Should I try to love math?

    Математика позволяет достигать успеха: запускать ракеты, обучать AI, и так далее. Самыми качественными кадрами считаются выпускники математических специальностей. Молодые работники, студенты и школьники, которые не идеально решают тренировочные задачи, часто комплексуют по этому поводу. Такие люди обычно переживают, что, если бы они могли полюбить и понять математику, то их жизнь изменилась бы к лучшему, но им этого, увы, "не дано".


    Объясняю, почему переживать и насиловать себя не надо.



    They say that mathematics is the queen and the crown of all sciences, that without mathematical thinking it is impossible to survive and succeed, and that everyone should be able to do it. Mathematical problems are set when entering universities and hiring. Mathematics is actively used by the technologies that shape our lives - in engineering, IT, finance ... A human mathematician is a superhero of our time, who takes on any tasks, solves all problems, and saves the world when no one else can.


    This story begins with elementary school: all children should know the mathematics for a good grade, and if this is not so, then they are problematic or perhaps just stupid. The phrases “good at math” and “very smart” become almost interchangeable. By the power of mathematical thinking they judge how capable and promising a person you are as a whole. At the same time, you may have been afraid of math at school, but solved / copied homework with gritted teeth and did not understand how this terrible obscure uninteresting subject can be loved.


    When the school has long been in the past, you graduated from high school and even got a normal job, math fever lets go a little. But not to the end. You read articles on vc.ru and channels in the Telegram about someone else's startups based on the latest technologies. And you in the background are thinking that if you had the mathematical skills and education, your life could be better. You would start doing artificial intelligence / blockchain / big data / algorithmic trading, start a unicorn startup and change the world for the better. But then you remember that you do not add fractions in your mind well. You realize that you are too stupid for this, or studied in the humanitarian class, or retook the matan in the first year, or just do not love mathematics enough ... And you accept these restrictions, and, recognizing yourself as second-class people, with a sigh, return to the routine. Maybe you give yourself a promise to learn math in the next year (when life goes well), and still return to this dull, tired of your current work.


    Although mathematics is used in a wide variety of professions and industries, it is rarely applied explicitly. Designers do not solve diffurs - they calculate the trajectory of a rocket (and maybe use software that solves diffurs for this). Economists do not equate derivatives to zero in the search for the optimal sales volume - they look at the numbers in Excel, and choose the option with the highest predicted profit (or NPV). Statistics do not calculate( X T X ) - 1 X T y on a piece of paper using the Gauss method - they write something likenp.linalg.lstsq(X, y)that, and spend their time thinking about whether theyXincludedall the necessary factors. We may not notice this, but intellectual work is almost completely automated. The computer will solve any complex equation for you if you run the correct program. For any task, you can pick up such a hammer that it seems to you just a nail.



    If you want to engage in analytical activities, then the ability to work with tools for you is much more important than the ability to count. "Work with tools" means:


    • adequately set the task;
    • find the tools suitable for its solution and choose the best;
    • to understand the specifics of this tool and apply it correctly to the task;
    • check the result for adequacy, and, if necessary, redo some of the previous steps - for example, change the tool.

    All these steps seem obvious and based purely on common sense. But this common sense is honed only by practice, and the more different tasks you set, provide with a tool, solve and check, the better you will succeed.


    Unfortunately, setting tasks, searching for tools among unknowns , quickly mastering new tools (at least asking questions and reading documentation), and working on errors in near-mathematical courses are often not taught. Instead, they give a ready-made task (often sucked out of the finger), and call a ready-made tool (for example, the theorem that is being passed now), to which there is already an instruction for use, and which is guaranteed to give a solution "for credit". Not surprisingly, in the end, mathematics seems to you a collection of abstractions, invented with the sole purpose of making your brain.


    And what kind of tools are there? In addition to narrowly targeted (software for calculating the trajectory, Excel, the SciPy ecosystem in Python, meta-tools are no less important: search engines, directories, forums, digital libraries. For example, you already answered any programming question that you can come up with (almost probably) on stackoverflow. The times when you could or needed to “know everything” ended in the last century, now it’s much more important to “know where to find everything.” Advanced educational institutions and employers understand this: for example, at the introductory school of data analysis can about bringing any literature, but you could use it.


    It may seem that treating mathematics as an instrumentation rather than a shrine humiliates you. But in fact, to be “cool, and as a scientist,” you just need to deal with the right and interesting tasks from your personal point of view, and treat them in good faith. If you want to make money or change the world, do it right away, not math! In the eyes of people you will become “smart” and maybe even a “mathematician”, but it will seem to you that in mathematics and in general in life you don’t understand anything. This is normal and not at all embarrassing. You can reassure yourself that the more knowledge, the greater the border of ignorance.


    By deeply working on the tasks you take, you will better understand what you want, until you turn it into an algorithm. For example, you need to attract more customers through the website (task). By tinkering with it, you will break a sales funnel and approximately evaluate the conversion at each stage, select bottlenecks, conduct experiments, try many options, and eventually find the best way to increase this conversion. This process of concretization of the problem is real mathematics. And the resulting algorithm (for example, a formula that selects which button to show the client) is not mathematics itself, but just its product.


    When you want to achieve a specific goal, you use all available means, including mathematical ones. If at the same time you cannot take the integral yourself, then you are looking for an assistant, ask a question on the forum, conduct a numerical experiment, replace the task with a simpler one, buy a more powerful computer - and you end up with everything. A motivated person does not sit and does not give birth to an “ideal” mathematical solution, but searches for any solution that satisfies his goal. The fear of math arises when you think that inability to solve a problem will prove to the world that you are stupid. But if mathematics is not an end in itself, there is nothing to be afraid of: you can cheat, you can write off, you can shift the task to others or choose the right solution at random. And no one will blame you for this (except for those who envy you).


    I can be objected to by students who cram mathematics to enter a university, or students who work it to finish this university. They can claim that their goal is just to prove that they are smart. But in this situation, you can continue to ask "why." Why graduate? To gain professional competence. Is it possible to get them differently? Yes, there are more direct ways: online education, paid courses, tutoring, internships, mentors, studying someone else's successful solutions from open sources ... Mathematics can also be found there. But at least you will understand that it is needed for the cause, and not for demonstrating your own dignity, and you will treat it not as an icon, but as a useful tool. As a result, you will save yourself from the pain of learning, in which you do not see the point,


    Another situation is also possible: you realize that you love mathematics in its best manifestations, but you still do not understand the theory well, it bores you. Then you can be advised:


    • light blogs about mathematics in life, from section n + 1 to public vk - there you are fed maths with a spoon and with jam;
    • the development of simple games. To create even a minimal game world (like a flappy bird) you will need a fair amount of equations, and while you come up with them and code, your intuition runs the risk of pumping a lot;
    • data analysis. Over the past year, big data, AI, ML and all this has become almost the main trend in the business, and, as a result, in the labor market. Many people come to this field, not knowing mathematics, but knowing how to program, and understand everything along the way. And it seems that such a strategy works well.

    Conclusions . I think you already understood how I answer the question from the title of this text: you don’t need to try to love mathematics by force. Because:


    1. There are many mathematics around us, and this creates social pressure: your achievements in mathematics become the measure of your entire personality, which, if you think about it, is absurd.
    2. To solve practical problems, deep mathematics is usually not needed - common sense in choosing tools is enough.
    3. When you do interesting and useful things, mathematics often comes to you. But not as a painful end in itself, but as a useful tool to achieve your real goals.

    Feel free to do what you like and do not force yourself to anything else.


    Good luck to you!


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