The goal of our broken educational system is not to teach.
It is simply a test of who can learn the most in the least amount of time.
What is being learnt is of little importance. it doesn't matter if it is useful or beautiful things.
The useless exams are set exactly at a difficulty level that produces a Normal distribution of grades:The difficulty is just set for your particular group of students.
- too hard and everyone gets 0, so you can't split people well
- too easy and everyone gets 100, so you can't split them well either
See: Section "Exam".
The only thing that matters is that students aim towards the goals described at explain how to make money with the lesson.
Any "homework for which the student cannot use existing resources available online" is a waste of time.
The ideal way to go about it is to reach some intermediate milestone, and then document it. You don't have to do the hole thing! Just go until your patience with it runs out. But while you are doing it, go as deep and wide as you possibly can, without mercy.
This is actually how Ciro Santilli learns new subjects he is curious about, even as an adult! Some examples:
And if you really can't make money from a subject, there is only one other thing people crave: beauty.
You have to give the beauty motivations upfront, before boring people to death with endless prerequisites, otherwise no one will ever want to learn it.
Ciro Santilli intends to move his beauty list here little by little: github.com/cirosantilli/mathematics/blob/master/beauty.md
The most beautiful things in mathematics are results that are:
- simple to state but hard to prove:
- Fermat's Last Theorem
- number of unknown rationality, e.g. is rational?
- transcendental number conjectures, e.g. is transcendental?
- basically any conjecture involving prime numbers:
- many combinatorial game questions, e.g.:
- surprising results: we had intuitive reasons to believe something as possible or not, but a theorem shatters that conviction and brings us on our knees, sometimes via pathological counter-examples. General surprise themes include:Lists:
- classification of potentially infinite sets like: compact manifolds, etc.
- problems that are more complicated in low dimensions than high like:
- generalized Poincaré conjectures. It is also fun to see how in many cases complexity peaks out at 4 dimensions.
- classification of regular polytopes
- unpredictable magic constants:
- why is the lowest dimension for an exotic sphere 7?
- why is 4 the largest degree of an equation with explicit solution? Abel-Ruffini theorem
- undecidable problems, especially simple to state ones:
- mortal matrix problem
- sharp frontiers between solvable and unsolvable are also cool:
- attempts at determining specific values of the Busy beaver function for Turing machines with a given number of states and symbols
- related to Diophantine equations:
- applications: make life easier and/or modeling some phenomena well, e.g. in physics. See also: explain how to make money with the lesson
Good lists of such problems Lists of mathematical problems.
Whenever Ciro Santilli learns a bit of mathematics, he always wonders to himself:Unfortunately, due to how man books are written, it is not really possible to reach insight without first doing a bit of memorization. The better the book, the more insight is spread out, and less you have to learn before reaching each insight.
Am I achieving insight, or am I just memorizing definitions?
As of 2020, university has the following very important applications:Notably, education is an IQ test, not a way to learn useful and beautiful things.
- meet an intelligent sexual partner (see also: Section "Sexual selection", Section "The main function of university is sexual selection") and or have fun and or come out of the closet
- get you in debt if you are from the United States
One major issue is that teachers don't have the right incentive to, nor are selected to, teach well. Thus the existence of Rate My Professors! But we can do better...
Which is why Ciro Santilli wants to destroy its current format with OurBigBook.com. He believes that we can find a more efficient organization to achieve both the social and research functions of university, by first doing as much as possible online
Ciro's university experiences are mentioned at: Ciro Santilli's formal education.