Is Mathematics a Philosophical Endeavor?

Years ago in a sterile classroom in the pacific northwest, a young professor leaned against his desk and asked a simple question:

Is mathematics created or discovered?

I was twenty-one and questioning everything about the world around me. Perhaps all the unknowns had compelled me to study mathematics in the first place.

Something steadfast. Concrete. Certain.

Something solvable. Knowable. Objective.

Then a single question challenged the entire premise for my studying mathematics. Was mathematics as solid and objective as I had once thought? I began to wonder about the influence of my beliefs with every proof I attempted, every theory conjectured, every interaction I had.

Mathematics had become both a rigorous study and a philosophical endeavor.

Did we create mathematics in order to understand the world or do we understand the world because we discovered mathematics?

Math as Creation

Some believe mathematics is the product of human invention alone. It’s an art form. Every new theory is just that, brand new. Created. Imagined. Solely built upon existing knowledge.

Humanity is the only determiner of its existence. The future of math is an empty book ready for us to write.

We are inventors of math.

Numerical creators.

Makers of a logical system.

Math as Discovery

Others believe we are uncovering a system that already exists. We aren’t creating math, we are finding it. Every new theory is a clue to a great puzzle humanity is solving. Mathematics is the language given to the inherent system of our universe.

We are finders of math.

Numerical explorers.

Seekers in a logical system.

Changing Perspectives

Long ago mathematics was needed to solve problems. Euclidean geometry was a formal pursuit of practicality and observation.

“Newton’s Method of Fluxions” by Senate House Library. Licensed under Public Domain via Commons. ( http://w01.ull.wf.ulcc.ac.uk/specialcollections/demorganexploration.shtml )

Newton derived a large body of calculus as a necessity for his theories on physics. Only later were these ideas formulated into calculus in The Methods of Fluxions and Fluents.

But now math has far surpassed science and application. It sits alone waiting for the future to make sense of it.

And time after time it does. Like perfect harmony, these nuggets of pure math find homes in future predictions and applications as if they were made for them, stirring up wonder in us all.

What came first mathematics or the mathematician?

Implications of Our Perspective

Perhaps what’s most important are the implications of our worldview. How do they influence our approach and success in mathematics?

Does the student who believes math is the key to unlocking the mysteries of the universe find more inspiration in the equations?

Do the researchers who believe they are creating the future of mathematics find more novel solutions and theories?

Is the child who was told that math is an invention that is outdated and useless in the modern world more likely to struggle?

Do the parents that see math as one of the greatest tools mankind has ever made increase the value of mathematics in their family?

Is the teacher who believes any student can discover new mathematical approaches more encouraging and understanding?

Is the mathematician who believes there exists a solution to an unsolved problem more likely to find the tenacity to keep searching?

How has your perspective on mathematics influenced you?

Please comment below.

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