You can use the Dirichlet-to-Neumann operator associated with an unknown elliptic operator to reconstruct the coefficient of the operator and consequently the structure of the inside of the domain. It's a problem proposed by Calderon and is well understood for the Laplacian. Good luck with the Stokes operator tomorrow though.

I've often heard say, among charities people who work with homeless people, that you need as long to get out of the street than you spent living in the street.

When world chess champion Anand won arguably his best and most creative game, with black, against Aronian, he said in an interview afterward "yeah it's no big deal the position was the same as in [slightly famous game from 100 years ago]".

Of course the similarity is only visible for genius chess players.

So maybe pattern matching and novel thinking are, in fact, the same thing.

On the politics part : one thing I like very much with the Roman republic system was the concept of the "cursus honorum". Basically if you wanted to go for a politician career you had to start at the bottom, get elected to a first position, do well, get elected to something more prestigious, etc. And it worked very well - a significant part of Roman success was that their government (and generals) were way better than competing powers, in this was mainly due to having a lot of experienced, competent politicians and generals with somewhat well aligned incentives.

That really depends of which part of France you are talking about. Provence uses mostly olive oil. In the South West they often use duck fat.

French are also apparently slightly less obese than their neighbours, the difference is not only with the US.

That used to be the French model, which imo kick way above its (abysmal) low funding.

Steelmanning is about finding the truth, ITT is about convincing someone in a debate. Different aims.

There's a big gap between "you have to complete the task in exactly this way" and "mistake is a mistake, only the end result count".

I routinely gives full marks if the student made a small computation mistake but the reasoning is correct. My colleagues tend to be less lenient but follow the same principle. I always give full grade to correct reasoning even if it is not the method seen in class (but I quite insistently warn my students that they should not complain if they make mistakes using a different method).

I do exactly what you describe with my students, but sadly with extremely limited results.