Below you find some thoughts on this wide question, I encourage you to think about. What is your vision of mathematics? It will be most probably the result of your own experience with the subject, traumas that happened along the way and realizing that, could make you more conscious about your relationship with the subject and the walls you might have built against the subject or part of the subject. In a sense, by understanding the bias and blockage, by objectively thinking about its value, you could allow yourself to be able to equip yourself with the full set of skills mathematics gives you to build your own greatest life.

Many of thoughts in the following around this topic are taken from the paper I recommend to read: Teaching and Learning “What is Mathematics and why we should ask, where one should experience and learn that and how to teach it”, by Gunter M. Ziegler and Andreas Loos, in Proceedings of the 13th International Congress on Mathematical Education. (https://link.springer.com/chapter/10.1007/978-3-319-62597-3_5)

If you type mathematics on google, you might find as a definition of Mathematics:

• the abstract science of number, quantity, and space, either as abstract concepts ( pure mathematics ),
• or as applied to other disciplines such as physics and engineering ( applied mathematics ).
• “a taste for mathematics”
• the mathematical aspects of something.
• plural noun: mathematics
• “James immerses himself in the mathematics of baseball”

Any of the definitions of mathematics on the web I found is not entirely wrong, but in my opinion, none of them is complete or satisfactory, no matter how descriptive they become.

To me, one could find mathematics aspects almost everywhere:

• “Mathematics is the part of physics where the experiments are cheap.”
• “Mathematics is the part of philosophy where (some) statements are true ” without debate or discussion.”
• “Mathematics is the study of numbers, shapes, and patterns.”
• “Mathematics is computer science without electricity.” (So “Computer science is mathematics with electricity.”) …..

None of these is, of course, completely true or completely false, but they present
opportunities for discussion.

“Some students might be motivated to learn mathematics because it is beautiful, because it is so logical because it is sometimes surprising. Or because it is part of our cultural heritage. Others might be motivated, and not deterred, by the fact that mathematics is difficult. Others might be motivated by the fact that mathematics is useful, it is needed – in everyday life, for technology and commerce, etc. But indeed, it is not true that “the same” mathematics that is needed in everyday life, for university studies, or in commerce and industry. To other students, the motivation that “it is useful” or “it is needed” will not be sufficient. All these motivations are valid and good – and it is also totally valid and acceptable that no single one of these possible types of arguments will reach and motivate all these students.”

“Many students and undergraduates seem to think of mathematicians as old men who are obsessed with their subject, lack social skills and have no personal life outside maths.” The student’s views of maths itself included narrow and inaccurate images that are often limited to numbers and basic arithmetics.”

It is quite important to address this question of the image of mathematics. Subconsciously, human beings might get curious and good at things they can somehow identify to, and they might not be willing to identify to a subject that when you become good at it, seems to make you mad, obsessed, outcast or asocial. To attract students and stimulate their interest, it might be important to be able to have many examples of mathematicians that are social and happy being while passionated about the subject of mathematics. If success at mathematics means a lonely and sad life, I believe psychologically the students would most probably reject the topic. Actually, it is what usually happens often that people hate the topic as they tell me because of their “very bad experience in mathematics”, sometimes with a so-called “bad teacher” they could never relate with.

“The public image of the subject of mathematics (of the science, and of the profession) is not only relevant for the support and funding it can get, but it is also crucial for the talent it manages to attract – and thus ultimately determines what mathematics can achieve, as a science, as a part of human culture, but also as a a substantial component of economy and technology.”

“The discussions about the classification of mathematics show how difficult it is to cut the science into slices, and it is even debatable whether there is any meaningful way to separate applied research from pure mathematics. So there is no real answer to the question of what is mathematics?”

One statement I quite like to show how powerful mathematics is one my colleague Dr. Ben Blum Smith stated in his TED Talk  about the relationship between Democracy and Mathematics:

“Do not get seduced by the lie that mathematics is not relevant to you. Whether you personally ever do any mathematics again, people are going to make decisions shaping your life and using mathematics to it. You can be at the table on those decisions or not.”

In his pursuit of making Democracy and maths correlated, he is also trying to show that maths can and also talk to those structural components of the society.

Mathematics is used all around you especially nowadays.

For myself, mathematics is independent of all of this, if one refers to Plato, Athenian philosopher founder of the Platonist school of thought. Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices.

I myself might not be as sure as Plato about his view of mathematics. But I view any form of abstraction as mathematics. For instance, any language could be seen as the outcome of a form of abstraction. To me limiting mathematics to its practicality could be missing the important skills, it equips you with.

To me, mathematics besides the well-known problem solving and critical thinking it endowed you with could also improve your rigor, focus, empathy, mindfulness, communication, organization, time management, your inner self at the same time as the possible improvement of the outer world if made clearer and more human. Let me give you some examples.
For instance, if you manage to do a very long computation only made of technics you very well know, very used to and you manage to do no mistakes at all, even not a small one then it means you are able to focus, be mindful for this entire moment with your work.

If when you write a proof in mathematics and you are very careful about making yourself understood by others, trying to anticipate other perceptive that the reader could have when he reads your work and you are concerned about him/her being able to understand you, you will be practicing empathy and communication. If you have a short test 20 min with quite a few questions that would take you longer if you had more time, you are practicing time management.

To me, at every given moment, you have a choice to learn something new or refuse the new learn, if you learn something new you will always have the option, the choice to either taking it inside your set of values or not, but if you do not, you even do not have this choice at all. Mathematics gives you a huge opportunity to learn, to improve yourself and your quality of life, if you make peace with it and see beyond its practicality one praises it for.

To conclude: mathematics is much more vast than you can imagine and give you much more important abilities that you might not even perceive yet, do not close the door to it, make sure you are not closing the door to being your best!

 How clear is this post?