It's great business to minimally modify valuable stuff and then take credit for it. As was explained to me by bar-certified counsel "if you take a recipe and add, remove or change just one thing, it's now your recipe"
The new trend in this is asking Claude Code to create a software on some type, like a Browser or a DICOM viewer, and then publishing that it's managed to do this very expensive thing (but if you check source code, which is never published, it probably imports a lot of open source dependencies that actually do the thing)
Now this is especially useful in business, but it seems that some people are repurposing this for proving math theorems. The Terence Tao effort which later checks for previous material is great! But the fact that the Section 2 (for such cases) is filled to the brim, and section 1 is mostly documented failed attempts (except for 1 proof, congratulations to the authors), mostly confirms my hypothesis, claiming that the model has guards that prevent it is a deus ex machina cope against the evidence.
The production of ignorance is booming as its trajectory takes it from roots in advertising, then lobbying, then political campaigns to center stage in political strategy and official government business.
I suspect the academics who study culturally cultivated ignorance will be playing catchup for at least a decade after this administration!
Maybe I'm too familiar with the set theoretic construction of the natural numbers (0 is the empty set, 1 = {0}, ..., 5 = {0,1,2,3,4}, etc.) but their example of "3 ∩ 4 = 3" or "4 intersect 3 is 3" doesn't seem weird, problematic or even useless to me, it just looks like a handy set theoretic implementation of the min() function.
By itself it's not a problem, but it's certainly useless. Perhaps you can tell me what use "3 ∩ 4 = 3" has.
The problem is that these properties get in the way of proving arithmetic theorems because if you are being absolutely strict, you have to distinguish things that are true of natural numbers as an algebraic structure, from things that just happen to be the case because you picked some specific representation to use for natural numbers. This introduces a lot of noise and makes formal proofs very frustrating, somewhat like when you're programming and you have to bend the type system of your compiler to accept your code even though the program is conceptually correct and you end up spending effort on type coercions, casts, "unsafe" blocks etc... mathematically this makes your proof significantly longer, more brittle, and harder to reuse because it accidentally depends on details of the chosen encoding rather than on the intrinsic properties of arithmetic.
> Perhaps you can tell me what use "3 ∩ 4 = 3" has.
As I said:
> a handy set theoretic implementation of the min() function.
i.e. if you wanted (for whatever reason) to define min(a, b) directly and briefly in your set theoretic reconstruction of the natural numbers, you can just use intersect operator and define it as "a ∩ b".
Perhaps because in terms of the interesting distinction you introduce:
> you have to distinguish things that are true of natural numbers as an algebraic structure, from things that just happen to be the case because you picked some specific representation to use for natural numbers
this particular operation seems to be part of the former rather than of the latter.
It's a leaky abstraction, in software terms. Ideally, an abstraction models the semantics of the problem domain "opaquely"; ideally our natural numbers have only the properties of the natural numbers and no others. An additional property leaking through is not like handy "bonus", but a point of confusion. You can't rely on it in proofs involving natural numbers without being careful to delineate which conclusions follow from the construction vs. which are inherent.
> [Indyke] was hired by the Parlatore Law Group in 2022, before the justice department settled the Epstein case. That firm represents the defense secretary, Pete Hegseth, and previously represented Donald Trump in his defense against charges stemming from the discovery of classified government documents stored at Trump’s Florida estate.
So I don't know about "not a Washington person", but clearly connections exist to the current administration.
We’ve noticed that the name creates unintended associations for some users, especially in English, and that’s not what we want to emphasize going forward.
We’re actively discussing a rebrand to better reflect the creative and model-focused direction of the product.
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