Is Maths Discovered or Invented?

Tom Rocks Maths intern Kira Miller debates the age-old question of whether maths is discovered or invented by presenting the common arguments on each side.

Arguments presented on the side of 'invented' include Formalism, Fictionalism, Art, and Social Construct. And in favour of 'discovered' we have Empiricism, Platonism, Logicism, and Intuitionism.

Produced by Kira Miller with assistance from Dr Tom Crawford at the University of Oxford.

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

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[coleuk]

But I can smell fermats last theorem, it smells like blood, sweat and tears.

[necaton]

i fell like the problem is the definition of "discovered" and "invented".

[elledoeslaw]

This is so great Kira!! Even as someone who knows nothing about maths or philosophy this was really interesting

[Grizzly]

Does the Number of comments that Mohamed Ababou posts here have an end?

[Marguerite-Rouge]

Personnally, I am more willing to consider maths as a discovery than an invention.

I currently study psychology and the work of Piaget about the development of intelligence during childhood seems to lead to that conclusion. For him, we develop logical thoughts in a process of co-construction : we observe the environment and we act on the environment, so we can adapt ourselves to that environment.

At the beginning, the little children discover the world with their senses. Then, they do their first inferences, but they make some logical mistakes (they need more experiences). Then, they do their first real logical inferences (with no mistakes), but they depend closely on the environment. Finally, they can generalize logical inferences to abstract subjects.

So, I think maths is already there and the more we act on environment or we experiment on it, the more we understand maths. We cannot reach the comprehension of "abstract maths" if we didn't already have the comprehension of "concrete maths". Even the more abstract subjects can be linked to the real world (for example, group theory is linked with symetry, symetries are observed in the everyday life).

For me, this notion of "adapt to the environment" explains why we can reach mathematical truth even if it is a discovery (to answer to the issue given in the end of the video). People and environment are interacting. If a conclusion is not true, early or lately, there will be an environmental reaction.

[simonhe]

This video is superb in the quality of contents!

[owensilberg]

My first thought is that math is invented from some axioms discovered by observation in reality, though that feels like it's missing something and I'm not sure what

[padrickbeggs]

We invent the tools to interface with connection space. We can make any tools or assumptions we want. We have no control over what deductions will be made, that is up to connection space. #discoveredGang

[mastershooter]

I say both, both invented and discovered, the underlying logic and the actual mathematics is always gonna be that same, like if an alien invented calculus, the underlying facts and logic are going to be the exact same, that's discovered, but the representation of that mathematics and the notation are discovered

[itsreeah]

Congratulations for 50, 000 subscribers!!!

[mohamedababou]

"You Cannot Swim Twice in the Same River."
This inevitably leads to Heraclitus knowing that everything is fleeting.
This is evidence that Heraclitus believed that Numbers have an end.
Pre-Socratic philosophy is the philosophy upon which the logic of Mathematics in particular and the sciences must be reconstructed.

[bengriffiths]

I think the underlying rules and axioms are discovered but our nomenclature and the way we describe them is invented. Obviously there is some interlink as the nomenclature is essentially the language and no language can ever truly describe something perfectly. This debate is unresolvable for the exact same reason why we can't put emotions into words. Emotions (maths) exist outside our ability to describe them with language (nomenclature)

[Reliquancy]

I feel like math is what would still be true even if there were no universe. But a friend of mine thought math doesn’t exist outside of an intelligence to perceive it. I guess I’m thinking it’s discovered and he that it’s invented.

[aditichegu]

this was a great video, personally love the Kantian view that maths is synthetic a priori

[somecreeep]

Both. Chess is invented, but the best strategies are discovered based on the setup, which could have been different if we wanted it to. Science invents math that matches with our observations, but we're inventing the math based on the observations we discover. We can make all kinds of math by making up an axiomatic system and making sure the axioms don't contradict each other. Eventually a scientist may discover that the structure of that math is just what we need to describe something, but that doesn't change the fact that it was first invented, not discovered.

[qwertyTRiG]

The idea that it's discovered makes the most intuitive sense to me, but I'll not claim that I have any kind of rigorous analysis to back that up.

[mustangjoe]

I have no formal philosophy education but have often thought of why are certain things described the way they are. Why do humans have an insatiable desire to find answers for things which do not have an answer as of yet.
The Universe is the way it is. Regardless of how we interpret or describe it, it is still the Universe with its governing rules.
The further I learn mathematics, the more I realize it is more of an art than I ever expected it to be. We learn in grade school concepts and for the most part, mathematics is just plugging in numbers.

The true beauty in mathematics seems to lie in the creativity of humans to join different ideas which seem unrelated, together.
Obviously humans invented the mathematical language. If an intelligent species somehow communicated with us, it would look nothing like what we would understand. What is the same are the universal constants.
Humans love to solve mysteries and puzzles. Mathematics is our language to solve mysteries and puzzles. When the Mathematics we have is insufficient, we invent more Mathematics to solve the problem.
Thank you for video.

[hzrd]

In my opinion we invented axioms and definitions and THEN discovered its properties. For example we invented natural numbers and from there get to real numbers and then discovered things like calculus

[mohamedababou]

Since immemorial time, human has invented the arithmetic and geometric shapes in order to understand what surrounds him in terms of nature and reality, and this is really what has come to be called Mathematics, and this ancient history of Mathematics proves that human wanted to understand nature and reality, so it is not possible to rely on Something surreal or metaphysical, meaning that the origin of Mathematics was devoid of the illusion of infinity.

[aniketeuler]

Another amazing session I'm ready sir 😃