Do you have to try to love math?

If you don’t like and don’t understand math, does it mean you are stupid?
Do you need to love math to achieve at finance/engineering/science? No.

Where you possibly are

People say that math is the queen of all sciences, that without mathematical thinking it’s impossible to survive and to strive, that everyone should be good at it. Mathematical problems are asssigned at school admission exams and job interviews. Mathman is a modern superhero, that solves all problems and saves the world when no one else can.

This tendency starts with junior school: all children have to get good math grades, otherwise they are difficult or, maybe, just stupid. The phrases “Good at math” and “very clever” are used almost interchangeably. But some of you were probably afraid of math at school. Nevertheless, you solved (or copied) math homeworks and wondered how anyone can love this dreadful, confusing and boring subject.

When school is far behing, when you have even finished a university and found a good job, this mathematical fever somehow relaxes. But not completely. Sometimes you read articles and posts about someone’s high tech startups. And you start thinking (in backround mode) that if you had a more technical education and mathematical abilities, your life could be better. You could start at AI/blockchain/big data/algotrading/etc, you could found a “unicorn” and make this world a better place.

But then you recall that you have difficulties adding fractions in your mind. You realize that you are to stupid for this, that you had majored in humanities or had to retake the calculus, or that you just don’t love math deeply enough… And you accept these constraints, and, feeling a little bit second-rate, you get back to your routine. Maybe, you promise yourself to learn math next year (when life gets better), and return to your hateful boring routine job anyway.

Where you could have been

Math has applications in many professions and industries, but rarely it is applied directly. Constructors don’t solve differential equations — they calculate trajectories of rockets (and maybe use the differential-equations-solving software to do it). Economists do not evaluate derivatives to find optimal sales volume — they look at numbers in Excel, and choose the option with the highest profit (or NPV). Statisticians don’t calculate OLS formula with paper and pensil by gaussian elemination — they code something like np.linalg.lstsq(X,y) and spend their time thinking whether all the facturs they need are included in X. You may ignore it, but intellectual work is already almost fully automatized. A computer can solve any difficult equation for you, if you run the right program. For any problem you can find such a hammer that the problem will look no more than a nail to you.

If you want to do perform analytical work, then skills of using right tools are more important than direct quantitative skills. “Using tools” means:

  • pose the sensible problem;
  • find the relevant tools and choose the best one;
  • dive into specifitx of this tool and apply it to the problem correctly;
  • check the adequacy of your result and redo any of the previous steps, if you have to (e.g. change the tool).

All these steps seem obvious and based on pure common sence. But this sense is sharpened only with practice, and the more problems you pose, provide with an instrument, and check, the better you would be at it. The secret is to do the whole cycle.

Unfortunately, many near-mathematical courses do not teach neither problem statements, nor search of new instruments among the unkown, nor their fast exploration (at least, asking questions and reading documentation), nor processing of the mistakes. Instead, they give prepared problems (often unnatural) and ready-to-use instruments (e.g. a theorem from the today lecture) which yield predictably passable (and boring) solutions. No surpize that math often seems a collection of abstractions which were designed with the only purpose to blow your mind.

By the way, what kind of instruments can exist? Highly specialized ones (the trajectory-calcilating software, Excel, SciPy ecosystem in Python, etc) are important. But “metainstruments” — search engines, handbooks, forums, digital libraries — are no less important. E.g. any programming question you can think of has been most probably answered on Stackowerflow 3 years ago.

The times when you had to “know everything” are long gone: nowadays you have to know “where to look everything up”. Advanced schools and employers understand this: e.g. you can bring any books on exam in Yandex School of Data Analysis, if you know how to use them.

How to get there

It may seem that the “it’s-just-an-instrument” attitude to math makes you less of a scientist. But in practice, “to be a cool scientist” means doing the right things (from your personal point of view!) and interesting problems, and do it conscientiously. If you want to make money or change the world, do it straight away — you don’t have to start with math. If you do cool thigs, you may have a geeky and even mathy image, but you will still feel that you aren’t good at math and in life in general. It is OK. The more you know, the larger is the border with the unknown.

When you dig deeply into the problems you accept, you continuosly improve your understanding of the process, until it turns into an algorith. For example, you may need want to attract as many clients as possible to your site. After playing with this problem, you decompose the sales funnel, estimate conversion at each stage, find the bottlenecks, conduct experiments, compare tons of options, and finally find the optimal way to improve overall conversion. This process of gradual problem concretization is the real math. The resuting algorithm (e.g. the formula to predict which of two buttons the user would click) is not the math itself, but only its product.

When you want to reach a concrete goal, you exploit all the available means, and math among them. If you need but aren’t able to take a complex integral, you look for a helper, ask questions on a forum, do a numeric experiment, replace the problem with a simpler one, or rent a more powerful computer — and finally you get it. A motivated person does not sit waiting for an “ideal” mathematical solution, but looks for any solution which satisfies the goal. The fear of math emerges when you think that your inability to solve a problem shows to the world that you are stupid. But if math is not an end in itself, there is nothing to be afraid of: you can cheat, you can copypaste, you can delegate the problem or find the right solution by pure guess. And nobody would judge you.

Not your case?

There may be objections from students who cram math in order to enter a university or to finish it. They can say that their goal is exactly to prove that they are not stupid. But I can go on asking “what for?”. Why do you need to finish an university? Probably, to acquire professional competencies. But there are more straight ways to acquire them: online education, paid courses, tutorship, internships, just studying best practices from open sources… In these ways, you could encounter hard math as well. But at least you would understand that it is needed for real business, and treat it not as an idol, but as a useful instrument. As a result, you would avoid the torture of useless education, and reach your final goal (employment) faster.

An opposite situation is also possible: you realize that you love math at its best, but the theory is too boring for you. In this case, I would advice:

  • light blogs about math in real life (like my public in Russian);
  • development of simple games. To create even a minimalistic game world (like flappy bird), you need lots of equations. You can dramatically upgrade your intuation while inventing and implementing them;
  • data analysis. Nowadays, big data, AI, ML, and all that is the main trend in business, and therefore on the labor market. Many people come to this field without deep math knowledge, but with good programming skills, and grasp the rest on the go. This strategy seems to be working OK.

Conclusions

You have probably already guessed that I answer the title question negatively: you don’t have to force yourself to love math. Because:

  1. There is lots of math in the modern world, and it creates social pressure: your success at math is used as a measure of your whole personal potential, and this is absurd.
  2. For most practical problems you don’t need deep math. Instead, you need common sence in choice of tools, and it is just enough.
  3. When you do interesting and valuable things, math often comes to you by itself. This time, not as a painful goal, but as a useful tool to achieve your real goals.

So don’t hesitate to do the things you like,
and don’t force yourself to do all the rest.

With love,
David.

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