About Mariana Trench in Maths education

"And what should I do with mathematics later? Work as a school teacher and earn peanuts?" asked a 17 years old Eddy who soon needs to decide on which subjects to do for his final exam.

His mum, who was sitting right next to him, perfectly understands the concerns and genuinely wants to help. Sadly she knows that she cannot give a better answer than: "Well, not peanuts... And just trust me, maths might be useful. Plus you liked some of the maths classes, didn't you?". However, saying this to her son yet another time will only make him angry. She wishes she could provide him with more convincing arguments, as she really wants Eddy not to cross out critical and logical thinking from his life. But she is not even sure that her own thinking is right... What if maths in schools is not that useful? Should she even try to consult her beloved son in this matter? What if she convinces him to focus on working with those stupid numbers and he ends up not being able to afford good life? That is definitely not what she wants for the person she loves the most...

I wish I could quickly interlude and simply show the job offers that me (the author of this post) and my friends-mathematicians have recently got. Each of them is for at least 10000$ dollars a month, with one of them actually being around 400000$ a year. And none of us are geniuses. But each of us is a hardworking mathematician who is around 21 years old.

But I am not saying everyone should do mathematics in their lives and actually Eddy's questions are reasonable. There is a hole in usual school-maths-education that is the size of Mariana Trench, and many people can feel it. And well, the things that all of us would be doing once we accept our offers fall right into that hole.

It will take a long time to describe all the issues with the school maths curriculum, I just want to point out one aspect of them: "probability and statistics". I have decided to pick that one because this is exactly what those jobs we got offers for are about.

It is mind blowing that "probability + statistics" is barely mentioned or not mentioned at all in most school curriculums. Even in some good schools, those things are basically omitted. And please do not say something like "we learnt that the probability of rolling a 5 is 1/6", so we had probability. Moreover, "we learnt what a histogram is" so there was statistics! No-no-no. No.

First of all, please answer yourself: "why is it that the probability of rolling a 5 is 1/6"? If you are going to say that this is because "there are 6 events that are equally likely and we need one of them, hence the 1/6", then you will be wrong. That is not the actual explanation. The real explanation is "by definition it is 1/6"... That thing about "equally likely events" is more like a motivation. But what is important is that before we proceed to solving those problems we ourselves need to pick a "model", i.e say something like "alright, let's work with dice. Assume they are fair, i.e assume that the probability of rolling a 1 equal to the probability of rolling a 2, ... equal to the probability of rolling a 6 and is equal to 1/6". If you did not know this (as the majority of the people), then you have not been explained the "why" of things when it comes to probability. Moreover, in most schools you do not really solve a lot of problems on probability and almost surely things like the Monty Hall problem are either left without attention or with no explanation.

Secondly, knowing what a histogram is and being able to read it is not knowing statistics. If you did get to interpreting even the simplest data, it is nice. But what is more important is to spend more than a week or two trying to interpret data sets, use some probability knowledge and also understand that it is all not easy. There are a lot of different caveats and the more of them you meet, the better. In particular, you will see how ridiculous a lot of the conclusions made by some media are and thus it will be much harder to get brainwashed.

Thirdly, if you are a high school student and you were not told about all the range of jobs and interesting researches that are related to probability + statistics, then you are not familiar with some fascinating interesting mathematical careers that can also bring a lot of money. For example, things like "Artificial Intelligence", "Machine Learning" or "Neural Networks" actually fit into that description and are all very hot topics right now.

Even though this post is long, I tried to be brief and not go into many details. Therefore, some of the claims might sound too general, sorry about that. And I know that people have different passions, different family situations, etc.. and therefore far not all will even think about doing maths. But what puzzles me is that the maths curriculum that is often 12 years long is still like a house from the picture attached to this post...

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