What Is Mathematics?

If you would have asked me the above question before I did some research on the answer to this question, I would have given you a response something like this: “Mathematics is the science and study of quality, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.”1 And then you would have said in response: What?


Let me provide some other answers to the above question.

Mathematics is a subject of rationality, the science of structural relation and order that has originated from elemental practices of counting, measuring, and explaining the shapes of objects. In addition, it deals with quantitative calculation and logical reasoning. Mathematics thus simply means to study, to learn or gain knowledge. The theories given in mathematics help us understand and solve different kinds of problems in academic as well as in real life situations. Solving mathematical problems is perhaps the best brain exercise.2

Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, computers, software, architecture (ancient and modern), art, money, engineering and even sports.3

Mathematicians know what mathematics is but have difficulty saying it. I have heard: Mathematics is the craft of creating new knowledge from old, using deductive logic and abstraction. The theory of formal patterns. Mathematics is the study of quantity. A discipline that includes the natural numbers and plane and solid geometry. The science that draws necessary conclusions. Symbolic logic. The study of structures. The account we give of the timeless architecture of the cosmos. The poetry of logical ideas. Statements related by very strict rules of deduction. A means of seeking a deductive pathway from a set of axioms to a set of propositions or their denials. A science involving things you can’t see, whose presence is confined to the imagination. A proto-text whose existence is only postulated. A precise conceptual apparatus. The study of ideas that can be handled as if they were real things. The manipulation of the meaningless symbols of a first-order language according to explicit, syntactical rules. A field in which the properties and interactions of idealized objects are examined. The science of skillful operations with concepts and rules invented for the purpose. Conjectures, questions, intelligent guesses, and heuristic arguments about what is probably true. The longest continuous human thought. Laboriously constructed intuition. The thing that scientific ideas, as they grow toward perfection, become. An ideal reality. A story that has been written for thousands of years, is always being added to, and might never be finished. The largest coherent artifact that’s been built by civilization. Only a formal game. What mathematicians do, the way musicians do music.4

I appreciate what Ziegler and Loos stated in their conference paper5: “Let us just point out that the fact that there is no agreement about the definition of mathematics….”

“There should be no such thing as boring mathematics.”

Edsger Dijkstra

What is mathematics? MATHEMATICS IS FUN! What do I mean? Mathematics is not about reaching a goal but enjoying the journey. When growing up, I (and maybe you) enjoyed playing games, taking things apart to see how they worked or even thinking about inventions that no one has yet invented. Even when you learned something, you may have asked more questions such as: Why does it work this way? Is there a better way? What can I do with my new knowledge? This is a combination of curiosity and imagination. Mathematics is no different. There are always new things to learn and discover. Mathematics is amazing!

“It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.”

Carl Friedrich Gauss

One problem we may face are phrases such as “That will never work.”, “It can’t be done.”, and “We have always done it that way.” Do these sound familiar? Nothing can stifle innovation or opportunity any faster than a culture that discourages new ways to do something or ways to improve something or ourselves. There are many examples in the real world of individuals who did not let others stop them from doing something extraordinary. Even if you do not do anything extraordinary, do the best you can. Enjoy the journey as you learn and apply mathematics! (Whatever that is!)

And always remember:

“Never give up – never surrender!”

Commander Quincy Taggart, Galaxy Quest


1 “Mathematics – What Is Mathematics”. 2022. tntech.edu. https://www.tntech.edu/cas/math/what-is-mathematics.php.

2 “What is the Definition of Mathematics”. 2022. Vedantu. https://www.vedantu.com/maths/what-is-mathematics.

3 “What Is Mathematics?” 2021. livescience.com. https://www.livescience.com/38936-mathematics.html.

4 Wilkinson, Alec. 2021. “What Is Mathematics?” The New Yorker. https://www.newyorker.com/culture/culture-desk/what-is-mathematics.

5 Ziegler, Günter M., and Andreas Loos. 2017. ““What Is Mathematics?” And Why We Should Ask, Where One Should Experience And Learn That, And How To Teach It”. Proceedings Of The 13Th International Congress On Mathematical Education, 63-77. doi:10.1007/978-3-319-62597-3_5.

Additional Reading

Dlin, Rich. “Studying Mathematics is Not About Getting the Right Answer!”. 2022. dlinacademy.com. https://www.dlinacademy.com/post/studying-mathematics-is-not-about-getting-the-right-answer.

Mathematics is a way of thinking. It is a philosophy, an art, a language and a science (maybe even in that order). Math is not “how do I do this”, but “why does it work when I do this?” It’s about using a foundational set of axioms (which are assumptions taken as true) and then using logical deduction and induction to study the blossoming conclusions. Mathematics is not about getting the correct answer. But math does give us the ability and insights to prove that “the answer” is correct.

Falk, Dan. 2020. “What Is Math?” Smithsonian Magazine. https://www.smithsonianmag.com/science-nature/what-math-180975882/.

“What Is Maths? | BBC Science Focus Magazine”. 2022. sciencefocus.com. https://www.sciencefocus.com/science/what-is-maths/.

“What Is Mathematics?”. 2022. Quora. https://www.quora.com/What-is-mathematics-7.



this video makes sense in my head but like WHY DID WE CREATE THIS STUFF

♬ original sound – gracie
What is Mathematics? Mathematics with Edward Frenkel

Edward Frenkel – mathematics superstar and acclaimed author of the book “Love and Math”. Edward Frenkel is a professor of mathematics at the University of California, Berkeley, which he joined in 1997 after being on the faculty at Harvard University. He is a member of the American Academy of Arts and Sciences, a Fellow of the American Mathematical Society, and the winner of the Hermann Weyl Prize in mathematical physics. Frenkel’s research is on the interface of mathematics and quantum physics, with an emphasis on the Langlands Program, which he describes as a Grand Unified Theory of mathematics. He has authored three books and over 90 scholarly articles in academic journals, and he has lectured on his work around the world.

The featured image on this page is from the Calculus Wallpapers collection on the WallpaperCave website.

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