Why mathematics?

Introduction

Sadly, school maths is usually taught in such a way that students think that the anecdote below stops being a joke if you replace the lecture's topic with "Mathematics". In this article, we will explain why it is wrong to think so, but unlike many other articles on a similar topic, we will avoid making general claims like: "the universe is mathematics" without supporting them with good examples.

This article should be interesting for pupils who finished primary school, adults, and everyone in between. It should be an easy read, even though it contains some mathematical arguments inside. But they are simple, so do not worry.

Among the things mentioned here: technology, famous people, media and even philosophy... All of these have some direct or indirect relation to mathematics. You might be quite surprised by them!

Among the things mentioned here: technology, famous people, media and even philosophy... All of these have some direct or indirect relation to mathematics. You might be quite surprised by them!

Critical and logical thinking

First things first. Good mathematical training should develop a number of skills like "critical and and logical thinking", which gives rise to the following abilities:

1)**Thinking from first principles**. This is when you boil things down to the most basic truths (or as mathematicians call it: the "axioms"). One should be careful with picking the axioms of course, but once they are chosen, the rest is a matter of working out logical conclusions. And it is ridiculous how often people fail to do so and therefore conclude wrong results. Even famous and smart people fail. For example, famous philosopher Immanuel Kant claimed that the question of whether the universe had a beginning is a contradiction of pure reason. He incorrectly "proved" his claim using the unspoken assumption (i.e statement that he picked as an axiom) that time continues back forever. And as it turns out the concept of time has no meaning before the beginning of the universe. By the way, all these question about the universe and time are great questions. Have you even wondered about them yourself? If it looks interesting to you, we recommend you read the wonderful book "A brief history of time" by Stephen Hawking.

1)

Another example: until the middle of the 19th century people were convinced that the so-called Euclid's parallel postulate is always true (it says that if there is a point *P* and line *L* then there there is a unique line parallel to *L* that passes through *P*). And guess what — it is not. The first person to publicly claim it, Nikolai Lobachevsky, was kicked out of university for that. However, now we would not even think about launching anything into space or having internet if we did not know that there are many different useful geometries, and in some of them Euclid's parallel postulate is totally wrong. So once again, if you do not pick that postulate as the fundamental truth (but pick something else) you can build a new geometry that is essential for things like internet, GPS, ....

2)**Questioning everything**. This one is that the authorities are not happy about. What we mean is that people in power usually do not want others to question their actions. Ask yourself: "which corrupt, thieving president wants a revolution in their country?". And when solving mathematical problems, the question "why?" rises every 7.48 minutes on average (just kidding, it is a random number). The point is, it crops up very often. So "mathematical minds" are designed to question everything. And sometimes it leads to interesting conclusions like: "Hm... This person is trying to deceive me..." or "We can do better than that. Shall I start my own company then?".

2)

Elon Musk

Statistics and probability

This one, especially in combination with the previous section, deserves personal attention. Let's look at the picture on the right:

Are you thinking the same thing as a mathematical-minded person would? That this speech is a load of crap? But we don't mean the numbers are wrong. No. The main point is that even if the numbers are correct, they do not mean as much as he wants us to believe they do...

Are you thinking the same thing as a mathematical-minded person would? That this speech is a load of crap? But we don't mean the numbers are wrong. No. The main point is that even if the numbers are correct, they do not mean as much as he wants us to believe they do...

First of all, the average increasing does not mean that middle-class started earning more. It might be actually the opposite! Indeed: suppose in 2020 there were 100000 middle class people each earning 500 dollars month and there were 1000 rich people each earning 25000 dollars a month. Then the average is about 742 dollars. Now suppose that it is 2021 and middle class people earn 400 dollars a month while rich people earn, say, 50000 dollars a month (on average). Then the average becomes 891 dollars a month which is 20% more than before! Also, what if together with average salaries, the prices for products also increased? Say by 40%? Then the increase, although an increase, is nowhere near enough. Thus, this statistic on its own does not really say much.

Second, this foolovid test they developed — it is totally useless. Suppose that someone is tested positive. What is the probability that he/she actually has foolovid? Using the information that that guy gave us, it will is around 9% (but to show this you need Bayes formula. It is not hard, but let's not go into details). Only 9%, what kind of test is it? And it costs 5 dollars as well... Tossing a coin will give much better results than that damn test!

Thus, answering that speakers question: "No, I do not agree that by just listening to that I should think that the government is great."

Second, this foolovid test they developed — it is totally useless. Suppose that someone is tested positive. What is the probability that he/she actually has foolovid? Using the information that that guy gave us, it will is around 9% (but to show this you need Bayes formula. It is not hard, but let's not go into details). Only 9%, what kind of test is it? And it costs 5 dollars as well... Tossing a coin will give much better results than that damn test!

Thus, answering that speakers question: "No, I do not agree that by just listening to that I should think that the government is great."

Just in case, the speech above is not a real speech of a politician. And you should not stop trusting the covid-tests, it is not like foolovid-test. Okay? The important conclusion here is different: you should be careful when dealing with statistics and probability. And maths will help here. Besides, we once again see that critical thinking and logical thinking play important role here.

We do not want you to think that statistics is just a tool to deceive/manipulate people (though it is often used as such!). It has a wide range of good applications, not related to any kind of fraud. For example, do you know what lead to requiring doctors to wash their hands when dealing with patients in hospitals? Sad statistics. Namely the observation from middle of 19th century that percentage of successful birth-givings in hospitals is much smaller than in the streets or some other not that specialized places. Or another medical example — the "machine-learning" that is all the rage now, which is an assortment of algorithms that use statistics, is used for formulating a diagnosis and recommending a treatment option. By the way, this same thing (machine-learning) is also used for speech and images recognition.

Isn't it all cool and interesting? Don't you want to get to know more about all that? If you do, then please dive into the world of mathematics: world of problem solving, critical and logical thinking, noticing patterns, ....

We do not want you to think that statistics is just a tool to deceive/manipulate people (though it is often used as such!). It has a wide range of good applications, not related to any kind of fraud. For example, do you know what lead to requiring doctors to wash their hands when dealing with patients in hospitals? Sad statistics. Namely the observation from middle of 19th century that percentage of successful birth-givings in hospitals is much smaller than in the streets or some other not that specialized places. Or another medical example — the "machine-learning" that is all the rage now, which is an assortment of algorithms that use statistics, is used for formulating a diagnosis and recommending a treatment option. By the way, this same thing (machine-learning) is also used for speech and images recognition.

Isn't it all cool and interesting? Don't you want to get to know more about all that? If you do, then please dive into the world of mathematics: world of problem solving, critical and logical thinking, noticing patterns, ....

Physics

Remember the phrase from the beginning of this article, saying that "the Universe is mathematics"? Well, this might not be true. We are sorry to make mathematics look a bit less perfect, but we just want to be honest with you.

However, here is the truth: the best model for the universe we have so far is mathematical. We do not know all the answers, but we know this: it takes approximately 1.41 times more time for apple to reach the ground if you let if go from 2m height rather than from 1m height. It is always the case (well, if you do the experiment "honestly"). What is that number 1.41? It is the approximation of square root of two. Why is that true, where do all these numbers come from? Please call Newton.

However, here is the truth: the best model for the universe we have so far is mathematical. We do not know all the answers, but we know this: it takes approximately 1.41 times more time for apple to reach the ground if you let if go from 2m height rather than from 1m height. It is always the case (well, if you do the experiment "honestly"). What is that number 1.41? It is the approximation of square root of two. Why is that true, where do all these numbers come from? Please call Newton.

And here is what one needs to appreciate and here is what supports the claim from the beginning of the previous paragraph: by just dealing with numbers and some formulas, we can predict what is going to happen very well. If you now give me an apple and ask me "so how long will it take for this apple to reach the ground if you release it from 37 metre height", I will take the apple from you and eat it. And also tell you that "It is about 2.7 seconds", instead of going around the city trying to find the corresponding building and a buddy who will assist me with measuring the time (plus I will then probably destroy the apple which is sad...).

So it is not how beautiful the weather is or how nicely some poem rhymes that helps with predicting the universe behavior. It is a bunch of scary integrals, derivatives, matrices, and so on that help...

So it is not how beautiful the weather is or how nicely some poem rhymes that helps with predicting the universe behavior. It is a bunch of scary integrals, derivatives, matrices, and so on that help...

What about humanities?

First of all, do not misunderstand the end of the previous section— we do not want to bully people doing literature, history, psychology (which heavily relies on statistics by the way), etc... They have their own use and purpose, but we will not talk about it here. Actually, one of the humanities subjects, philosophy, is a predecessor of almost all of STEM, including mathematics. That is why you can hear something like "PhD in mathematics" which means "philosophiae doctor in mathematics".

Secondly, doing mathematics/physics/IT properly in no way means that you will not be able to do anything else, that you will not know how live in a society, how to joke, how to do sports, .... It is such a silly cliche actually. Well, everything but maybe the jokes part :-/

For the sake of being consistent and providing good examples to support the claim, let's have a look at the list of people who got mathematical/physical/... education at university which means that after many years at school they decided to study mathematics/physics/... seriously and spent many years doing that (and thus their main education is in the corresponding STEM-subject). In no way this list is complete, it is just we do not want to overload you with information:

For the sake of being consistent and providing good examples to support the claim, let's have a look at the list of people who got mathematical/physical/... education at university which means that after many years at school they decided to study mathematics/physics/... seriously and spent many years doing that (and thus their main education is in the corresponding STEM-subject). In no way this list is complete, it is just we do not want to overload you with information:

Final words

For the sake of keeping the article short, we will stop here. Please do not be angry that we did not mention some important benefits of doing mathematics. We know we did not. Instead please spread the word about this article and make us understand that it is popular, and then we might write a sequel.

We hope that this article will increase the interest in the mathematics and the amount of people now knowing how to answer the questions "why mathematics? what is it good for?" will decrease. Especially among the younger generation.

In case you have any suggestions or questions — feel free to email us on kvantaen@gmail.com. Thank you for your attention!

In case you have any suggestions or questions — feel free to email us on kvantaen@gmail.com. Thank you for your attention!