The question sounds as if the mathematical mindset is something innate. I don't know the scientific data on this, but I know the pseudoscientific myths. So I'll give you my personal opinion. I will highlight three components that are necessary for mastering mathematics, and which are brought up in the process of studying mathematics.

1. A tendency to play math; a kind of aimless curiosity, a desire to try “What if?”, to experiment. So the professional mathematician Ulam accidentally built the Ulam tablecloth. This is how small children solve riddles and riddles. The spontaneous desire to learn new things is innate, but it can fade away in an unfavorable environment, often in elementary school.

2. The desire to check everything and not leave misunderstandings in the rear. The habit of slowing down, not grasping at the first thought that comes along, justifying your reasoning logically, and not losing special cases. This is not innate, but should be brought up in the course of systematic education.

3. Easy movement on the ladder of abstractions, when the same object is viewed from different positions. For example, when working with an equation, it can be perceived as an element of a wide class of equations (for example, integer or diophantine). You can work with it “personally”, transform it somehow, expand brackets, etc. You can look at the equation as a testing ground for different values of a variable, substitute individual values in it and see what happens. This is generally rare.

For mathematics, you need to be able to arbitrarily direct your thought both in width (experimenting), and in depth (reasoning and justifying), and in height (changing the focus and detail of the approach). Changing approaches arbitrarily and purposefully is probably the most difficult thing in mathematics.

2. ivan_chistyakov says:

To begin with, it is worth understanding that the mathematical and humanitarian mindset are concepts put forward by it is unclear who else in the scoop, which do not have any more or less sane evidence, and assume that mathematicians and humanitarians are fundamentally different people, that they are almost born like this.

In fact, they are generally similar people, but they differ quantitatively in three parameters : the level of development of cognitive abilities necessary for performing mathematical operations (the ability to manipulate imaginary objects, working memory, etc.); the development of math skills (the amount of practice in performing mathematical operations) and the severity of avoiding tasks that require math skills. Moreover, it is not a fact that the one who is called a mathematician has both more developed cognitive abilities, more practice, and less pronounced avoidant behavior.

I haven't studied this question systematically, but in my experience, people who call themselves humanitarians simply avoid practicing mathematics and, accordingly, do really poorly with mathematical operations. They might be able to learn all of this, they don't have any dementia or humanitarian mentality, their required cognitive abilities may be at or above the level of “mathematicians”, but they don't develop math skills out of fear. This phenomenon is called mathematical anxiety and is now actively studied, because it greatly hinders the growth of the population of scientists and the development of science.

Perhaps the concept of the humanities mindset was created not to solve the problem of mathematical anxiety – having it in service, we can say that these people are not like that because the education system did not find a way to teach them mathematics and now they are afraid of it like fire, but that they are just special and see the world differently.

3. alexander_shestakov says:

A mathematical or other mindset is determined experimentally – what a person or child is interested in (enthusiastically systematically interested, chooses as a hobby or profession), then proves what they are looking for. A big mistake is excluded here.

Specific material for the experiment – a variety of toys or tasks or topics/texts.

There are people who are intensely interested in everything useful from different sciences and spheres of life (generalists-encyclopedists).

There are people who are more dominated by logical or geometric or applied or abstract talent. For example, mathematicians, lawyers, and inventors need logical talent.

4. skysmart_online_school_for_children_and_teenagers says:

Hello.

I would say that people are right-brained and left-brained. The first – “humanitarians”, the second – “techies”. The former tend to think holistically, integrally, more often through intuition. They prefer to study languages, literature, history, art history, etc. The latter are mainly inclined to differential, analytical thinking, more often through the conscious mind. They prefer to study mathematics, physics, and technical sciences.

But do not think that the former are more stupid than the latter. They're just different ways of seeing life. Let's compare them. In terms of languages, there are linguists (language mathematicians) and philologists (language humanities). The former analyze texts in parts, calculate grammatical changes, correlations, and emphasize the linguistic correctness of speech (just like in mathematics). The latter look at the artistic and expressive means of language, the ability to convey feelings and emotions through linguistic realities. Here it is not the correctness of grammar that is valued, but the accuracy of meanings and emphasis on moods.

Mathematicians and techies are more open to the analysis of thought, better explain how they came to this, because the very essence of their thinking is the operation of the mind in consciousness. No, there is mathematical intuition, but reason prevails. Without intuition, complex problems are not solved. But the routine is performed with the help of reason and ready-made rules.

And humanitarians are sincere people. They don't really like it, and they don't always know how to explain how they solved the problem. They can't always put it in simple words. This is understandable, because they work with intuition – the subconscious part of the mind. And their tendency to emotional-volitional sphere does not have them to make conclusions, it is boring for them. But their intuition is sometimes very strong. And it's hard to see how they can do that. Some consider it a special gift. I wouldn't say it's a special gift. They just think inside, and the subconscious mind works faster, has more time to view, and draws conclusions on its own, without regard to logic (although not without it, it just doesn't think about it). So the impression of a gift is created. A real gift is only from God. And this is not necessarily just the humanities. But this is a separate conversation.

In the end, each of these two types is good in its own way and deserves respect.

Be reasonable and polite!

5. alexey_krugov says:

A mathematical mindset is usually understood as the ability to analyze and structure a problem. Take it apart, plan it, create algorithms for solving it in your head, and so on

6. artem_khojayan says:

I liked Artyom's answer better, but like the others, I still don't think it's correct either. I won't give you an answer either, because it's a mystery to me.�

I don't have an outstanding knowledge of mathematical sciences. I solved everything in lessons/pairs “naotvali”. I am a three-year student in higher mathematics and discrete mathematics, but for some reason the school teacher, a sooo wise person, everyone respected him, once brought me a textbook from a technical university and offered to enroll there. I was shocked at this moment for the first time. The second one happened at uni, when two different teachers, a man and a woman, asked me if I had previously studied at Matmech, to which I replied-no. It looked spontaneous and with nothing but gorgeous knowledge I didn't show. There was a guy in the group who really rummaged in matana and decided everything 100 or 90+.�

I mean, you need to ask and listen to real mathematicians, not psychologists. I think so. They see what no one else sees.