face intensifying scrutiny over their impact on society. https://cnn.it/4yWTjTJ

cnbc.comTrump Accounts top 70 million as new stock-donation rules open door to 'mega donors,' official saysThe Trump administration said new changes to Trump Accounts could pave the way for several multimillion-dollar donations.

See www.cnbc.com/2026/10/08/t... for some more details on this.

nypost.comMom who survived school shooting coaches son through Oregon attack: ‘Please be as quiet as possible’The traumatized mom was fearful every time she dropped off her sons years before the school shooting.

Ah yes, Trump is laser focused on those kitchen table issues

Aaron Rupar@atrupar.com

Trump: "The Department of Interior wants to take a terrible and very unsafe golf course, and make it into a great, safe, and prestigious golf course ... They do not need an approval. Work is scheduled to begin IMMEDIATELY!"

green496.bsky.social reposted

Alex Ip 葉清霖

@alexip718.com

America now has second-generation school shooting survivors nypost.com/2026/10/17/u...

This is the natural consequence of electing Trump and Republicans into office!

The Washington Post@washingtonpost.com

Average hourly earnings, in real terms, fell 0.5 percent from August to September, according to data released by the Bureau of Labor Statistics, as inflation fueled by a recent surge in energy prices wiped out yet another month of wage gains. https://wapo.st/4yhxUmX

nymag.comKirsten Gillibrand, Crypto’s Favorite DemocratThe senator says she set out to regulate a grift-y industry. Now, she’s in an ethical morass.

An ambitious New York politician should do us all a favor and primary Gillibrand, who is clearly not interested in the anti-corruption politics that are urgently needed.

Nate Weisberg@nateweisberg.bsky.social

I asked Sen. Kirsten Gillibrand if it bothers her that her staff trades crypto while she works on legislation that benefits the industry. “This is not a nanny state,” she said. Profiled crypto’s favorite Democrat for @nymag.com

green496.bsky.social reposted

Jonathan Howard

@joho.bsky.social

sciencebasedmedicine.orgDr. Jay Bhattacharya on Measles: “I Think I’ve Done My Best.”As football coach Bill Parcells famously said, “you are what your record says you are”.

NBC News@nbcnews.com

Two babies died. An 18-year-old with measles died from a rare complication that caused inflammation in the brain. At least six infants have been born infected with measles. There’s no way to predict which kids will get hit hardest.

nbcnews.toPennsylvania doctors are seeing what measles can do to previously healthy, unvaccinated kidsThe virus is proving it can attack multiple organs, including the gut, liver, lungs and brain, even in children who were previously healthy.

green496.bsky.social reposted

Catherine Rampell

@crampell.bsky.social

Billions of dollars’ worth of contracts predicting oil would fall and the S&P 500 would rise were placed about 15 minutes before Trump announced a U-turn on Iran in a post on Truth Social. CFTC staff began to investigate...then were told to lay off. www.bloomberg.com/news/feature...

bloomberg.comCFTC Staff Were Told to Retract Analysis of Suspicious Oil TradesChairman’s adviser intervened to take over examination of lucrative bets that were made around Trump reversal on Iran power plant attack.

@jakemgrumbach.bsky.social

I get that Trump cannot help himself to base racism, but I seriously doubt that this messaging will be effective. The median American voter might indulge this messaging if Trump were delivering results, but he isn’t, so this only plays to his base.

Aaron Rupar@atrupar.com

Trump: "The Republican Party, we believe that Somalia bandits, third-world gangs, and jihadist sympathizers do not belong in Ohio, they do not belong in America. We got to get them the hell out of here." More "De-port! De-port!" chants from the crowd.

green496.bsky.social reposted

Jake Grumbach

New working paper: the Norwegian wealth tax was a huge success. The "exodus" of wealthy people never happened (less than 100 individuals left). Tax revenue increased by 71.5%. No changes in business activity or investment. www.nber.org/papers/w35854

washingtonpost.comPentagon raises official toll of troops killed during war with Iran to 21The Post exclusively reported last month that the numbers of service members lost was greater than what the Pentagon was reporting in its public database.

Just a reminder that you can't trust anything coming out of the Trump admin, even if it is the most sacrosanct, grave information the US government has.

The Washington Post@washingtonpost.com

Breaking news: The Pentagon acknowledged that the number of troops who have died in the Middle East during its operations against Iran is higher than previously reported, and updated the official count to include two more noncombat deaths.

Direct File was one of the best government initiatives in recent memory, and would have had clear benefits had it scaled to the entire US population. So no surprise it was killed by the usual suspects.

Don Moynihan@donmoyn.bsky.social

New open-access paper: Direct File showed that govt could build its own user-centered platform without relying on contractors. But the product was killed after a DOGE lead spoke with the private tax preparation industry lobbying against a private option. onlinelibrary.wiley.com/doi/10.1111/...

arxiv.orgNavier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofsAutoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this pro...

Earlier today I came across this preprint: arxiv.org/abs/2610.08144 TL;DR: The Navier-Stokes OpenAI natural language proof does not match the Lean proof exactly, so it is unclear if the natural language proof is actually correct.

Unfortunately, this bodes poorly for human understanding of AI-generated mathematics. Without high confidence in the correctness of the English language papers, mathematicians will need Lean formalizations to have confidence the proof is correct, and to build understanding on a correct foundation.

And indeed 3 of the hundreds of papers OpenAI announced earlier this week were withdrawn to serious flaws in their purported proofs: www.reddit.com/r/mathematic... Not surprisingly these did not have Lean formalizations.

However, the problem is that we no longer know that the English language paper is correct. Instead, the Lean formalization is the thing that is correct, and it is *much* harder to read than the English language paper (which is already very hard to read).

Wait - you might be wondering, how could a wrong English proof lead to a correct Lean formalization? Because even if a minor error is made in an English language proof, it may be "fixable" via some minor changes. Which is what the Lean autoformalization is forced to do (if there were errors).

So what did the preprint in the first post find? It finds specific examples where a statement in the English language N-S paper does not match the corresponding portion of the Lean formalization, so in actuality the Lean formalization does not do the exact same proof as the English language paper.

In some sense, this isn't surprising. An LLM can hallucinate/make mistakes etc. while formalizing something into Lean. Of course, the Lean compiler detects this error and returns a message explaining the error, and then the LLM tries again taking that feedback into consideration.

If you have a Lean proof of a particular statement, then that lends a high degree of confidence that statement is true. Of course, you need to know that the statement that was proven in Lean is an accurate translation of the human-language statement.

In the case of N-S, everyone essentially accepts that the statement of the theorem was formalized into Lean properly, since it is a very high profile problem (and was done before OpenAI's proof anyway: eg, google-deepmind.github.io/formal-conje...)

lean-lang.orgLean Programming LanguageLean is an open-source programming language and proof assistant that enables correct, maintainable, and formally verified code.

Before, say, 2025, a painstaking effort to formalize more and more of mathematics was gradually building momentum. Much of this took place in a library called mathlib (lean-lang.org/use-cases/ma...), which was gradually formalizing more and more of the standard corpus of mathematics.

However, once LLMs became good at programming, they also became "good at" Lean. In particular, they became good at translating proofs from human language (mostly English) into Lean. This means that you can point an LLM at a mathematical paper and have a good chance of formalizing it.

If you haven't heard of Lean, it is a specialized programming language one of whose aims is to allow the expression of mathematical proofs in a language that computers can verify, but is still (relatively) comprehensible to humans.

A theorem, definition, etc. can be stated in Lean. And its proof can also be expressed in Lean. Of course, like in real mathematics, you can build more complex mathematical concepts from simpler ones.

Some background: AI is notorious for hallucination. So why did mathematicians accept the correctness of OpenAI's N-S proof? The primary reason is because it was accompanied by a Lean formalization of the proof.

One more set of meta comments on this: after OpenAI's announcement of Navier-Stokes, they got lots of pushback from the math community. One of the things OAI did in response was to ask for recommendations from an independent advisory board of mathematicians on how to conduct future releases.

openai.comSharing AI progress in mathematicsOpenAI publishes new results on open problems in mathematics from an internal frontier model and shares Lean proof formalizations and research details on GitHub.

green496.bsky.social@green496.bsky.social

Open AI just released hundreds of proofs of new mathematical results: openai.com/index/sharin... Here are some notable (to me) points:

In summary, we see that most of the suggestions were either outright ignored or mostly ignored. OpenAI did a reasonable attempt at writing papers to be comprehensible to people and formalization, but not much else.

Clearly, OpenAI's priorities differ from the academic community's, and this will be a source of tension for the foreseeable future.

green496.bsky.social@green496.bsky.social

Open AI just released hundreds of proofs of new mathematical results: openai.com/index/sharin... Here are some notable (to me) points:

"5. Each time a solution to a problem is released, it should be clearly documented how exactly AI came to be used on that particular problem." ❌: OpenAI gave vague details about problem selection (~ 4000 total), and did not explain how they prompted for solutions nor the LLM infra that was used.

Finally, the group recommends broad access to models used for mathematical research: "We therefore advise the AI labs to grant the global mathematical community broad, equitable access to their publicly available models." Obviously, this did not happen.

green496.bsky.social@green496.bsky.social

Open AI just released hundreds of proofs of new mathematical results: openai.com/index/sharin... Here are some notable (to me) points:

Hardly any prompts or chain of thought was revealed, and no precise token counts were given (only an averaged estimate of time spent per problem).

"4. As far as possible, a proof released by an AI lab should be formalized." ✅/❌: Partial credit here! Some proofs were formalized on release, but many were not. Apparently this is work in progress? It is unclear why they were not all formalized.

green496.bsky.social@green496.bsky.social

Open AI just released hundreds of proofs of new mathematical results: openai.com/index/sharin... Here are some notable (to me) points:

"2. When results are announced, they should be deposited in a timely manner in appropriate scholarly repositories..." ❌This did not happen. They put the papers in github under an anonymous submitter. The traditional location would be arXiv.

"3. For each result released, the AI lab should make public the name of the model, the prompts used, a (summarized) chain of thought, the time taken, and the estimated cost of computation" ❌ This did not happen. The model was internal (it doesn't have a public name!), ...

green496.bsky.social@green496.bsky.social

Open AI just released hundreds of proofs of new mathematical results: openai.com/index/sharin... Here are some notable (to me) points:

1b) "The model, or some other model, should be prompted to produce a version of each proof that is written up in a style that follows the conventions of a traditional mathematical paper..." Again, just based on a skim, this set of papers seems to do reasonably well here.

They have introductions, theorem statements, outlines of key ideas in the proof, etc. Of course, LLMs excel at this sort of summarization. However, I do not know if the details of the technical exposition are as friendly to read. LLMs are notorious for producing lots of dense jargon.

green496.bsky.social@green496.bsky.social

Open AI just released hundreds of proofs of new mathematical results: openai.com/index/sharin... Here are some notable (to me) points:

1a: "The literature should be scoured for any ideas that are related to the ideas in the proofs of the results released. Even if the AI lab’s model discovered those ideas independently, it should follow standard mathematical practice and cite the papers in which the ideas were first introduced."

Obviously, it is impossible to audit this within a day of release. But this was one of the main complaints of the NS paper, to which additional citations were silently added a few days after the first release. So if that is any precedent, it is unlikely recommendation was systematically followed.

green496.bsky.social@green496.bsky.social

Open AI just released hundreds of proofs of new mathematical results: openai.com/index/sharin... Here are some notable (to me) points:

First, they outline two possible scenarios: one where a human understands the AI proof; essentially, this is where the AI is copilot, and how many mathematicians do research today. They advise no change from how mathematics has been distributed in the past.

The other case is when no human understand the AI proof (in all its detail). This is the case for essentially all recent OpenAI proofs. Here they have several detailed suggestions:

green496.bsky.social@green496.bsky.social

Open AI just released hundreds of proofs of new mathematical results: openai.com/index/sharin... Here are some notable (to me) points: