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

This allows other people to:

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.

The projects you do must always aim to achieving some novel result.

You don't have to necessarily reach it. But you must aim for it.

Novel result can be taken broadly.

E.g., a new tutorial that explains something in a way never done before is novel.

But there must be something to your project that has never been done before.

You can start by reproducing other's work.

Many of the student exchange programs Ciro witnessed in the 2010's in Brazil were inefficient because they were requiring students to come back immediately after university or PhD in fear that those students will never come back.

This is useless, because you don't learn anything unique during university: the truly valuable knowledge is obtained when you work for several years as a postdoc in a world class research laboratory or as an engineer in a world class company.

Therefore, Brazil should learn from the Chinese exchange system, which lets students go do whatever they want, and once they are Gods of the domain, entices them back with great positions and pay as heads of laboratory back in China. Just don't do fraudulent stuff like this like China did, or else you will get a bad rep.

To help this university collaboration happen, we should create communication channels between exchange students and professors of the origin country who work on the same domain so that they can discuss the subject. For example, once Ciro Santilli wanted to contact some of his former teachers at the University of São Paulo about "advanced" topics he had been exposed to as part of his job. However, they didn't even reply to his email, and Ciro didn't know who else to contact. This must never happen. We need a way to informally contact several professors of a given domain informally, to increase the chances that at least one might be interested. It is pointless to just let students loose abroad and hope that they will bring things back to their home country: a more cohesive infrastructure is needed to nurture that.

There is basically one sane way to achieve these goals: the exchange programs must be organized at a national level, not in an ad-hoc per-university manner.

Another good idea is to have taxes that depend on your nationality alone and which only start collecting when you reach a very high amount of net worth. So e.g. if someone leaves the country and makes it big, then and only then does the Government starts clawing back the benefits of its investments in the person. Furthermore, such taxes could be reduced if the person brings some of the business back to the country. And mandatory taxes should be charged if the person decides to drop their nationality at some point.

The above points would also be greatly eased by having a national-level exchange program. E.g. in Brazil in the 2010's which Ciro experience, every university had different terms and conditions, which made everything a mess. Exchange programs must be treated as a unified federal policy.

Ciro actually had to return for just six months from the École Polytechnique to the University of São Paulo, to finish a course he had only done the generic Maths/Physics introduction to. Students from other Brazilian universities were forced to return for up to 3 years even to get their Brazilian diplomas! Ciro was lucky that his teachers understood the situation, and allowed him to develop online learning projects instead of his supposed control engineering projects, which hopefully will have led to changing the world with motivation one day. And for this, Ciro is eternally thankful.

This shows the complete and total lack of any Brazilian strategy to send its students abroad to really learn valuable things and then come back. There is no strategy at all. Things have just reached an equilibrium point of bureaucracies, Brazilian universities trying to bring students back to validate useless diploma pieces of paper, and foreign universities no caring about that, and just wanting the students to say abroad forever.

Ciro was once talking about why so few Brazilians go study abroad compared to the Chinese. Besides the likely true "there are a lot of Chinese" argument, his wife made another: good point Brazil is not so bad to live in, because you have good food and freedom, while China only has good food.

But Ciro still fells bad that so few of his University of São Paulo colleagues, who learnt automation and control engineering, are doing deep tech. Nor physical engineering. They have all basically become computer people like Ciro.

This is not their fault. They basically don't have a choice: all physical science and technology is done in rich countries.

Yes, someone has to implement the newest tech to improve local country efficiency in projects that will never spread abroad.

But who will be left then for the next big thing problems that would really make Brazil richer? 6 out of 30 person class ended up working on a gaming company at one point, even though they were not crazy passionate about the field! What could possibly be a worst investment for society?

This lack of technological innovation can also be clearly seen when you research investment options available in Brazil. Huge emphasis is put on fixed return financial products (often inflation adjusted) linked to base non-tech business such as housing market and agriculture. And when you look to the returns of the stock market on s&P 500-analogue backed exchange-traded funds, they do not seem obviously better, especially considering inflation and taxation benefits that exist for some of the other investment possibilities.

When the companies of a country are not clearly the best investment, you know that something is wrong. They are highly specialized money making machines, remember! And housing and agriculture are not such innovative markets where people can hugely influence efficiency.

When it is best to send students is a good question. Undergrad studies could be easily reproduced in poor countries if they had any intelligence at all, since even in rich countries laboratory usage is always limited. Masters and PhD are generally more valuable moments to send people out. The question is if the students will actually have a fighting chance without having been out, in particular in terms of language skills. Ciro feels that Masters are a good focus point for entry, as that is where PhD links are more actively done.

Future self, answer these.

10 years:

20 years

40 years:

The square root of 7 is approximately 2.64575131106.

The McShane integral is a concept in real analysis that extends the notion of the Riemann integral to certain situations where the Riemann integral may not be applicable. It is named after the mathematician James McShane. ### Definition The McShane integral is defined for bounded functions on an interval \([a, b]\) in such a way that it can handle some functions that are not Riemann integrable due to issues like discontinuities.

Mathematics is a broad field of study that deals with numbers, quantities, shapes, and patterns. It is both a formal science and a practical tool used in various disciplines, providing a framework for understanding and describing the world around us. Here are some key aspects of mathematics: 1. **Branches**: Mathematics can be divided into several branches, including: - **Arithmetic**: The study of numbers and basic operations (addition, subtraction, multiplication, division).