Ciro Santilli @cirosantilli  40

The neutron temperature example is crucial: you just can't give the cross section of a target alone, the energy of the incoming beam also matters.

Existence and uniqueness results are fundamental in mathematics because we often define objects by their properties, and then start calling them "the object", which is fantastically convenient.

But calling something "the object" only makes sense if there exists exactly one, and only one, object that satisfies the properties.

One particular context where these come up very explicitly is in solutions to differential equations, e.g. existence and uniqueness of solutions of partial differential equations.

This is Ciro Santilli's name for the idea that we should not have structured degrees at university that require entry exams, only tests that anybondy could take, likely for free, and then they would just have proof that they know the stuff for e.g. teachers that care about a subject while selecting students to work with them in research.

We just need control rooms where someone can watch students for cheating. Multiple different exams can be taken in the same room of course, students just have to sign up in advance. The exams should happen regularly depending on demand. E.g. extremelly common subjects should happen every month, and highly specialized ones every 6 months or 1 year.

Questions should be always taken from an open question pool which also contains answers, thus allowing anyone to effectively study for it.

How many questions can you actually come up with about a given non research subject, right?

We then make an API available, so that students can grant access to specific results to anyone they choose, or even make the results public for anyone to see. This way the people that care about the exams can just machine learn what exams correlate with their desired performance.

Bibliography:

See: exam.

Same remarks as Section "Exam".

The identity matrix.

A way to defined geometry without talking about coordinates, i.e. like Euclid's Elements, notably Euclid's postulates, as opposed to Descartes's Real coordinate space.

Postulates are what we now call axioms.

There are 5: en.wikipedia.org/w/index.php?title=Euclidean_geometry&oldid=1036511366#Axioms, the parallel postulate being the most controversial/interesting.