A conversation with Alejandro Piad Morffis about education

Optimizing the right target variables

Hi there,

The Palindrome is back in business! I’ve spent the last (almost) two months developing a small little application called Lilla, whose primary purpose was to cure my imminent burnout. 

(And also to learn web development from scratch. I picked up JavaScript for the first time around October 1st, and I’ve built and deployed a full product. This was quite a ride.)

My creative energies are full, and you can expect the usual weekly post from The Palindrome. (For the premium subs out there: your billing cycle will continue on December 1st.)

The first project is going to be a collaboration with

Alejandro Piad Morffis

, one of my favorite technical writers online. Many of you know him; if you don’t, he’s the mind behind Mostly Harmless Ideas and the The Tech Writers Stack. (Both of which I recommend.)

Before our idea-focused introductory series on graph theory, Alejandro and I had a lengthy conversation about the state of education. We talked about

• what’s the role of talent,

• what’s missing from education, and

• why does an academic environment optimize for the wrong variables,

• and how can we do education better.

Our conversation is quite long; even the heavily edited version clocks in at about six thousand words. Still, education is a subject that deserves a nuanced discussion.

Here we go!

---

Tivadar: Alejandro, you are a really interesting person to me because you are a computer scientist by training, but you are extremely well-spoken, and you are also very well versed in philosophy.

That’s quite a knowledge stack. How did you become that way? Walk me through your life.

Alejandro: My student life was very traditional.

I was more or less a good student in high school. In Cuba, we have a so-called vocational school; usually, the best students in the country go to these places. The top 20 students of each high school, or something like that. It's a very good place because you spend three years fully studying from Monday to Friday. You don't see your parents, you stay in school, and you have to sleep with everybody in the same room. So, a very nice experience.

They have special classes there, and I got into the one for physics. I spent those three years studying everything more or less that you study in high school, but also competitive stuff and advanced math before university. A little bit of calculus, geometry, and whatever is needed for physics. However, I was exposed not only to math but also to scientific thinking as well.

When I was asked what I wanted to study, I said computer science. It was a bit weird because usually, the chemistry students go to the chemistry major, the math students go to the math major, and so on. So I was one of the few physics students who went into the computer science major.

But that's the way I got into university. And computer science in Cuba, since it's a poor and a small country, you really have one top university. But it's not like in the US, where you can have 20 top universities and you can really compare them. Here, you have one university, where 50% of all the science is done. In computer science, this is the University of Havana, which is the biggest one.

So, you are studying computer science, but you have the law students next to you, and in the next building, you have the philosophy students, the physics faculty, and so on. You interact with everybody from the university.

In Cuba, computer science education is much more math and theory-oriented. So it's a lot of computability and everything. The foundation of formal methods like proofs and logic, that's very strong. That’s where my love for math and logic comes from.

And then the philosophy. Everybody who's curious at some point reads. You read a bit of Sci-Fi, and you watch a couple of interesting movies, you ask questions. And we had the luxury of having the person who designed the computer science curriculum in Cuba in the 1960s.

The one person who was like the mastermind of the entire computer science curriculum was a philosophy graduate who was sent to the math department to teach philosophy. But he decided to teach logic, and eventually, he became a computer scientist by profession.

I had that professor as a teacher. He's 85-90 years old, and he's still teaching. And if he teaches you, you’ll learn things with a philosophical twist.

Tivadar: So many things for me to reflect on!

Let's talk about the divide between the Western and Eastern styles of education. I was also trained in the Eastern tradition: I'm from Hungary, a post-socialist country. I was born in 1990, around the collapse of the Soviet Union.

One of the biggest divides between Eastern and Western education is a focus on practicality, as you hinted at. If you study in the United States, your focus is on building things. (That’s not a hard rule, of course, but the US curriculum is generally geared towards an engineering mindset.)

Which one is better?

It's a wrong question: it's not like one is better than the other. Rather, they are different, each having their own strengths and weaknesses. For instance, this philosophical inclination you mentioned is very beneficial if you take a look at the big picture. Science is governed by curiosity and the pursuit of truth, not just by technological and industrial considerations.

If you want to do science, you should always have the betterment of humanity in mind. As a scientist, you have the power to change the world, do good or evil.

Another thing. I was a terrible student before university. I don't know about you, but I did a lot of stupid things, like going to my classes drunk. Fast-forward ten years: at the end of my PhD, I was a top student. And in between, there was a spark that ignited my love for mathematics.

Where did this spark come from? It's a really interesting topic to discuss, and we almost never do. Soft skills, motivation, psychology. In our courses, we tend to focus on technical aspects. But it's essential to talk about, say, how you develop a curious mind.

How did you get started? What was your spark? What made you want to do and build?

Alejandro: Everything that happened to me and everything that I did until I finished my PhD, I have to credit somebody else for pushing me to do it. Because at these stages, you simply don't have the knowledge to decide what to do and how to do it.

I want to get there eventually, but up until finishing my PhD, everything that I did that got me into some good place was because there was somebody — almost always more than one person — who told me, “oh, this is a good thing to do.”

Perhaps some people have this romantic story of, like, “I was completely lost, and I had that one professor who gave me that one book, and then it all started.” But I don't think that this happens with most people. For most of us, what happens is that there is a kind and supporting environment: family, school, and friends. If your environment inspires you to go into science, math, engineering, or whatever else and become a professional, then you will.

If your environment doesn't inspire, then you won't. And it doesn't really matter how much talent you have!

I think that talent is distributed uniformly across the population. And if you take a random kid from the poorest part of the country and you put them in the right environment, you can get a PhD. And if you take a kid from the best family and you put them in that other kid's environment, they won't get to university.

Thankfully, I was in a good environment, and good environments create good students. I have to thank my parents. My parents both studied humanities: my father studied journalism, and my mother studied philology (the study of language).

They both graduated in '86, then the Iron Curtain fell, and the Socialist world collapsed. So did Cuba’s economy, because we were a USSR satellite state. We had no economy. This meant that they only worked in their profession for like three years. After that, they had to do whatever they had to make ends meet. So, they didn't develop their professional careers.

One thing they taught me was to pick something that you want to do and be good at it. Whatever you want to do, be good at it. Whatever I was interested in, they pushed me to do it better.

My father used to read a lot. He wasn't very tech-savvy, and he wasn't from the quantitative side of the world. But he read a lot, and he got me into it.

I also went to a good school, and I had very good teachers. I had two physics teachers that were very good not only in teaching problem-solving but thinking about physics at a deeper level.

So, the short answer: there is a kind of environment that stimulates people to grow intellectually, and if you put (almost) anyone into it, they can get to a PhD level. The influence of biology is minimal.

I think almost anybody will become interested in science given the right circumstances because science matters. There are very few jobs where you can really push the boundaries of what civilization is doing, even if just a tiny bit. But you can really say, "I'm doing something that is different from everybody that was before me, and I want to do that just because of that, not because it pays more or whatever."

Tivadar: For me, finance is a typical example of a job that's very high skill. But if you look at the big picture, you are not really pushing the boundaries of human knowledge. On the other hand, it's a really difficult and technically interesting field.

The point you raise regarding parental pressure is a really interesting topic. I think it's a tightrope walk because many parents want to reach their (unfulfilled) dreams through their children. This is definitely at the dangerous end of the spectrum.

At the other end is the parent who doesn't care about their children's personal and professional development. It's important for parents to push their children, but it's also essential to recognize the occasional directional changes.

The job of a parent is to push but not break.

Alejandro: Do you have kids?

Tivadar: No, I don't, unfortunately.

Alejandro: I have a one-year-old, and this is the thing that terrifies me. This balance. Right now, we're teaching her the letters.

How much do you push to get her to learn another letter, versus how much do you just let her do her own thing and put a piece of dirt from the ground into her mouth just to see that dirt doesn't taste right?

Tivadar: You have to accept that she is a person on her own.

An analogy came to my mind. Swimming is "simple": you dive into a pool, swim as fast as you can, and the fastest one wins.

In Hungary, we have tons of famous and successful swimmers, and the swimming education is world-class. There are some swimmer dynasties, passing down the torch with each generation. However, the skeletons started to fall out of the closet recently.

As it turned out, the successes were built on abuse in several instances. A father forcing their daughter to realize their broken dreams, etc. If you keep yourself up to date with sports, you see that many young athletes break in this process. They are pushed too hard in a direction which is not really theirs.

This is what I'm also afraid of as a future parent. I'm that type of person who can push too hard.

By the way, we have a slight disagreement on the role of biology. I think the role of biology is huge, but I don't see it as ultimate. You can certainly complement genetics with other skills. Right?

Alejandro: I guess, yeah. The end result can be widely different regardless of biology.

Tivadar: Yeah. I often imagine "success" as a numerical score. You have a score for talent, emotional resilience, environment, etc. Each one is a number between zero and one. The measure of "success" is a sum of these. Say, you have to reach 1.5 in order to complete a PhD.

You have lots of factors, and most of them are not even fixed! One of them is how disciplined you are. If you have the discipline to put in tremendous practice into something, you can complement the lack of talent up to a point.

This is true for mathematics as well, and I think this is my case. I do not consider myself especially talented. I'm not a genius, but I have an iron will. I sit down and I do the job, I do the work. I put in hours of practice. This is how I eventually ended up getting a PhD. I was also emotionally resilient, so I was not discouraged by a loss.

On the other hand, I have seen lots of talented people dropping out early from university because they relied too heavily on their talents. They sat on a really high horse and they fell down because they thought that they didn't have to work hard because of their talent. The truth is, success is hard work AND talent. If you put in the work, you can go from zero to 95%. If you are talented, you get there much faster, and you can even go from 95% to 100%.

There is this huge debate on Twitter right now regarding this. How high can you go in math? The two most popular answers: 1) there is a hard limit for everyone, and 2) there are no limits at all.

In my opinion, there is a limit, but everyone can go fairly high. There is even a limit for geniuses like Terrence Tao. (Who is one of the brightest minds in contemporary mathematics.) However, this limit is much higher than most imagine, because it's easy to get stuck early.

And talent is not your only tool, right? You have practice, discipline, environment, as you say. Talent, you cannot control. Discipline, you can control. Your environment, you can control. (Up to a point, at least.)

Thus, the question "How important is talent?" is a wrong question because you can't change your talent, but you can change your environment, your attitude, your mindset.

Alejandro: I think we agree there, it's a matter of perspective. If you take the most talented person, like you said, the most talented person, and they don't really have the resilience, it doesn't matter how talented they are, they won't get to the top level of anything. You must work hard enough because somebody else will be almost as talented as you. And they will work a little bit more than you, and they will surpass you.

You cannot be at the top of the world and be the least disciplined person, and then the second one is just super disciplined but doesn't have your talent. It doesn't work like that. So I agree with everything that you said, and I do agree that the things you can change are the ones that should matter. Environment is the key thing to optimize.

But when you are going through this, when you're a kid and you're studying, you don't really know that all these things matter, and you don't really know that, and you cannot really see.

Tivadar: Yeah, because no one teaches you that. Because they teach you that talent is the most important thing.

Alejandro: Yeah, exactly. With cognitive abilities, people always make the assumption (or the analogy) that these things work like sports. Math is a sport, science is a sport, and everything you do, like playing music, is a sport. Like swimming is a sport.

I don't want to oversimplify sports either because it takes a lot of hard work, but I think you can much more clearly see the connection between biology plus hard work in the context of swimming than in doing a PhD. Because swimming faster depends on the strength of muscles and a few other mechanistic things, and these can be measured quantitatively.

Michael Phelps has a perfect body for a swimmer, and if he put in the same amount of effort as everybody else, he will be beyond everybody. But I don't think that you can do this with math. There is definitely biology involved, but I think it's extremely complex. There are way too many factors to claim something as simplistic as saying, "Oh, you have a score for talent, and then you have another one about discipline," etc.

Speaking of wrong questions, "How do I identify which student to invest in?" is another one. This is what happens in every educational system because if you don't do it, the result is that random people get to university. Every educational institution has places where they filter out people that at this moment didn't pass some bar. There are points in your life (sometimes when you are very young) when if you didn't cross a certain bar, you are already almost completely filtered out from the possibility of improving later. Because society decided that "I don't want to invest in these kids anymore."

And I think that's kind of the wrong question for that reason because at eight years old, if you measure that kid's performance at that moment, what are you measuring? You're measuring that weird sum of environment plus whatever intrinsic skills they have. (Not speaking about the way you measure it.)

Like math skill is not equal to solving arithmetic problems at eight years old. That's a very bad proxy for how good you can be at doing science. But that's what you can do for eight-year-old students.

I'm just trying to criticize the quantitative mindset of education. And I think this happens in Eastern and Western education as well: in Cuba, we have a combination of both because education here was inherited from the Soviet Union and from democratic Germany as well. The mindset of this education is putting kids through a lot of basic math and physics before everything else, providing a good basic education before university. They don't know how to do anything, but they have a very good basic background to study things. So we have kind of a mix of the two mindsets here. The university is a little bit more modern, but you see the remains of this Eastern-style education of "just make it hard for the student."

What I'm trying to criticize is that education is not a sport, you are not optimizing for a single ability. And if it were a sport, it would be a much more complex one where team skills matter, where communication skills matter, where long-term planning matters more than your ability to do one single task at this moment. And I think most educational paradigms view education as an engineering problem. How do I get the most students through this pipeline with the least amount of resources and get the best people at the end?

If you see it as an engineering problem, of course you want to filter the material at different places and see, "Oh, this bar of this rod of metal is not good enough, I'm not going to invest in it." But people are not material, and the role of education shouldn't be just putting a bunch of people through a pipeline and seeing which ones come out best at the end and investing only in them.

Tivadar: Sure, our educational system certainly over-emphasizes one aspect, right? Problem-solvers are glorified, but there are multiple ways of adding value to science and engineering. Even to mathematics.

Besides problem-solvers, you need networkers who can build communities. Then there is teaching. In academia, most teachers are researchers, but teaching and researching are two completely different skill sets. I know people who are excellent researchers, but absolutely horrible teachers, and the people who would be really good at teaching, they are filtered out by this "engineering process" you mentioned in your analogy, just because academia is fixated on problem-solving.

And the funny thing is, even the scientific work itself is not focused on problem-solving. Perhaps when you are a student, a PhD student, you are judged by your problem-solving ability, maybe also if you are a postdoc.

But the moment you step outside your research group, you are judged on your ability to communicate your ideas. As a principal investigator, your entire research group depends on your ability to bring in grant money. And there is this huge divide between these two worlds.

I was working in life sciences for two or three years; it was very interesting to see academia from that perspective. Essentially, successful researchers are managers. They are not problem-solvers. Some of the very famous professors can't even pick up a pipette because they forgot how to do wetlab work a long time ago. They manage people, write grants, maintain public relations, give talks.

It's very interesting that we are still so fixated on problem-solving. Even in a life science environment, people who are more interested in organizing events or building communities are looked down upon. This is not something which I like to see.

Alejandro: Yeah, it's the same with our students as well. Right now, I'm teaching the first programming course for computer science majors. This is the first thing they see in their university life: basic programming, loops, and whatever. I'm also teaching algorithmic design, the last course that they take. And it's completely different because all the students in that latter course have already passed through university, and they are super good students.

It's amazing because you can see the evolution of these fearful students who are in university for the first time, and they don't know if they're going to pass. They're just concerned about exams, but not nearly concerned enough about learning and growing, just about passing the exams. And then you have these graduating students: it's very hard for you to fail them. Whatever you do, they will pass the exam. They're super optimized for university. And there is little correlation between this and their skills, which you find out when you get to know the students.

I also do a lot of thesis advisory. I always get like ten student applicants every year. In the CS majors, we do a bachelor thesis, then you have a masters, and then you have a PhD. So, you have three times where you have to do a project and present a thesis and everything. So, I always get like ten applicants. And what do you ask as an advisor in the final year?

"Who are the best students? The ones that have the highest grades. Those are the ones I want to advise because those will be the best students doing the thesis."

No, it doesn't work like that. There is very little correlation between how good a student is at doing one single project with their school grades. (It's not exactly uncorrelated because discipline plays a role in both things, but it's basically discipline the only thing that plays a role in both.) What matters is being excited about the topic and pushing through the difficulties to do something incredible.

However, students that lack discipline won't get through university no matter how talented they are, no matter how excited they are. And a disciplined student will get through university almost regardless of how talented they are and how much they enjoy their classes.

So, when I see these ten students, it's very hard to predict their abilities by knowing their academic results. It's very hard to predict who will make a good thesis here because that only depends on how much you get them excited about the problem, how much you guide them, and how much they want to do something that is better than what you ask of them.

For example, one thing that I see a lot — and I think it's one of the biggest dangers of this problem-solving mindset of education — is the competitive mindset in computer science. (I wrote a post on my blog about this.) The top students almost all want to go to the ICPC programming contest. We have like four students every year who are preparing themselves for contests. And this does build a lot of important skills, like problem-solving, identifying common patterns, and whatever. And it also develops a little bit of teamwork because contrary to competitions in physics and mathematics, you go in teams of three and work with one single computer. So you have a bit of teamwork there.

But what I've seen is that a lot of these students who optimize themselves for university to be good competitive programmers are very bad at open-ended kinds of problems. When you put them into a project and tell them, "We want to do a better cat classifier," they ask you, "What is the objective? What is the metric?"

I want you to discover the objective and the metric! I just have this big question. I want you to find yourself what is the right problem.

They are very optimized to solve a very well-defined problem that has a very well-defined success metric. They are very good at that. But if you give them an open problem, they almost always get bored.

To optimize something is easy. It's easy to measure that you're making improvement if you're solving math problems. The number of problems that you solve and the difficulty of each problem is a very easy metric of "I'm making improvement." And if you give them an open problem and say, "Here, you have six months, come and show me something," it's very hard to say, "Oh, I'm being the best at this right now."

Tivadar: Yeah, most students are used to immediate feedback. This is not something you have in real life. Say, you make a decision to start a company. You’ll have feedback years from now, but not at that moment. In practice, (almost) no problem is well defined.

Problem-solving in academia and in practice requires different skill sets. An analogy of mine, which I always think about, is that if you are a soldier, you are basically doing all kinds of physical training. Push-ups, pull-ups, whatever you need to get in shape. But in the battlefield, you never have to do push-ups. Then why practice them?

Because by doing push-ups and pull-ups, you train your body. And you need a trained body on the battlefield. This is how I think about competitive programming. The skills you mention, like problem-solving, are essential, but you have to be able to put these problem skills into context.

Another great point you raise is that those who optimize for problem-solving are usually really bad at teamwork. And I have also seen people who are decent problem solvers, but they are excellent at teamwork. A team with great teamwork always outcompetes a team with brilliant problem solvers who are unable to work together.

Alejandro: This is related to an interesting thing that I observed. We might even be able to explain it with a little bit of machine learning theory. What I observed is that if you have different people with different mindsets and different skill sets, they will make uncorrelated mistakes. So it's more likely to move in the right direction because the ensemble works better than any of the individual components. But if you get a lot of people that have the same mindset, the same skills, the same way of thinking, and they all push forward like a bunch of dogs pulling a sled, things can go super fast in the wrong direction.

When you look at successful startups or research groups, you’ll see that the ones that survive are the ones that have the right mixture of people. There probably are people there who are good at communicating, people who are good at teamwork, and people who are good at just pushing through difficult problems and spending a night implementing something so you don't have to.

If you're a student, you don't really have the negative examples to see “Oh, this is what I shouldn't do.” No, you only have the positive examples. So I think it's natural that when you finish your PhD or postdoc or basically your education and you become a professional in science, your role switches completely. You now have to become a communicator and a seller of ideas instead of a problem solver.

However, nobody teaches you how to do that, but everybody assumes that everybody will be able to make that transition. And that's survivorship bias. Everybody who is doing science are the ones who were able to make that transition. But nobody who is a student at a PhD can see the negative examples and say “Oh, I should optimize my communication skills more because otherwise, I won't be able to make this transition.” Because you never see the people who fail. Because the people who fail are not in the university. They drop out. Students get very little feedback on what they're doing wrong.

Tivadar: One of the biggest issues in education and academia is that it's a one-way road. Once you enter the industry, you can (almost) never go back to academia. This magnifies the survivorship bias effect you just mentioned.

Because a typical researcher spends their entire life in academia, they are unable to bring in the ideas, processes, and mindsets from the industry.

For example, in math, most research takes place at universities, which is also where the teaching happens. Most people never see anything outside this system. They are born, go to school at six years old, attend university at 18, finish their PhD at 26 or 27, and then they go right back into the same system.

This is very harmful because they don't see these other mindsets. And when they choose their successors, they will be very biased. So these filters that we talked about are stuck in place because we don't have fresh minds coming in.

Alejandro: Here is something we are experimenting with in our faculty. Traditionally, we have math and computer science majors, which are very concept and theory-heavy careers. The first three years of these majors are primarily focused on theory. A student in the third year of a computer science program doesn't know how to do much beyond proving theorems. They have barely undertaken a single practical project by that point.

However, we have recently introduced the data science major, the first one in our faculty in 50 years. We have designed the data science program quite differently; we start with practical skills. In the second year, students are already working with modeling in Jupyter notebooks. They may not fully grasp why machine learning works, but they are already engaged in forecasting in time series. Then, in the final year of the major, we provide them with a solid math background.

In our traditional majors, if you take a student midway through their education, you essentially have "half a computer scientist," which doesn't amount to much. In math, you have "half a mathematician" – someone who is familiar with algebra, analysis, and calculus but lacks practical skills. Statistics is only introduced towards the end of the major. Our approach is to produce graduates who may not fully understand the math behind it all, but they can actually apply their knowledge.

It's quite challenging to convince our math professors to embrace this kind of education. We believe there's no need to teach multivariate calculus before probability. Probability can be introduced in the first semester of the program because we want students to develop a probabilistic way of thinking about the world, rather than focusing on theorem proving.

So, it's super hard to explain the math professors that the curriculum for data science is completely different. It's based on practical matters and we’ll to teach them measure theory and sigma-algebras in the final year.

As you mentioned, most university professors primarily engage in "professoring" at the university. They often have a limited perspective and tend to shape our curriculum with the goal of producing more university professors. We inadvertently select and retain students who fit this academic mold. Consequently, the university system acts as a pipeline for creating more professors, while those who don't fit this mold often pursue productive roles in society.

Tivadar: So, it's a snake biting its own tail.

Usually, mathematicians make horrible professors, especially when they teach non-mathematicians. This is something which I myself want to overcome. As a mathematician, I had to study measure theory and real analysis before probability theory. The idea of probability is a very simple thing, and measure theory is extremely complicated. But this is how we teach computer scientists. This is much more math than a computer scientist would ever need.

As a content creator, I'm trying to solve this problem. This is what I'm going towards all the time, creating educational material about mathematics for non-mathematicians.

Alejandro: I honestly think that there is a gap in science communication. There are scientists who write publications. These are for scientists as well. And then you have people who write popular science, which is often full of bad takes and bad analogies. They are often not scientifically sound because they try to be popular. And, of course, you have to water down the language and make it as intuitive as possible, but you cannot introduce logical contradictions.

This is where the gap is. For example, in the case of math, content is going to be as accurate as it has to be, but not more. I'm not going to make any leaps that aren't logically consistent and that I cannot make. I'm going to make my arguments rigorous but in a language and format with the right amount of complexity. You have to take a lot of time to put all the intuitions in place so that anybody can understand it. And I think there is very little of this in popular science. I really like some people like Neil deGrasse Tyson who are science communicators but also good scientists. But most good science communicators are not good scientists. They became science communicators for a reason. So they have a popular view of machine learning in their head, and they will tell you things like, "Oh, no, language models understand what we are saying and they get things out of context." Context and understanding are something that you have to define precisely.

So I think that's a very important work to do, and I really hope more people with a strong formal background will decide to do it. We have one professor who is always on TV and communicates about math, and people look down on him, saying, “You're not doing the real science; you're doing the communication part.” And that's deemed unimportant. And I think that, just like you said, this is as important (or probably more important) than proving a new theorem.

Tivadar: Elitism is indeed a problem on academia's side. On the other hand, industry has an incentive and pressure to sell you stuff. The content creators claiming that machine learning is easy are doing it because they want to sell you their course.

I make my living from selling my Mathematics for Machine Learning book. I am trying to strike a balance. I try to be kind but also fair. I don't want to lie and overestimate the importance of mathematics. If you ever see me claiming that you must learn all of math to do machine learning, correct me on the spot. I never do that.

I always assert that math becomes important after a certain level, and you can easily get stuck without it. I won't be a multimillionaire from this; I'm barely making a living doing it full-time, but I will never make that compromise. I won't ever do marketing instead of education, and I will stay on this path.

Alejandro: I feel you.

I'm a full-time professor, and I don't plan to make a living out of content creation. It's because the incentives are weird. So, you are in a very difficult position.

If you want to make a little bit more money, you have to either convince a lot of people that the kind of thing you are doing is very important or you have to do something that is easier to sell. It's very hard to be in your position and decide to stay on the good path. So, I'm happy that I don't have to be in that position. I'm also really happy that some people decide to do it because it's important.

Sadly, there is no marketplace for thoughtful, deep ideas. No, the ideas that everybody talks about on Twitter are cheap.

---

…and it’s time to wrap this up here.

We’ve talked about quite a lot here, with quite a strong opinion about learning and education.

So, can we actually do better? Can we show how to focus on ideas instead of the unnecessary technical details?

We’ll release the first installment of our introductory graph theory series, and we’ll see how we do!

See you there!