I’m not sure what the author had in mind when he wrote the paper, but its light-hearted content reveals well how to structure a math paper: (1) state the problem and why the reader should care about it, (2) state how the paper builds on prior work, (3) summarize the main results, and then (4) develop them in theorem-proof style.

An economics paper in the same spirit (though of course economics addresses more practical problems than mathematics, in this case whether one should leave the toilet seat up or down) shows quite well how to present and develop an economic model [0].

0. https://jaypilchoi.com/wp-content/uploads/2021/06/Economic-I... [PDF]

Economics humor is a bit droll: https://www.ft.com/lol-404

Mixing powdered mustard at the point of delivery would optimize for freshness. Something akin to large construction site concrete, which is mixed from raw materials on demand, but built into a pocket watch.

Just in time mustard if you will.

French version, as a proper PDF: https://girard.perso.math.cnrs.fr/moutarde.pdf

Theorems 1 and 2 are a little weak. For theorem 1, once a mustard watch reaches a sufficiently enormous size, material weaknesses become relevant problems to overcome, and it is not clearly shown that adding a few more grains will in fact allow the watch to still operate. And theorem 2 doesn't discuss how much time is needed to measure the current time. I'm not entirely sure this has been peer reviewed. No notes on theorem 4, though.

You can prove it easily by induction. If Wm(n) is a mustard watch containing n micrograms of mustard, then it suffices to show that Wm(0) exists, and that if Wm(n) exists then Wm(n+1) must exist. Obviously a single additional microgram of mustard could not overload the structure of a watch. Therefore, Wm(10^100) or any other size must exist.

material weaknesses would be more of a problem for ketchup watches. dijon mustard is strong enough so you don't require that much for it to become an issue

In the classic 2002 feature film "Undercover Brother" the titular character had a hot sauce watch which enabled him to eat white people food. James Bond was surely jealous.

https://www.imdb.com/title/tt0279493/

After moving somewhere with criminal amounts of unexpected mayonnaise I have referred to that scene often. Great movie.

Nah. Hotsauce is for people with damaged taste buds.

I imagine the British taste bud of 007 was not damaged by low quality super high oil foods.

Eh? More for the rest of us, then!

I'm always surprised how many other mathematicians don't know what I'm talking about when I reference this paper. It should be in the canon of math essays.

What precisely is the complaint the actual author is making wrt temporal logic? Surely it is more than the assertion that there is no such canonical one?

I can’t decode French elitism.

I think it’s the lack of mustard. From the first paragraph: “what is the point of knowing time if you cannot get mustard?”

Actually a LOL line. A long with his very skilled and meaningful schematic.

>I can’t decode French elitism.

It is a clear case of "langue-dans-la-joue"

(or is it "langue-dans-la-fesse"?).

It would not be "langue-dans-la-fesse" for sure, even if this expression is very humoristic itself! Tongue in cheek can be said "pince-sans-rire" : https://fr.wikipedia.org/wiki/Pince-sans-rire

pince-fesses obviously

Is there a garmin siracha device?

An ideal sriracha timepiece would include an element of time-travel, allowing the operator to summon quantities of the Huy Fong product from before the lawsuit with their chili pepper supplier.

There should be a suitable structure-preserving morphism.

I have one full of thyme.

I often wonder if the mustard watch is a microcosm of all of our inventions so far.

See also hunting lions using math: https://news.ycombinator.com/item?id=29106064

This reminds me that I was going to write up a paper on my breakthrough encabulator escapement watch.

Love mine. I can discreetly squirt mustard onto boring hors d’oeuvres.

I would find more use from a mustard-cat treat watch

I’m not sufficiently familiar with French culture or maths culture (and barely at all with their intersection!) to tell whether this is satire/parody, or just bonkers in general. Which is it?

It's a satire of a typical kind of paper from logic, in particular modal logic. Jean-Yves Girard has been very vocal against these academic papermills where the authors consider ad-hoc meaningless logical systems. For a more in-depth critique of semantics, you can also read the broccoli logic paper: https://girard.perso.math.cnrs.fr/meaning1.pdf

As I understand it (also neither a mathematician nor French), it's a parody on a certain type of math paper, I'm guessing in abstract algebra, where the author does nothing but present a theory that is a "generalization" of some other theories, with no concern whether this generalization is helpful in any context.

So you get a "mustard watch", a thing which behaves simultaneously as a watch and as a mustard container, and finding a situation where that would be useful is an exercise for the reader.

highly entertaining read for a mustard fan, but what is this demonic presentation of a pdf

Given the date of publication and the hand drawn figure, it's likely there never was a PDF.