Is Mathematics discovered or invented?
To elaborate: is mathematics like the DNA molecule that was discovered by a scientist, or is it like an ipod that's invented by a technician? Were the concepts of arithmetics, calculus, trignometry, and algebra invented by some mathematician or the other, or did these concepts always exist - just waiting for someone to discover them? Did someone invent the equation that proved that the area of a circle is the number Pi times the radius squared, or did this equation always exist since the dawn of time and was just waiting for someone to discover it?
13 comments:
I don't exactly understand how mathematics could be discovered, invented sounds more right.
I guess that through out history, humans have always used mathematics, for example a caveman holding up three fingers signalling the amount of fish he would like to purchase from the other caveman.
We've always naturally used mathematics, perhaps when someone began putting it to writing and created numbers maths was invented.
Actually I’d have to disagree with Charlie, I think Mathematics isn’t a concept that was invented. I think it was discovered.
You see, if it were invented, we would be making up our own formulas right now to solve equations and whatnot, instead of learning and discovering how to solve them. I think that the equations and formulas we use now have been here since the dawn of time, waiting to be discovered. Just like many other things man have discovered and have yet to discover on this planet.
I can’t quite put my mind to it that someone could invent a formula such as, tita or x over 360 times Pi times the radius squared to find the area of a sector in a circle or that the area of the cross section times the length gives you the volume of a prism. I don’t think our minds are capable yet of inventing such formulas. Such equations have always been here, waiting for someone to discover them.
Yes Shenny, but who has created it for us to discover? I doubt that it magically appeared on this earth somehow, if that's what you mean by discovered?
Pi was first invented and used by the Ancient Egyptians, later on advanced by the Ancient Greeks and finally rigorously estimated by Archimedes. As we humans develop through time, so do our formulas such as the funky one you mentioned.
I understand how baffling those equations are but if a group of scientist managed to invent mobile phones, Space stations and all the other mind-blowing wonders technology brings today, I'm pretty sure they could have come up with 2+2=5.
=]
I agree with shenny. I also am convinced that mathematics has always existed amongst nature. For instance, Rabbits tend to breed in a pattern of the fibonacci sequence.The sequence also appears in leaves and flowers of all kinds. Many other patterned species also have their natural ornaments in forms of sequences and most follow a faultless symmetry. If pay attention, we will discover that there is a rotational symmetry in many flowers and reflective symmetry in leaves. Shapes such as circles, triangles etc have always existed in mother-nature and obey the formulae that we learn in school.
No man decided to invent shapes such as spheres, But he discovered how to tackle them in terms of mathematics. I also agree with shenny about how our minds are incapable of inventing formulae. As a matter of fact, our minds can't even produce facial features. It depends on the store of all the faces that we've seen in our lives to utilize it in our imagination and dreams. I believe it is the same circumstances when it comes to numbers.
Perhaps we human beings have originated a few extra formulae, but the roots have always been discovered and not invented. It was the maths that we encountered in nature that set off to so many theories in the world of math. I believe, It was discovered and developed.
Mathematics to me is an enigma embedded in the nature,waiting for the right,gifted mind to come along to unravel it.
Although the symbols are what we've made up,the basic concept,the virtual idea is always there in the milieu around us like how Raya mentioned about the fibonacci sequence in which the rabbits unknowingly adapt while engendering.
If we,the human,are the ones to create formulas and equations out of thin air, I can bet that we wouldn't have as many equations as we have today,due to the fact that we would use most of the time disputing and debating with others as we all have different ideas and opinions.
Personally,all the inventions we have today are mainly the result of references to multitude of other present ideas around us rather than constituting them from scratch.
I think it’s a little bit of both.
The number of leaves on a tree, the fact two and two makes four- these are things that have been discovered, not invented. But the actual value of two, that is something that I believe was invented. I mean, a couple hundred years ago, we could have decided that the number three should be named two. The labels put on these numbers are very much invented, and, correct me if I’m wrong, I think the names are a pretty important aspect of maths too.
The facts I am using numbers like two for explaining just goes to show how totally unsuitable I am for commenting on this topic. The fact that I had to read the word Fibonacci twice just further proves this sad fact.
i actually disagree with Shenny. just because mathematics might possibly be invented doesn't mean we could make up our own formulae when we need to answer an equation, since that would be the same as inventing an Ipod when we may need to.
I think that all the concepts of mathematics were discovered rather than invented, just because of the fact that they probably didn't spring into existence when someone needed to find a formula to calculate the circumference of a cylindrical face or the adjacent side of a triangle.
it' seems more logical that these concepts always existed but weren't discovered until Archimedes or Pythagoras decided to find some sort of relation or systematic way to calculate lenghts, side, area, etc. without having to pull out you're measuring tape every single time! :P
I think that mathematics is something, as Raya mentioned, present in every molecule of everything that exists, so much so that it could very well be a universal language as seen in an aged movie called Contact.
This leads me to believe that it is discovered rather than invented. I know it sounds contradictory since languages are often invented rather than discovered but even something such as sign language, emotions shown through our faces, little grunts to rude gestures of any sort, have been present since the dawn of timed. Mathematics is something that is omnipresent and something that fantastic
human minds have minutely started to comprehend and
reason with.
I believe it's a bit of both. Im convinced that the basic concepts of mathematics like 2+2=4 were merely discovered. However, formulas and equations like finding the hypotenuse of a triangle and the spherical surface area or even the quadratic equation were invented after years and years of research and development.
I think it is a bit of both too.
Mathematics has evolved over time, the new ideas are invented with the roots of the discovery.
However, I think it is more of an invention as I have seen in documentaries. They say that numbers were created in the middle east.
Why are there mathematicians with formulas attached to their name?
I strongly believe that math was something discovered, because as you know in maths it is a straightforward thing that doesn't allow room for opinion, it cannot be altered the way an Ipod can to suit our needs.
We can only change our standpoint to suit it. In math there is usully only one possible answer. All that we have done is discovered ways to find it.
To me, mathematics was definitely invented. Invented to make sense out of concepts one could not otherwise make any sense of, to give reason and meaning to everything that happens. It's not like ancient civilisations 'discovered' a chest of magical formulae that answered all their questions! It was developed over time, and as societies and people became more complex, so did mathematical concepts.
In my rather straight forward opinion,i believe math was discoverd and invented.
Allow me to explain.It is proven that ancient civilisations such as the Aztec used numbers to communicate therefore it is almost safe to say that figures had been injected into their brains since childhood,as a form of communication and trading.
But then we also have to take to heart the fact that certain areas and forms of calculation within math have more recently been invented,as compared to far more ancient civilisations.These invented more recent forms of calculation may include Trigonometry,Percentages and Algebra.
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