Online Journal Entry 1: On Mathematical Experience

EDMT 208

Mathematics, Technology and Society 

On Mathematical Experience

By Edmar Oandasan 

Hello everyone! Welcome to my first ever Mathematics blog although I am not new to blogging. In fact, I had some few blogs about my travels almost a decade ago but it stopped when I moved to Europe when life became preoccupied with other concerns that my modes of reflection turned into another form.

I am intending to blog again hoping that it will put my reflections into tangible form something that can be revisited anytime. This time will not be about travelling without – to the wild untamed world waiting to be discovered but travelling within – towards the enrichment of the mind in the subject of Mathematics especially into its interconnections with technology and society.

For the past few weeks I have been diving deep into our materials for the course Mathematics, Technology and Society. We are on the part of exploring the historical and philosophical side of Mathematics, how this magnificent branch and body of knowledge was both discovered and invented and how its ancient beginnings enriched the experiences of humans and catapulted the names of those who contributed to its development for us to appreciate it in its beautiful and noble form.

Today, I want to share some personal reflections on a question that really made me rethink everything I knew about the subject:

What is mathematical experience, and how does it differ from other forms of human experience?

Let me relate that when I was in high school, I had a eureka moment with Mathematics through my Physics subject. It happened when our teacher patiently explained the meaning of direct and inverse realtionship of variables. I understood it well that I began to solve the problems with great interest even if the subsequent problems were difficult. Soon, I began to extend this enthusiasm in Mathematics. 

For the longest time, I thought of math as just a collection of formulas in a textbook, as a subject to be ¨feared¨ and a subject only for those who are ¨naturally gifted¨. And as a philosophy by undergraduate education and a former English language teacher, I tend to believe that the pinnacle of quest for human wisdom is found in philosophy and that all forms of knowledge for us to be conscious of as meaningful needs to be understood in language. But after reading our course materials, I realized that mathematics is actually a fountain of knowledge that weaves a deeply human story—an evolving form of experience that began long before it became the "specialized knowledge" we study in school today.  

Mathematical experience: A Way of Life

One of the most interesting things to learn is the contemplation of the meaning of the word "mathematics" which originally comes from the Greek mathematikos, which simply means "something that has been learned or understood". In ancient times, particularly among the Pythagoreans, it wasn't just a subject; it was a "way of life". To them, a "mathematician" was simply a learner in a general sense. (Leonor, 1998)

I find it fascinating that mathematics was once considered "universal knowledge"—the foundation of general education—because it was seen as intrinsically superior and more organized than other fields like rhetoric or grammar. It only later contracted into the specialized discipline of geometry, astronomy, and calculation that we recognize now.  

Another aspect of mathematics being experienced as a way of life is its application in modelling. Since the start of known human existence, it has been used to solve life´s practical problems such as in construction to commerce and even applied in the sciences. While modelling is understood as the application of mathematical method to solve contemporary problems in engineering and sciences today, I suppose that there is also an ancient form of modelling applied by the Greeks in the west, and the Egyptians, Mesopotamians and even the Chinese in the east due the complexity of the building structures they constructed, the dynamics of commerce around those regions and the rich ancient mathematical records they possess. While ancient mathematics was influenced by the spiritual leaders´ ritualistic formulations, it was soon developed and directed towards its proper scientific form by the great questions of the Greeks starting with Thales then perfected by the Pythagoreans and has its relative pinnacle in Euclid in his postulates in Elements (Leonor, 1998). 

Given that mathematics has been applied in many aspects of human experience spread throughout history, we can say therefore that it is not only a way of life; it must be a driving force of development of civilizations that enriched the experiences of humanity. It´s enlightening to realize that "mathematical experience" isn't just a slow crawl of progress—it was a radical revolution in the process of humans´ quest for the truth.

 

How Mathematical Experience is Unique

So, how does this "mathematical experience" actually differ from our everyday experiences? From my reading, I’ve gathered three main distinctions:

First, mathematics experience is intentional and that leads to the creation of mental models. Unlike physical phenomena that just happen, a mathematical computation is an intentional act. For example, if I eat apples, I'm not "doing math" unless I intend to perform an addition of how many apples I ate. Mathematics isn't just about the objects themselves; it's about the "mental models" we create to represent the real world.

Second, it is a shift from empirical to deductive. Most human knowledge is empirical—based on trial and error or what we can see and touch. Early civilizations like the Egyptians and Mesopotamians used math this way, for practical things like tax accounting and building pyramids. However, the "mathematical experience" truly changed with the Greeks. They moved away from "stretching the holy cord" (a physical act) to seeking logical proofs that exist entirely in the mind. As Thales and Pythagoras realized, a true mathematical proof doesn't depend on how well a person can draw a circle, but on the purely logical relationships between statements - a deductive process.

Third, is the human act of idealization and abstraction in Mathematics. In our daily lives, we deal with the disorganized reality of physical objects. Mathematical experience involves idealization—the organizing of things through representing them in the mind as symbols and concepts in the mind. As abstractions in the mind, they stay the same even when we aren't looking at them. We take a concrete experience (like counting apples) and apply "abstraction, imagination, and logic" to turn it into a symbol or a concept. Idealization is manifested in Thales´ realization that a true mathematical proof should not depend on the "ability to draw a straight line or a perfect circle". Instead, he idealized the problem by making the proof depend entirely on purely logical relationships expressed in language or symbols. In this "idealized" mathematical space, a drawing in the sand only serves as a rough illustration for the ¨ideal¨ thing in the mind.

 

The Logico-Mathematical Experience

It is also fascinating to highlight the analysis of the elementary forms of human experience made by Leonor (1998) which he based on Jean Jacques Piaget. These are: affective experience, physical experience and logico-mathematical experience. Affective experience happens when emotion is involved such as listening to music, watching a play, appreciate poetry, etc. This is an experience in the arts and humanities. Physical experience combined with logico-mathematical experience make up the sciences. It involves using our senses to decipher physical characteristics such as weight, volume, size shape, movement of population, behaviour of people, etc. However, Logic, Mathematics and Philosophy are disciplines that use logico-mathematical experiences. This experience goes beyond the observation of concrete object from their physical characteristics to an intentional analysis of their relationship when we try to add them or analyse the logical principles in them.

This analysis clearly delineates the difference of mathematics experience compared to the experiences in other disciplines. The appreciation of the beauty of Math experience lies not in the appreciation of physical changing characteristics of objects but on the deduction of the unchangeable truth from our analysis of the concepts of objects.

 

Conclusion

Looking back at the history of mathematics—from the notched bones of prehistoric man to Euclid’s complex deductive chains—I see that mathematics is essentially the process of turning our practical needs into systematic, logical thought.  

The "dilemma" of whether math is invented or discovered is still debated, but what's clear to me now is that the experience of doing math is a unique bridge between our physical reality and our capacity for pure reason. It’s not just about numbers; it’s about how we, as humans, choose to understand the inner workings of nature and improve the quality of our lives through mathematical applications.

As a teacher and student of mathematics, I realize that when I require students to solve an algebraic problem, we are not just working for our future, we are participating in a 2,500-year-old tradition of "postulational thinking" that started when someone finally dared to question the established practices of their society.

References:

Leonor, C. D. (1998). MATH H: Mathematics, technology, and society. (p. 2) University of the Philippines Open University.

Hansson, S. O. (2020). Technology and mathematics. Philosophy & Technology, 33(1), 117–139. https://doi.org/10.1007/s13347-019-00348-9

Berggren, J.L., Folkerts, M., Fraser, C.G., Knorr, W.R., Gray, J.J. (2025, December 13). mathematics. Encyclopedia Britannica. https://www.britannica.com/science/mathematics