By Prof Lawrence ETIM
In case, you can’t read to the end, the answer is that maths was both discovered and invented.
INTRODUCTION
This is a classic – and genuinely profound – philosophical question. The most careful answer is: mathematics is BOTH DISCOVERED and INVENTED, depending on what aspect of it we are talking about.
Let me explain clearly and systematically.
1. THE CASE FOR DISCOVERY
Many aspects of mathematics feel as though they exist independently of human beings.
The ratio of a circle’s circumference to its diameter is always π, whether or not humans exist.
Prime numbers have the properties they have regardless of culture or language.
The Pythagorean relationship holds in any right-angled triangle anywhere in the universe.
From this perspective, mathematics resembles physical laws: humans do not create them; they find them. This view is known as MATHEMATICAL PLATONISM – the idea that mathematical truths exist in an abstract realm, waiting to be discovered.
ANALOGY:
Just as continents existed before explorers mapped them, mathematical structures may exist before mathematicians describe them.
2. THE CASE FOR INVENTION
At the same time, the language, symbols, systems, and frameworks of mathematics are clearly human creations.
We invented numerals (1, 2, 3), symbols (+, −, ∫), and notation – the letters x, y, etc used in algebra, geometry etc were invented by humans.
We chose axioms (e.g., Euclid’s postulates).
We developed different branches – calculus, algebra, topology – to solve specific problems. Newton developed calculus and more before he was 26 years old.
DIFFERENT CIVILIZATIONS DEVELOPED MATHEMATICS DIFFERENTLY:
The Babylonians used base-60.
The Mayans used base-20.
Modern mathematics uses base-10 and abstract symbolic logic.
These choices reflect human creativity and utility, not inevitability.
ANALOGY:
We did not invent the landscape, but we invented the maps, the coordinate systems, and the names of places.
3. A BALANCED VIEW: Mathematics as Structured Discovery
A more nuanced position – favoured by many contemporary thinkers – is this:
Humans invent mathematical frameworks, but within those frameworks we discover unavoidable truths.
Once you accept certain axioms:
Some theorems must be true.
Some results are impossible to avoid.
Logical consequences unfold whether we like them or not.
In other words:
The game is invented.
The rules are chosen.
But the outcomes are discovered.
4. WHY THIS QUESTION MATTERS ❗
This debate touches deeper issues I have recently been reflecting on – *time, weeks, years, and human constructs.*
Counting is rooted in nature (objects exist).
Numbers are abstracted from reality.
Calendars, weeks, and years are human conventions layered or superimposed onto astronomical cycles.
Similarly:
Nature provides structure.
The human mind abstracts, formalizes, and systematizes it.
5. SUMMARY: A Concise Answer
Mathematics is discovered in its truths and invented in its expression.
Or more poetically:
We invent the language of mathematics, but we discover what it says.
More simply
That one orange plus two oranges gives three is natural.
But to represent one as 1 or i, two as 2 or ii and three as 3 or iii – are human inventions.
Additionally, mathematical symbols such as +, x, – and /, ∆, √, and so on are all human inventions, helping to carry out mathematical operations (or solve maths problems).
Prof ETIM is of the University of Uyo
