The Situation at Columbia XXXII

Posted on August 25, 2025 by woit

Actually, nothing really new at Columbia. New students arriving, classes start next week. Still tight security at the gates and the administration’s highest priority is to continue to ensure that no “antisemitic” protest of the war crimes going on in Gaza occurs on this campus. Some people here think this is great, some are appalled, most just don’t care.

I don’t think there’s anyone now unaware of the ongoing wholesale killing of innocents going on in Gaza as part of an ethnic cleansing campaign to drive the Palestinians from that land. The trustees and administration of Columbia know what is going on and have made their decision about their role in it.

In case you think this description of what is happening in Gaza is just the misguided opinion of one particular “antisemitic piece of shit”, here’s a clear explanation of what is going on from a New York Times commentator not known to be an “antisemitic piece of shit”:

I will leave it to historians to debate whether Israel is committing genocide in Gaza. But what is absolutely clear to me right now is that this Israeli government is committing suicide, homicide and fratricide.

It is destroying Israel’s standing in the world, it is killing Gazan civilians with seemingly no regard for innocent human life, and it is tearing apart Israeli society and world Jewry, between those Jews who want to still stand with Israel no matter what and those who can no longer tolerate, explain or justify where this Israeli government is taking the Jewish state and now want to distance themselves from it….

It is one thing for a country at war to justify collateral damage when going after the enemy’s top leaders. It is something entirely more sinister when you are killing and wounding dozens of civilians to try to kill, say, the deputy to the deputy commander.

It is also devious and sinister when you use your military to move hundreds of thousands of Gazan civilians from one part of Gaza to the other — under the guise of evacuating them from fighting zones — and then deliberately bulldoze the homes they left behind for no real military reason but with the clear ulterior motive of making life so miserable for them that they will leave the area entirely. And it is shameful when you stop and start humanitarian aid, with the hope that people will get hungry enough to leave.

But as I said, this is not just homicide pure and simple; it is also suicide and fratricide. Israel is now well on its way to making itself a pariah state.

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Pet Peeves

Posted on August 13, 2025 by woit

It’s getting hard to wake up every day, read the latest news of the slaughter of civilians in Gaza and the plans to finish off or exile the rest, then go through the two ID checks at the campus gate designed to make sure that no protests about this happen on campus, and when I get to my office resist the temptation to write a rant. But no one wants to read this, and it would probably violate the new rules we’re now living under here. So, I’ll complain instead about some pet peeves about theoretical particle physics.

This week there is the newest edition of a Pre-SUSY School in Santa Cruz, designed to train graduate students and postdocs. My first pet peeve is the whole concept of the thing. It starts off with an Introduction to Supersymmetry which introduces the MSSM, but why is anyone training graduate students and postdocs to work on supersymmetric extensions of the Standard Model? These were a failed idea pre-LHC (see my book…), and the LHC results conclusively confirm that failure.

The Introduction to Supersymmetry lectures given by Ben Allanach are an updated version of similar lectures given at other summer schools designed to train people in SUSY. These lectures trigger several of my pet peeves even before they get to SUSY. I’ve written about some of this before in detail, see here.

The first pet peeve is about the insistence on using the same notation for a Lie group and its Lie algebra. In both versions of the lecture notes, we’re told that
$$SO(1,3)\cong SL(2,\mathbf C)$$
and
$$SO(1,3) \cong SU(2) \times SU(2)$$
There are lots of problems with this. In the first case this is about the group $SO(1,3)$. In the next it’s about the Lie algebra $SO(1,3)$, but the same symbol is being used for both. One would guess that $\cong$ means two things are isomorphic, but that’s not true in either case.

More completely, in the older version of the notes, we’re told

there is a homeomorphism (not an isomorphism)
$$SO(1,3)\cong SL(2,\mathbf C)$$

“Homeomorphism” is nonsense, which has been fixed in the newer version to

there is a homomorphism (not an isomorphism)
$$SO(1,3)\cong SL(2,\mathbf C)$$

There’s still the problem of why a homomorphism that isn’t a isomorphism is getting written as $\cong$. The text does later explain what is really going on (there’s a 2-1 Lie group homomorphism from $SL(2,\mathbf C)$ to $SO(1,3)$).

The other equation is more completely given as

locally (i.e. in terms of the algebra), we have a correspondence
$$SO(1,3) \cong SU(2) \times SU(2)$$

The “locally (i.e. in terms of the algebra)” does help with the fact that the symbol $SO(1,3)$ means something different here, that it’s the Lie algebra of $SO(1,3)$ not the Lie group $SO(1,3)$ of the other equation. The word “correspondence” gives a hint that $\cong$ doesn’t mean “isomorphism”, but doesn’t tell you what it does mean.

A minor pet peeve here is calling the Lie algebra of a Lie group its “algebra”, dropping the “Lie”. For any group, its “group algebra” is something completely different (the algebra of functions on the group with the convolution product). Mostly when mathematicians talk about “algebras” they mean associative algebras, and a Lie algebra is not associative. Why drop the “Lie”?

What’s really true (as explained here) is that the Lie algebra of $SO(1,3)$ and the Lie algebra of $SU(2)\times SU(2)$ are different real Lie algebras with the same complexification (the Lie algebra of $SL(2,\mathbf C)\times SL(2,\mathbf C)$). In the earlier version of the notes there’s nothing about this. There’s the usual definition of two complex linear combinations
$$A_i=\frac{1}{2}(J_i +iK_i),\ \ B_i=\frac{1}{2}(J_i -iK_i)$$
of basis elements $J_i$ and $K_i$ of the Lie algebra of $SO(1,3)$, giving two separate copies of the Lie algebra of $SU(2)$. All we’re told there is that “these linear combinations are neither hermitian not anti-hermitian”.

In the newer version, this has been changed to describe these linear combinations as “hermitian linear combinations”. We’re told

The matrices representing both $J_i$ and $K_i$ have elements that are pure imaginary. (2.2) then implies that
$$(A_i)^∗ = −B_i$$
which is what discriminates $SO(4)$ from $SO(1, 3)$.

which I don’t really understand. Part of the source of the confusion here is confusion between Lie algebra elements (which don’t have a notion of Hermitian adjoint) and Lie algebra representation matrices for a unitary representation on a complex vector space (which do). Here there are different defining representations involved (spin for $SU(2)$ and vector for $SO(1,3)$).

There’s then a confusing version of the correct “$SO(1,3)$ and the Lie algebra of $SU(2)\times SU(2)$ are different real algebras with the same complexification”

the Lie algebra of $SO(1, 3)$ only contains two mutually commuting copies of the real Lie algebra of $SU(2)$ after a suitable complexification because only certain complex linear combinations of the Lie algebra of $SU(2) \times SU(2)$ are isomorphic to the Lie algebra of SO(1, 3).

Here’s an idea for a summer school for physics theory grad students and postdocs: teach them properly about $SO(3,1)$, $SO(4)$, their spin double covers, Lie algebras, complexifications of their Lie algebras and their representations. About SUSY extensions of the SM, just tell them these are a failure they should ignore (other than as a lesson for what not to do in the future).

Update: I strongly recommend Sabine Hossenfelder’s latest video, Scientific research has big problems, and it’s getting worse. She’s been attacked over the years for this kind of critique, most recently as “a disgusting fraud peddling propaganda for fascist oligarchs”, but it’s a very important one that deserves to be taken seriously. In the video she starts out by pointing to a huge problem with scientific research that is getting much, much worse very fast: paper mills and bogus papers, a problem now being turbocharged by AI.

SUSY research is I think one of the things that has, for good reason, motivated her critique. Why is there a huge still active field of people writing papers about a failed idea? What are the incentives and sociology that create this sort of phenomenon? The topic of this posting explains where I very much disagree with Hossenfelder. She likes to name the problem in fundamental physics as “Mathematical Fiction” (quotes others as describing the problem as “Mathematical Gymnastics” or “Mathematical Cosmology”). But looking at the training of SUSY researchers here, the problem is not too much mathematics, but too little. Too many physicists firmly believe that understanding the basic details of what they are doing is a waste of time, that mathematician’s insistence on clear, unambiguous and precise statements is nothing but pedantry. But if you have only a hazy idea of what the fundamental objects in your theory are and how they behave, absent the discipline of experimental tests, you have no hope of distinguishing what works from what doesn’t. SUSY research is an extreme case, where even failed experimental tests only slow the enterprise down, don’t stop it.

Given what is happening in the US, it is important to make clear the sort of reevaluation of federal support of science that Hossenfelder’s critiques implies is needed. Such a reevaluation would require a strong dedication to distinguishing truth from lies. The current defunding of science at US research universities based on pro-genocide fanaticism and a mountain of lies about “antisemitism” is the opposite of what is needed.

Update: The problem with theorists being totally confused about Lie groups vs. Lie algebras and the symmetry groups of spin in 3 and 4 dimensions is not just in the SUSY subfield. For another example, take a look at Appendix A here which starts off with a definition of the SU(2) group that is half a definition of the Lie algebra (up to i, self-adjoint matrices), half a definition of the group (det=1). Things go downhill from there in the rest of the section. Why would anyone write this “pedagogical” discussion when they didn’t understand this at all? Why did none of the five co-authors or a referee notice that this section was complete nonsense?

Update: For the latest on SUSY claims see here. The same story as at any time for the past forty years: no superpartners = no problem, since SUSY “predicts” superpartners just beyond the reach of current and past searches. Nowadays this is accomplished by invoking the landscape and “string naturalness”.

Update: The yearly SUSY conference is over, and you can check out the concluding “Vision Talk”. The “Vision” (see page 30) is just basically extreme wishful thinking that future experiments will find superpartners.

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The Situation at Columbia XXXI

Posted on August 1, 2025 by woit

Columbia’s new policies intended to stop and punish any on-campus criticism of the Gaza genocide by characterizing it as “antisemitism” have made it impossible for Rashid Khalidi to teach his planned fall course. See his explanation here, which ends with:

Columbia’s capitulation has turned a university that was once a site of free inquiry and learning into a shadow of its former self, an-anti university, a gated security zone with electronic entry controls, a place of fear and loathing, where faculty and students are told from on high what they can teach and say, under penalty of severe sanctions. Disgracefully, all of this is being done to cover up one of the greatest crimes of this century, the ongoing genocide in Gaza, a crime in which Columbia’s leadership is now fully complicit.

Update: The Knight First Amendment Institute here at Columbia has put up on its website a document What the Columbia Settlement Really Means, which explains in detail many of the problems with what the trustees have committed the institution to. Some extracts:

The settlement is an astonishing transfer of autonomy and authority to the government—and not just to the government, but to an administration whose disdain for the values of the academy is demonstrated anew every day. It will have far-reaching implications for free speech and academic freedom at Columbia—even if we assume that the provisions that are susceptible to more than one interpretation will be construed narrowly, as the settlement itself says they should be (¶ 5). We also doubt that the Trump administration will be satisfied with the territory it has won. The settlement does not foreclose the Trump administration from demanding more from Columbia on the basis of the university’s real or imagined failure to comply with the settlement’s terms, or on the basis of purported transgressions that are new or newly discovered. Indeed, the settlement itself gives the administration an array of new tools to use in the service of its coercive campaign…

The July 23 settlement also limits Columbia’s authority over the hiring of faculty and administrators. It obliges Columbia to appoint new faculty members “with joint positions in both the Institute for Israel and Jewish Studies and the departments or fields of economics, political science, or [public policy]”—faculty members who will (the settlement says, without explaining) “contribute to a robust and intellectually diverse academic environment” (¶ 13). We know of no precedent for the federal government compelling a private university to hire faculty in specific fields, let alone dictating the specific institutes and departments to which they must be appointed…

The cumulative effect of these terms will be, again, to subject Columbia’s administrators, faculty, and students to a regime of intense surveillance. The surveillance is a significant incursion into the university’s autonomy and will inevitably deter faculty and students in their exercise of constitutionally protected freedoms. It may also provide the Trump administration with pretexts to make new demands of the university…

Columbia has been the target of a months-long campaign of extortion by a presidential administration that is contemptuous of legal constraint and deeply hostile to the values that universities exist to promote. We are not convinced the settlement will put this behind us. What we can say with confidence is that the settlement comes at a very steep price to Columbia’s autonomy and to the constitutional freedoms of Columbia’s faculty, staff, and students. All of us affiliated with Columbia should understand this—and administrators, faculty, and students at other universities should know how much is at stake in their own institutions’ negotiations with the Trump administration.


Update: Another open letter to Claire Shipman, this one from Marianne Hirsch.

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Various and Sundry

Posted on July 31, 2025 by woit

Some random things that may be of interest:

  • Ethan Siegel has a discussion of “vibe physics“, people convincing themselves that they can solve fundamental scientific problems by chatting with an LLM. For a story about one billionaire doing this, see here.

    LLMs should be much better than the usual crackpots at generating worthless papers about theoretical physics, likely should be able to generate papers not easy to distinguish from a lot of what is on the arXiv. I’m wondering how much of this has already happened.

    In math, Daniel Litt has noticed a bunch of recent LLM-generated worthless papers on the Hodge conjecture. As examples, he points to these, four papers posted during the past month. Unfortunately the arXiv does not seem to now have an effective way to protect itself against these things getting posted, or to get them removed once identified (Daniel identified them publicly two weeks ago, no indication anything will be done about this).

  • Also on the arXiv is an article by George Lusztig which goes over some history, with this summary

    By publishing this document I aim to rectify the historical narrative for the benefit of the mathematical community and of the general public and to ensure that proper attribution and academic integrity is upheld by all.
    I trust that all readers -including Kashiwara- will recognize these established facts:

    (a) The canonical basis was first defined in my work [L90] and Kashiwara’s subsequent contribution built directly on this foundation.
    (b) The crystal basis is not solely Kashiwara’s discovery.

    And everyone who knows the history would suggest Kashiwara to publicly acknowledge (a) and (b), to correct all false and misleading information once and for all.

  • Another one has been added to the list of Leinweber Institutes for Theoretical Physics, discussed here. It’s the new Leinweber Institute for Theoretical Physics at Stanford, previously called the Stanford Institute for Theoretical Physics.
  • UCSB has announced that they’ve digitized Joe Polchinski’s papers. The link they give doesn’t appear to work and I don’t know of any other way to access this archive. The link now works.
  • The Chinese each year are now organizing a conference that covers mathematics and theoretical physics on a truly massive scale, called the International Congress of Basic Science. You can keep busy by watching 390 talks on Youtube.
  • At Strings 2025 earlier this year there was not yet a plan for a Strings 2026. The Chinese have also taken this on, Strings 2026 will be in Shanghai.
  • For a podcast worth watching, see Curt Jaimungal’s interview with Nikita Nekrasov.
  • For another one, there’s Sean Carroll talking to David Tong. I especially recommend the part around 52 minutes in, where Tong advertises a crucial hole in our understanding of the Standard Model: the non-perturbative formulation of the chiral gauge theory of the electroweak sector, in particular the lack of a viable lattice formulation.
  • Last month there was the Open Symposium on the European Strategy for Particle Physics in Venice. Crucial numbers are in this report: 8-9 billion to build a linear collider, a big new ring (FCC) would be 15 billion for an initial lepton machine, another 19 for a higher energy proton machine (these are rough numbers, think of as dollars, euros or swiss francs). The FCC project has been the leading proposal, but the crucial question is whether such a thing is financially viable.

Update: Daniel Litt has also written about this on his blog. There’s a comment there from “knzhou” saying
“This is also happening in hep-ph, which now has an average of 1-2 nonsensical papers per day.”


Update: Terry Tao’s NSF grant at UCLA has been suspended (along with 279 others), because UCLA is “antisemitic” since there were anti-genocide protests there last year. Unclear to me in this case which pro-genocide forces are collaborating with the dictator to shutdown Terry Tao, and why they are doing it.

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The Situation at Columbia XXX

Posted on July 26, 2025 by woit

The trustees on Friday changed the Charters and Statutes of the university, something it seems they can just do when they feel like it, without consulting with anyone or telling the community what they’ve done. Stand Columbia (Tao Tan) is pleased they’ve done this, so has checked the new version against the old, you can see his analysis here.

This has all been done as part of the capitulation to Trump and those forces inside and outside the university that want to make sure that any anti-Israeli protests are punished as severely as possible. The changes to the statutes remove control of the discipline process from the Senate and put it completely under the control of the trustees. The Senate no longer has any say in the Rules of University Conduct, these will be set by the trustees (with the help of the provost’s office). The disciplinary process will be managed purely by the provost’s office, which vets anyone involved to be sure that they will follow trustee policy. If you’re wondering how Columbia could now be expelling students for participating in a library reading room non-violent protest against genocide (a sort of harsh penalty for non-violent protest unheard of in the institution’s history) this is how it’s being done.

Of course the reason that they’re doing it is that Stephen Miller has demanded it. If they don’t expel students who protest the Gaza genocide, Columbia’s federal funding will again be removed. No matter how awful the Gaza situation gets, if you try and protest it on the Columbia campus this fall, you will face expulsion. I doubt we’ll see many cases of this actually happening, the threat alone will do an excellent job of keeping everyone quiet.

Bari Weiss has spent 25 years fighting for punishment of anti-Israeli sentiment at Columbia. Her Free Press yesterday explains how this will now work:

A senior Trump administration official familiar with the negotiations said that “this is just step one.” The official added: “In late August, the kids and faculty come back to campus, and many of them believe they—and not the board or administration—are in charge of Columbia. . . . The substantive challenge is resetting the balance of power and reasserting the leadership of the school and letting the students and faculty know that for the first time in many decades, there will be order on campus and consequences for breaking the rules.”

If that doesn’t happen, “the administration is not going to let Columbia embarrass us,” the senior Trump administration official added. “We’ll be watching you.”

Among the many messages from Shipman and others announcing the new cave-in, I didn’t see any discussion of these changes. There were a lot of claims that Columbia was not giving up its independence, and it remains true that it is not Stephen Miller who is deciding to expel students. Instead he’ll be calling up the trustees and telling them they have to do it, since he “is not going to let Columbia embarrass us.” Actually, since everyone involved knows he can do this if displeased, he won’t have to do anything: they’ll be sure not to make any decisions Stephen Miller would not approve of.

The FAQ here asks everyone to

Please use this form to report violations stemming from demonstrations and protests under the Rules of University Conduct.

There, if you see anyone protesting the genocide in Gaza, you can file an “Alleged Protest/Demonstration Violation”.

Update: People are wondering who gets the \$21 million for being a victim of “antisemitism”. James Schamus has questions about this:

it’s quite possible that those of my fellow Jews who “may experience antisemitism” the most when encountering campus protests against Israel’s genocidal mania may end up getting the biggest bucks. Like maybe there will be different categories, ranging from the small-change hand-wringing “I’m-uncomfortable-with-what-Israel-is-doing-but-Hamas-tunnels-something-something-your-keffiyeh-makes-me-nervous” category; through the Bret Stephens/New York Times mid-tier “Genocide? What genocide?” bunch; and ending with the Megabucks Jackpot we’re-in-the-money Shai Davidai “We are not ok!” crowd. Maybe there can be a special bonus for the Columbia OU-JLIC director who WhatsApp’d hundreds of Jewish students last year urging them to flee campus for their lives.

As you can see, under this possible scenario, the more you go all-out weaponizing antisemitism in the context of Israel’s mass murder spree, the more Columbia \$$$ you earn. Nice work if you can get it!

In any case, I’m standing by for further instructions, with just one last favor to ask: please don’t hire some outside consulting group, such as, say, the Boston Consulting Group, Orbis Operations, or Safe Reach Solutions, to administer distribution of the fund. We wouldn’t want the giveaway to turn into some sort of Hunger Games now, would we?

Israeli human rights organizations are now agreeing that the students were right, the Gaza war is genocide. Latest news today is that Netanyahu is promising to annex Gaza in order to appease the part of his government which wants to starve the Palestinians to death. If you are at Columbia and all this seems to be worth protesting, better you stay quiet or you might face expulsion. On the other hand, if what upsets you is anti-genocide protest, maybe Columbia is going to write you a large check (if you’re the right ethnicity).

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The Situation at Columbia XXIX

Posted on July 24, 2025 by woit

The long-awaited second cave-in by the Columbia trustees to Trump demands was announced yesterday, details here. A few initial comments:

  • Columbia law professor David Pozen explains that this is part of a new form of autocratic government in the US:

    the agreement grows out of the executive branch’s first-ever cutoff of congressionally appropriated funds to a university, so as to punish that university and impel it to adopt sweeping reforms, without any pretense of following the congressionally mandated procedures. Lawyers have been debating the exact circumstances under which the executive branch may freeze particular grants and contracts to particular schools. Yet as far as I’m aware, no lawyer outside the government has even attempted to defend the legality of the initial cutoff that brought Columbia to its knees and, thereafter, to the “negotiating” table.

    We’re now governed not by laws and courts, but by a dictator, who can at any moment take illegal actions to try and compel you to do what he wants. Laws and courts are replaced by extorted “agreements” like this one, where the dictator agrees to leave you alone (for now) in return for your agreement to a specific list of demands.

  • The deal the trustees have negotiated in order to (for now) get money back and stop further illegal actions is not as bad as expected. It’s mostly a mix of the already agreed to set of policies designed to ruthlessly stop any criticism of the Israeli genocide in Gaza, as well as shutting down past DEI and admission favoritism policies that already were either banned by court decisions or likely to be banned by legitimately legal changes in federal government policies. This is much less than the demands the dictator’s people had been making. The Chronicle story about this has:

    “Columbia couldn’t tolerate the administration holding up billions of dollars in current and future grants, so they paid what is essentially ransom,” said Michael C. Dorf, a professor of law at Cornell University. “The ransom that they ended up paying strikes me as a pretty good value if you decide you’re going to pay ransom. But the problem with paying ransom is that it incentivizes the taking of more hostages.”

  • The only reason they were able to get these relatively favorable terms was that Harvard decided to go to court and fight the illegality. Harvard has won a series of injunctions stopping illegal actions regarding foreign students, and appears likely to very soon win a summary judgment that the withholding of grant funds was illegal. In late March, Columbia’s initial cave-in (in return for nothing) made it look as if there was no way to stop the exercise of dictatorial powers. While the Columbia trustees adopted a policy of publicly supporting the new dictatorship (telling us that it was all legal, and all necessary to deal with the fact that our community had a terrible “antisemitism” problem), throughout the country luckily other groups and institutions did go to court and fought back. They’ve had mixed success, but have slowed down the onslaught and caused Trump to back off at least for now in some areas.

    In early April the trustees were about to sign off on a second cave-in much more onerous than the one announced yesterday, but stopped this when they saw that Harvard was going to fight. They can argue that the set of facts Harvard was facing was different, but there’s no denying that their choice not to fight but to capitulate to extortion by the new dictatorship did damage to US democracy, while Harvard’s decision to fight reversed some of that damage (at least for now).

    What Harvard has done has helped Columbia and other institutions a great deal by blunting the dictator’s onslaught. What Columbia has done has hurt all other universities, as the success here of illegal dictatorial action will encourage its use against others. This wider campaign surely is just about to get started, maybe could have been stopped by a Columbia refusal to give in.

  • The really big winners here? Those so devoted to supporting the Israeli government slaughter of civilians and ethnic cleansing of Gaza and the West Bank that they were willing to collaborate with and help a Fascist dictatorship destroy US democracy and seriously damage the university in order to get what they wanted: expulsion of student demonstrators and a campus lockdown that would put a stop to the demonstrations, together with university support for a campaign to characterize opposition to genocide and ethnic cleansing as “antisemitism”.
  • A crucial part of what the trustees agreed to is in section 8c:

    Nothing in this Agreement prevents the United States (even during the period of the Agreement) from conducting subsequent compliance reviews, investigations, defunding or litigation related to Columbia’s actions occurring after the Effective Date of the this Agreement.

    So, the trustees explicitly agree that if Columbia does anything Trump doesn’t like, he can defund the university again. Instead of going to court to fight illegality, the agreement explicitly acknowledges that the illegality is a tactic that can be used against Columbia at any time it offends the dictator. What this means in practice is every university decision from now on will be made through the lens of “will this upset Steven Miller?”

  • Sone things to watch for:

    Will the university gates be reopened, or will we live in security lockdown forever?

    Our next president will have to meet with Steven Miller’s approval, and be willing to run the university in a way that will not annoy Steven Miller. Who is that going to be?

    As the genocide in Gaza proceeds, will anyone at Columbia be protesting this on campus?

    The trustees have agreed to a discipline process designed to achieve the expulsion of anti-genocide demonstrators. This requires the participation of the provost, some administrators, deans and faculty. Will we be told who has agreed to do this dirty work?

There’s a lot of good commentary about this coming out. The NYT published this piece by Suresh Naidu. Some people at CUIMC have created a wonderful satirical version of Columbia Spectator, call The Specter. They’re covering the cave-in with Columbia Buys Back Its Federal Grants and Sells Off Its Spine.

Update: Stand Columbia (Tao Tan) is ecstatic. Illegal dictatorial action has gotten him changes at Columbia he has always wanted. The only problem he sees is that maybe they won’t be as much as he wants. He is creating a Stand Columbia Society Scorecard so that, in the case of insufficient devotion to the new order, Steven Miller will get a heads up that he needs to pull funding again.

Lawrence Summers is also very happy that extortion by the dictatorship is getting him what he wants. “the best day higher education has had in the last year.”!!

Update: In case anyone was thinking that the “agreement” meant reopening of the campus and a less repressive security environment, there’s this from the Free Press:

A senior Trump administration official familiar with the negotiations said that “this is just step one.” The official added: “In late August, the kids and faculty come back to campus, and many of them believe they—and not the board or administration—are in charge of Columbia. . . . The substantive challenge is resetting the balance of power and reasserting the leadership of the school and letting the students and faculty know that for the first time in many decades, there will be order on campus and consequences for breaking the rules.”

If that doesn’t happen, “the administration is not going to let Columbia embarrass us,” the senior Trump administration official added. “We’ll be watching you.”

So, if you’re a Columbia student or faculty member, and all those photos of dead, emaciated children in Gaza are getting you upset about the genocide there, don’t even think of saying or thinking anything about this on the Columbia campus. A senior Trump administration official says “we’ll be watching you”, and discipline via the Provost’s office will be ready to deal with you.

What the trustees have done is make themselves and the Provost’s office the enforcers for those defending the Israeli genocide. They will have to play this role, or get a letter from the “senior Trump administration official” telling them they have embarrassed him and funding is cutoff again.

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The Situation at Columbia XXVIII

Posted on July 22, 2025 by woit

When I first started writing here about what was going on at Columbia, part of the motivation was that I didn’t understand myself a lot of what was happening, especially the actions of the trustees. Things are different now, I think I understand pretty well what is going on and why the trustees are doing what they are doing. A new cave-in is in the works and at some point I’ll write about the complicated story of that, perhaps waiting until it’s a done deal, which might be soon.

At the moment though it seems to me important to just focus on a basic point of morality: an appalling genocide is going on in Gaza, and Columbia University’s response to this genocide is an all-out campaign to stop people from protesting it. This is completely disgraceful.

It’s difficult to get reliable information about what is happening in Gaza, partly because the Israelis have killed most journalists there (and are starving to death the few remaining). All indications are that the Israeli government is pursuing a policy of destroying all homes and infrastructure there, to make sure the inhabitants driven out have nothing to return to. Civilians are being killed and starved with the goal of forcing them somehow to leave. Among the most reliable sources of information are the New York Times and the Wall Street Journal, which have detailed stories (see here and here) explaining how starving people seeking food are being killed.

The New York Times has recently published a long article by an Israeli scholar considered a leading authority on genocide entitled I’m a Genocide Scholar. I Know It When I See It. that strongly makes the case that what is going on is genocide.

What has been Columbia University’s response to the moral challenge of this ongoing US-supported genocide?

  • A new set of policies promulgated last week, including adopting a definition of “antisemitism” that can be used to tar criticism of Israeli genocidal policies as “antisemitic”. For some commentary on this from a Columbia faculty member, see here.
  • For the past year the university has been locked-down, with an intensive security apparatus whose main goal appears to be to make sure that no anti-genocide protests take place on the campus.
  • As part of the first cave-in back in March, the trustees removed control of the student disciplinary process from the University Senate, with the trustees taking control themselves of the process through the provost’s office. The intent was to make sure that any student guilty of violating university regulations during an anti-genocide protest would be severely punished. One goal is to make sure that students engaged in such protest are removed from the university and can’t do it again. Another is to make sure that anyone else thinking about what they can do to oppose genocide will be properly intimidated. Last week the trustees issued a statement emphasizing that they, not the Senate, are now in control of student discipline.
  • The last two actions have been almost completely successful at stopping any anti-genocide protest on campus. The main exception was the short-lived occupation of a library reading room (see here) back in May. Today the university announced that a large number of students were being suspended or expelled under this new policy. News stories like this one say that 70 students were involved, with two-thirds of them expelled or suspended for at least two years. The news stories make clear that the motivation for these unusually harsh punishments is the desire of the trustees to appease our Fascist dictator and recover grant funding.

The question of what to do about students who engage in disruptive protests is a complicated one. For a history of how Columbia has dealt with such cases in the past, see here. What the trustees and some administrators have done today appears to be completely unprecedented, and part of a deeply immoral set of policy decisions about how to respond to the problems caused by the genocide in Gaza.

Update: For more of the story of how the disciplinary process at Columbia was taken over by the trustees, in contradiction to university statutes, see here. I can’t find on university websites a list of current members of the new University Judicial Boards. Much of the information on university websites still refers to the old Senate-controlled board (see for instance the link describing the UJB at this page). There is an updated FAQ posted yesterday.

The only description I can find of the new UJB panels is that they are made up of “professors and administrators”. Until now, the cave-in has been mostly in the hands of the trustees. With these new actions the moral rot has spread from the trustees to the office of the provost and to (unknown?) groups of faculty and administrators who have signed on to participate in this. There now is some sort of appeals process which is in the hands of “three deans”. Will we find out who they are and will they go along with this?

Haaretz today has this story with the details of how the murder of civilians through starvation is being accomplished.

Update: As expected, Columbia has reached some sort of agreement with the Trump people. I’ll try and write something about this tomorrow. In the meantime, there’s a story at the NYT, and also a very good NYT opinion piece by Suresh Naidu.

For comments discussing the agreement, better if you can wait for the next blog post which will be about that topic.

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Mathematicians interact with AI, July 2025 update

Posted on July 4, 2025 by Aravind Asok

This is a guest post from Aravind Asok1. If you have comments about this, you can contact him at asok@usc.edu. We’ll see if there’s some way to later post moderated comments here.

Recently, several symposia have been organized in which groups of mathematicians interacted with developers of various AI systems (specifically, reasoning models) in a structured way. We have in mind the Frontier Math Symposium hosted by Epoch AI and the Deepmind/IAS workshop. The first of these events received more coverage in the press than the second. It spawned several articles including pieces in Scientific American and the Financial Times, though both articles are currently behind a paywall.2 Curiously absent from these discussions is any kind of considered opinion of mathematicians regarding these interactions, though hyperbolic quotes from these pieces have made the rounds on social media. Neither of these events was open to the public: participation in both events was limited and by invitation. In both cases the goal was to foster transparent and unguarded interactions.

For context, note that many mathematicians have spent time interacting with reasoning models (Open AI’s ChatGPT, Google’s Gemini, and Anthropic’s Claude among others). While mathematicians were certainly not exempt from the wave of early prompt-based experimentation with initial public models of ChatGPT, they have also explored the behavior of reasoning models on professional aspects of mathematics, testing the models on research mathematics, homework problems, example problems for various classes as well as mathematics competition problems. Anecdotally, reactions run the gamut from dismissal3 to surprise.4 However, a structured group interaction with reasoning models provides a qualitatively different experience than these personal explorations. Since invitation to these events was controlled, their audience was necessarily limited; the Epoch event self-selected for those who expressed specific interest in AI,5 though the IAS/Deepmind event tried to generate a more random cross section of mathematicians.
Much press coverage has a breathless feel, e.g., including coverage of comments by Sam Altman in, say, Fortune.6 It seems fair to say that mathematicians are impressed with the current performance of models, and, furthermore, see interesting avenues for augmenting mathematical research using AI tools. However, many mathematicians view the rhetoric that “math can be solved”, extrapolating from progress on competition-style mathematics viewed as a game, as problematic at best, and at worst presenting a fundamental misunderstanding of the goals of research mathematics as a whole.

Our discussion here will focus on the Epoch AI-sponsored meeting for concreteness, which was not “secret” in any dramatic or clandestine sense, contrary to some reports. The backstory: Epoch AI has been trying to create benchmarks for the performance of various released LLMs7 (a.k.a., chatbots like Open AI’s ChatGPT, Anthropic’s Claude, Google Deepmind’s Gemini, etc.).8 Frontier Math is a benchmark designed to evaluate the mathematical capabilities of reasoning models. This benchmark consists of tiered lists of problems. Tier 1 problems amount to “mathematical olympiad” level problems, while Tiers 2 and 3 are “more challenging” requiring “specialized knowledge at the graduate level.” Frontier Math sought to build a Tier 4 benchmark of “research
level” problems.

Building the Tier 4 benchmark necessitated involving research mathematicians. Earlier this year, Epoch reached out to mathematicians through varying channels. Initial requests promised some amount of money for delivering a problem of a particular type, but many mathematicians unfamiliar with the source of the communication either dismissed it as not credible or had no interest in the monetary compensation.9 To speed up the collection of Tier 4 problems, Epoch came up with the idea of hosting a symposium. The symposium was advertised on several social media outlets (e.g., Twitter) and various mathematicians were contacted directly by e-mail. Interested participants were sometimes asked to interview with Frontier Math lead mathematician Elliot Glazer and also to produce a prospective problem. Mathematics is a fairly small community so many of the people who attended already knew others who were attending; also the vast majority of attendees came from California. Participants did sign a non-disclosure agreement, but it was limited to information related to the problems that were to be delivered. Symposium participants also had their travel and lodging covered, and were paid a \$1500 stipend for their participation.

Participants were given a list of criteria for problem construction; problems must: 10

  1. Have a definite, verifiable answer (e.g., a large integer, a symbolic real, or a tuple of such objects) that can be checked computationally.
  2. Resist guesswork: Answers should be “guessproof,” meaning random attempts or trivial brute-force approaches have a negligible chance of success. You should be confident that a person or AI who has found the answer has legitimately reasoned through the underlying mathematics.
  3. Be computationally tractable: The solution of a computationally intensive problem must include scripts demonstrating how to find the answer, starting only from standard knowledge of the field. These scripts must cumulatively run less than a hour on standard hardware.

The participants were divided into groups based on field specificity (number theory, analysis, algebraic geometry, topology/geometry and combinatorics) and told to produce suitable problems.

How did participants contextualize this challenge? In mathematics research one frequently does not know in advance the solution to a given problem, nor whether the problem is computationally tractable. In fact, many mathematicians will agree that knowing a problem is soluble can be game-changing.11 Moreover, deciding which problems should be deemed worthy of study can be difficult. As a consequence, by and large, participants did not frame the challenge as one of producing research problems, but rather one of simply producing appropriate problems.

Unsurprisingly, ability to construct such problems varied from subject to subject. For example, one geometer said that it was quite difficult to construct “interesting” problems subject to the constraints. There are also real questions about the extent to which “ability to resist guesswork” truly measures “mathematical understanding”. Many participants were rather open about this: even if AI managed to solve the problems they created, they did not feel that would constitute “understanding” in any real sense.

While most participants had written and submitted problems before the symposium started, few people had an idea at that point of what would be “easy” or “hard” for a model. Most of the first day was spent seeing how models interacted with these preliminary problems, and the subsequent discussions refined participants’ understanding of the stipulation that problems were resistant to guesswork. Along the way, models did manage to “solve” some of the problems, but that statement deserves qualification and a more detailed understanding of what constitutes a “solution”.

One key feature of reasoning models was explicit display of “reasoning traces”, showing the models “thinking”. These traces displayed models searching the web and identifying related papers, but their ability to do so was sensitive to the formulation of the problem in fascinating ways. For example, in algebraic geometry, formulating a problem in terms of commutative ring theory instead of varieties could elicit different responses from a model. However, it is a cornerstone of human algebraic geometry to be able to pass back and forth between the two points of view with relative ease. In geometry/topology, participants noted that models demonstrated no aptitude for geometric reasoning. For example, models could not create simple pictorial models (knot diagrams were specifically mentioned) for problems and manipulate them.12 In algebraic and enumerative combinatorics, models applied standard methods well (e.g., solving linear recurrences, appealing to binomial identities), but if problems required several steps as well as ingenuity models were stymied, even if they were prompted with relevant literature or correct initial steps.

When a model did output a correct answer, examining the reasoning traces sometimes indicated that happened because the problem was constructed in such a way that the answer could be obtained by solving a much simpler but related problem. In terms of the exam solution paradigm, we would probably say such a response was “getting the right
answer for the wrong reason” and assign a failing grade to such a solution!

Participants were routinely told to aim to craft problems that even putative future reasoning models would find difficult. From that standpoint, it was easy to extrapolate that a future model might behave in a more human way, demonstrate “understanding” in a human sense, and isolate the missing key ingredient. This created a pervasive fear that if reasoning traces indicated models seemed “close now”, then one should extrapolate that the problems would be solvable by future models.13 Participants did observe that if literature in a particular domain was suitably saturated, the models could identify lemmas that would be appropriate and generate relevant mathematics. This was certainly impressive, but one wonders to what extent the natural language output affects perception of the coherence of responses: it is easy for things to “look about right” if one does not read too closely! Eventually, participants did converge on problems that were thought to meet the required bar.

The language models that we worked with were definitely good at keyword search, routinely generating useful lists of references. The models also excelled at natural language text generation and could generate non-trivial code, which made them useful in producing examples. However, press-reporting sometimes exaggerated this, suggesting that reasoning models are “faster” or “better” than professional mathematicians. Of course, such statements are very open to interpretation. On the one hand, this could be trivially true, e.g., calculators are routinely faster than professional mathematicians at adding numbers. Less trivially, it could mean automating complicated algebraic computations, but even this would be viewed by most mathematicians as far from the core essence of mathematical discovery.

The participants at the meeting form a rather thin cross-section of mathematicians who have some interest in the interface between AI (broadly construed) and mathematics. The symposium Signal chat became very active after the Scientific American article was posted. Undoubtedly participants felt there were exciting possible uses of AI for the development of mathematics. There are also real questions about whether or when future “reasoning models” will approach “human-level”competence,14 as well as serious and fascinating philosophical questions about what that even means; this is a direct challenge for the mathematics community. What does it mean to competently do research mathematics? What is valuable or important mathematics?

Finally, there are important practical questions about the impact, e.g., environmental or geopolitical, of computing at this level.15 All these questions deserve attention: barring some additional as-yet-unseen theoretical roadblock, reasoning models seem likely to continue improving, underscoring the importance of these questions. As things stand, however—particularly when it comes to mathematical reasoning—caution seems warranted in extrapolating future research proficiency of models.

  1. With the aid of generous input from Ben Antieau, Greta Panova, Kyler Siegel, Ravi Vakil, and Akshay Venkatesh.↩︎
  2. Some discussion of the IAS/Deepmind event is available on Michael Harris’ June 8 substack post.↩︎
  3. It seems many people have a collection of standard mathematical questions for which reasoning models produce only hallucinatory outputs. Some discussion of the disconnect between stated AI benchmark progress on mathematics as opposed to “real” research as of March 2025 can be found in the article The Disconnect Between AI Benchmarks and Math Research.↩︎
  4. The performance of language models on standard exam questions for undergraduate and graduate classes was a routine source of surprise. However, one expects reasoning models should perform better in areas where literature is dense. People are also routinely impressed by the fact that the models have improved so much over time.↩︎
  5. We would be remiss not mention that many mathematicians justifiably have concerns about legitimizing corporate technological endeavors. Such worries are especially important since the companies developing reasoning models plausibly view “mathematical progress”, say in terms of ability of models to solve mathematical problems of various types, as a way to distinguish amongst themselves. The vague statement “our model is good at math” can simultaneously be propaganda or simply false depending on context and audience.↩︎
  6. Altman states: “In some sense AIs are like a top competitive programmer in the world now or AIs can get a top score on the world’s hardest math competitions or AIs can do problems that I’d expect an expert PhD in my field to do”. When Altman makes such a statement, given his role, it’s easy to question his intentions. However, one cannot help but interpret his comments differently if there are also mathematicians making statements that can be construed as “AI systems are good at math”. Even vague statements to this effect by mathematicians could be used to minimize legislative targeting, or avoid scrutiny.↩︎
  7. See Epoch AI’s benchmarking dashboard for a more detailed discussion.↩︎
  8. See here for a blogpost giving some context to math benchmarks, a little bit of background in “reasoning models” as well as discussion of computational
    efforts involved.↩︎
  9. Some discussion of these requests took place at the Joint Mathematics Meetings (JMM), which was held in Seattle in January. According to some comments here, mathematicians expressed skepticism at delivering problems for money
    exposing a fundamental disjunction between academia and industry: pure mathematicians aspire to study mathematics to advance understanding, but industry researchers are required to deliver creations that buoy their supporting institutions.↩︎
  10. See https://epoch.ai/frontiermath/tier-4 for further discussion of Tier 4 problems.↩︎
  11. It is also worth pointing out that formalizing “inherent difficulty of proof discovery”, say in terms of decision problems, led to significant theoretical challenges to previous generation approaches to artificial intelligence. For a recent revision and extension of this notion of difficulty, see Artifical intelligence and inherent mathematical difficulty by W. Dean and A. Naibo. Once again, it is unclear whether such an approach has any bearing on what mathematicians might view as important for mathematics.↩︎
  12. More broadly, the sense was that forthcoming AI systems would be able to navigate the literature, including obscure corners, and would be quite capable at performing “standard”computations. Mathematicians themselves have created plenty of open source computational packages (SnapPy, Regina), which are already integrated
    into Python and hence automatically part of the toolkit to which a model has access. However, models seemingly lacked what mathematicians call geometric intuition.↩︎
  13. There’s a phenomenon alluded to in the Scientific American article as “proof by intimidation” which exposes a relevant phenomenon. If someone asserts boldly that they have solved a problem in a particular research domain, they have sufficient status and the approach they describe includes keywords/techniques that seem like they
    should have bearing on the problem, mathematicians tend to give them the benefit of the doubt. Indeed, mathematicians will frequently believe the problem has been solved without going through the “solution” in detail. It also routinely happens in mathematical practice that such “solutions” break down under additional scrutiny, e.g., because some subtle part of the argument was not sufficiently well explained. This discussion seems relevant to participants perception of putative “solutions” provided by the models. Moreover, many of the stories of “solutions to problems” travelled between groups, creating a kind of echo effect.↩︎
  14. Recent mathoverflow posts raise the question: Is this a bad moment for a math career in the context of news over AI models. The conversation around AI and jobs also extends to current fears. For example, without being precise yet about what we mean by AI, graduate students, especially at some larger public universities, are being tasked to “use AI” to speed up their workflow, frequently leading to despair.↩︎
  15. Environmental impacts of generative AI include increased electricity demand and water consumption sometimes localized to data center construction. See Michael Harris’s substack for a recent discussion with some links.↩︎
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This Week’s Hype

Posted on July 4, 2025 by woit

Absurd press releases from major universities hyping the idea that “string theorists have finally found a way to test string theory” have been a feature of theoretical physics for decades now. This nonsense is never going to stop. Latest example is here, based on this paper.

If the LHC were to find states such as those discussed in this paper, it would take less than 24 hours for there to be several papers on the arXiv giving a “string phenomenology” explanation for them. As a way to discredit science and the scientific method, this kind of press release is pretty effective.

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The Situation at Columbia XXVII

Posted on July 2, 2025 by woit

I’ll be heading out on vacation tomorrow morning, on a road trip first to Montreal, then Nova Scotia and Newfoundland, back at work on the 21st. While away I’ll try to detox from reading or thinking about the topics of this series of postings. Very much looking forward to being away from Columbia and outside this country for a while.

In non-Columbia news, yesterday Penn bent the knee and caved-in to Trump. The interesting question now is whether this gets them back the \$175 million in grants which was illegally withheld from them based on this Title IX accusation. It may be that they’ve just put themselves in the same position as Columbia, humiliating themselves for no reason and inviting further demands. If they do get the money back, that would provide some encouragement for what the Columbia trustees are trying to do (negotiate a new and better cave-in).

The long outage of Columbia servers last week was due to a hacker (also see here), seemingly with a pro-Trump agenda of stealing data to show the guilty nature of “woke” university policies. In particular this hacker gave the data for 2.5 million applications to Columbia over many years to Bloomberg News. Not sure what this would show of significance other than the already heavily litigated fact that Columbia and most other universities have been practicing affirmative action and giving preference to applications from specific disadvantaged groups since the 1960s-70s. One thing that this could resolve might be the big debate over whether Barron Trump was rejected from Columbia, perhaps explaining Trump’s campaign to destroy the university.

The Trump assault on Columbia via the accreditation system continues. See this and a university statement here. It seems unlikely that the US higher ed accreditation system will go ahead and make itself an effective arm of the Fascist dictator’s illegal attempt to gain control of the universities. But, these days, who knows…

One of the Columbia trustees, Shoshana Shendelman has gone on right-wing media (Fox News, Breitbart) to attack a large part of the Columbia community as “destructive”, effectively supporting the Trump attack on the university. That the trustees allow this indicates that many if not most of them agree with her. This unfortunately seems to be a big part of the explanation for the cave-in, the firing of Armstrong, the failure to support arrested students, etc.

Remarkably, Shipman and other trustees last year were well aware that Shendelman was already then attacking the university community from within. Elise Stefanik and some House Republicans are continuing the assault on Columbia as “antisemitic”. They point to the fact that on January 25,2024 Shipman wrote to others about Shendelman “I just don’t think she should be on the board.” In later text message exchanges with the vice-chair of the board, Shendelman was described as “a mole” and “a fox in the henhouse”. Clearly Shipman and other trustees by 2024 realized that Shendelman was collaborating with Republicans in an attempt to damage the university with “antisemitism” accusations. That they did nothing about this then has put us in the current situation of having a partially MAGA board of trustees devoted to caving-in and unwilling to fight Trump and those who want to destroy us.

Update: Getting ready for vacation, with Columbia craziness level very high. We have a trustee who has been collaborating for a long time with the Republicans trying to destroy Columbia for being “antisemitic”, and is now going on Fox News/Breitbart to attack the university she’s a trustee of. In any other such situation, this would be grounds for immediate removal. Presumably she feels she can do this kind of thing with impunity because Trump has his boot on the necks of the trustees. At other institutions like Harvard, Trump’s people are plotting how to force a settlement that would give them some control, e.g. by having someone on the board. At Columbia, they’re all set, already have their person on the board.

Shipman has sent out a letter abasing herself and saying she didn’t really mean it. Stefanik and Ari Schrage are demanding her resignation. The trustees already did something incredibly stupid last time this happened (Armstrong), if they do it again they will make it crystal clear that the Columbia president serves at the pleasure of Trump and his people.

I really need to get away from this, now…

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