Have you considered the possibility that Enoch Powell was right?

There’s a scandal/controversy occurring right now after someone leaked photos of the inside of Ariana Grande’s apartment.

yikes! that's pretty gross. I hope there's some appropriate consequences.

I just don’t like the name.

I've definitely been in situations where managers tell me to "spend X amount before the end of the year." They don't want higher ups to think they can cut our budget.

Indeed I would bet he knew he would lose money on Twitter but did it anyway.

He tried to back out of the purchase after signing an agreement, but was forced to buy it for $44b in the end.

"The burn rate is unsustainable: The US fired 850+ Tomahawk cruise missiles in 30 days but purchased only 57 in the FY2026 budget. That is 14.9 years of production consumed in a single month."

Does the author think the US can only make 57 missiles a year?

Do you think the US has idle capacity that can be activated at a moment's notice?

> Do you think the US has idle capacity that can be activated at a moment's notice?

I'm sure some very smart MBA increased profits by eliminating spare capacity or making cuts that would make it much harder to spin up. That's American business culture: focus on this quarter or this year, nothing else matters.

Indeed, regular drinkers know what to expect as far as pour and price from any given bar. If I drop into a new bar and I feel ripped off then I don't go back. I do the same with burritos.

I don't think it's overanalyzing to point out a typo.

"He proved that if a curve’s equation has a variable raised to a power higher than 3, then it must have a finite number of [rational] points."

This must be an incorrect description of what has actually been proved, since x^4 is a counterexample.

My understanding, which is to be taken with a grain of salt, is that there's an additional constraint, not stated in the Scientific American article, that the plane curve be irreducible. The example of x^4 is reducible, it's x^2 * x^2 among other thing. The actual conjecture is expressed in terms of genus, but this follows from the genus-degree formula.

The curve they mean y = x^4 is irreducible but the genus is 0 since it’s isomorphic to the affine line.

The correct description is “a smooth curve of genus at least 2”.

https://en.wikipedia.org/wiki/Faltings%27_theorem

The reason for the confusion is that a smooth, projective plane curve of degree d has genus (d-1)(d-2)/2, which is 2 or greater starting at d=4. Hence the phrasing in the article, which is missing the “smooth, projective” hypothesis. The equation y = x^4 doesn’t define a smooth curve when extended to the projective plane, because it has a singularity at infinity.

I think the theorem applies to any curve, if you take geometric genus.

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