Typically the software engineers also do more maths than CS students. Reasoning from first principles is an important skill for professional engineers to have.

Does model performance also concentrate into a 'typical case' where things work pretty well and a non-typical case where it's completely unpredictable as the number of parameters increase?

A contract for purchasing Parent Co.'s HR, legal, and compliance expertise for child co.

And a contract for sharing technology infrastructure.

The terms and pricing of the contract would likely be strictly regulated to prevent preferential treatment and encourage a clean separation over time.

I'm not a lawyer though, so who knows.

Professional Engineers are qualified to take on more liability than just creating a design. So you don't need an Engineer to design a product, but (depending on jurisdiction) you will need an engineer to certify that your product won't hurt or kill people.

If you do a lot of design work, then you may want to hire a Professional Engineer in-house so that your company has more confidence that they will produce compliant designs with fewer iterations.

Engineers are often the best people to work with if you need to do things that are done infrequently since theoretically, they're trained in the prerequisite first principles so they can make judgments that are rooted in rigorous analysis in addition to their practical experience.

"Doctor", is for instance a protected title. You can not advertise yourself or your services as a doctor unless you're a qualified and practicing medical professional. I believe some kinds of legal practices are the same.

It's still not clear to me from this discussion whether the term "Software Engineer" is legally protected in Germany (or any other European country) or if it's just a cultural convention.

The distinction is basically, if a software developer started a consultancy developing custom software solutions and called the company XY Software Engineering, would they be penalized for false advertising if they didn't have professional engineering qualifications?

The company that needs a webapp because everyone else has one is never going to value "taste".

To adapt to this AI world, we need to either ship more lower-quality software, or start seeking out higher value problems. I don't see any other way around it.

The general consensus of developers is that AI can only do the work of a strong 'junior'. Yet as soon as we are presented with pure mathematical results, people seem incredibly ready to accept that AI can do more than what a strong student could achieve.

I'm trying to understand if these specific problems were the kinds of problems that would have justified an expert investing weeks or months to solve. Or if they were the kinds of problems that would normally have been given to students to investigate.

But the wording of the result makes it sound like we don't know what the lowest possible complexity bound might be. So, prior to this result did we think there couldn't be a lower possible bound? Or did the arithmetic circuit community think there were lower possible bounds but didn't see it as a high value target for experts to tackle (maybe a problem that was instead regularly given to students to study).