Once you have crated something awesome, you have to advertise it, otherwise no one will ever find it.

This means:

Eventually, people will find you on the front page of Google searches, and then you will know that you've truly made something useful.

Then, if people find errors, or have questions, they will write a comment near the content itself.

Then, next person that comes along and has the same problem, will also find that comment, and your answer will solve their problems too.

The perfect way to do this is to use GitHub issues

For example, if you write LaTeX files for you PDFs, give both PDFs and the LaTeX.

This allows other people to:

People will be more interested if they see how the stuff they are learning is useful.

Useful 99% of the time means you can make money with it.

Achieving novel results for science, or charitable goals (e.g. creating novel tutorials) are also equaly valid. Note that those also imply you being able to make a living out of something, just that you will be getting donations and not become infinitey rich. and that is fine.

Projects don't need of course to reach the level of novel result. But they must at least aim at moving towards that.

This is one of the greatest challenges of education, since a huge part of the useful information is locked under enterprise or military secrecy, or even open academic incomprehensibility, making it nearly to impossible for the front-line educators to actually find and teach real use cases.

This way people have to link back to you, which makes you more famous.

And they can't steal your material without giving anything back.

This is what Wikipedia and Stack Exchange use.

When you do get face to face time with students, don't teach a large group.

Everything you want to teach is already online.

And if it is not, then you are wasting your time saying it face-to-face instead of creating such online resource.

The only goal of meeting students is talking to them individually or in small groups to:

and letting them do the same amongst themselves.

If you talk to a large group, you will only reach / understand a very small percentage of the group, so your time is wasted.

It is better to deeply understand what 25% of the students feel and adapt the course material, than to talk to everyone at once, and have only 5% understand anything.

There is only one thing that can truly motivate you to make good materials: becoming famous.

Strive for that. Make good materials. Publish them. Get good reviews. Loop.

This generates a virtuous loop, which makes you produce better and better material.

Just make it very clear what you've tried, what you observed, and what you don't understand if anything at all.

This will already open up room for others to come and expand on your attempt, and you are more likely to learn the answers to your questions as they do.

And there's a good chance someone who knows more than you will come along and correct or teach you something new about the subject. For example, this has happened countless times to Ciro Santilli when doing Ciro Santilli's Stack Overflow contributions.

Perfect is the enemy of good.

See also: there is value in tutorials written by beginners.

Examples of famous fails:

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:

The Moonshots in Education project also has a fantastic related quote:

Other people with similar philosophies:

Finding a complete basis such that each vector solves a given differential equation is the basic method of solving partial differential equation through separation of variables.

The first example of this you must see is solving partial differential equations with the Fourier series.

Notable examples:

What big companies have been created in Europe after World War II, that have not been bought or utterly defeated by American or Japanese companies?Because of all these failures, much fanfare was made as Spotify reached a $50B market capitalization in 2020. An art company, so cute!

As of 2023, the LVMH was the most valuable company in Europe by market capitalization^[ref]. Luxury goods. An area of industry that borders between the useless and the evil.

Europe has basically become an outsourcing hub for the United States. The fact that its starts are all sold if they become large enough just means that R&D is also outsourced.

ASML, and perhaps more meaningfully its parent/predecessor ASM International from 1964 is perhaps the biggest exception.

The key problem is that there are so many small countries in Europe, that any startup has to deal with too many incompatible legislation and cannot easily sell to the hole of Europe and scale. So then a larger company from a more uniform country comes and eats it up!

Talent mobility is another issue:

So why can't Europe unify its laws?

Because the countries are still essentially walled off by languages. Europe is the perfect example of why having more than one natural language is bad for the world.

There isn't true mobility of people between countries.

You just can't go study or work in any other country (except for the UK, when it was still in the EU) without putting a huge effort into learning its language first.

Without this, there isn't enough mixing to truly make cultures more uniform, and therefore allow the laws to be more uniform.

Europe can't even unify basic things like:

Equally so, it can't force little fiscal paradises who effectively benefit from being in Europe like Ireland, Luxembourg, Monaco, Switzerland ("not European", but should that be allowed?) and Cyprus (the EU can't even maintain its territorial integrity, let alone fiscal) to not offer ridiculously low taxes and incentives which make them entry points for foreign companies to rape Europe.

For this reason, Europe will only continue to go downhill with the years, and the United Kingdom will continue to try and endosymbiose into a state of the United States (although at times it seems that it would rather endosymbiose with China instead). On 2025 the British parliament beautifully put it that the country:

Historically, this disunion is partly due to the European balance of power, whereby countries would form alliances with old enemies to prevent another country from taking over. Also linked are failed military unification attempts by Napoleon and Hitler, though we are likely better off without the latter succeeding!!! Though those also partly failed due to wider balance of power issues involving the United Kingdom, the Soviet Union and USA, not only due to internal balance. Of course, none of that matters anymore after World War II, where other more unified Europe-sized potencies rose, first the USA and the Soviet Union, and then China, and now European disunion is nothing but a burden.

Evidence such as those makes it clear that the European Union is a failure.

One thing must be said in favour of Europe's mess however: it favours international collaboration in huge projects as a more neutral middle ground. This can be seen more clearly in the ITER and the fiasco that was the Superconducting Super Collider that was cancelled a couple of billion dollars in partly because it failed to attract any foreign investment, compared to the Large Hadron Collider which went on to find the Higgs boson as mentioned at www.scientificamerican.com/article/the-supercollider-that-never-was/.

Bibliography:

Directly modelled by group.

For continuous symmetries, see: Lie group.