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I was just having this very old, neverending debate. I would like to have your opinion about this. It all started with geometry, but I think the argument extends to mathematics altogether.

According to my friend, mathematics first come from experiment and thus belong to the category of

I will first re-phrase my opinion since it is eaiser for me

Considering that

He, on the contrary, argues that everything comes from experiment, and that just like other physical models of reality, geometry somehow belongs to physics. The mathematics we choose to study come from experiment, and are thus a reflection of the physical world

The all debate actually seems to stem from the

I also want to push the two previous opinions to their extreme :

One could consider that mathematics are

I am even among those who think that mathematics is just like

According to my friend, mathematics first come from experiment and thus belong to the category of

**physical models of the world**. In my opinion, mathematics belongs to the**ideal platonic world**.I will first re-phrase my opinion since it is eaiser for me

Considering that

- one can study mathematics without knowing anything about the outside world : I know of a blind geometry professor
- the physical world we use as a source of inspiration to
*choose*the geometry we want to study, but we can*invent (but see later)*as many as we want, as wild as we can think of

**universal**, a circle is a circle no matter if I am a french man, or an alien in another galaxy...He, on the contrary, argues that everything comes from experiment, and that just like other physical models of reality, geometry somehow belongs to physics. The mathematics we choose to study come from experiment, and are thus a reflection of the physical world

The all debate actually seems to stem from the

**.**__The Unreasonable Effectiveness of Mathematics in the Natural Sciences__I also want to push the two previous opinions to their extreme :

One could consider that mathematics are

**just a toolbox**. If a piece of mathematics serves no practical purpose it is useless, should be disregarded and not taught.I am even among those who think that mathematics is just like

**art**, because I often experience deep esthetics feelings while reading a mathematical proof, intense as one can feel while contemplating a painting of listening to a beautiful musical composition. I do not want to develop to much at this stage and/or go into philosophical consideration, but earlier I would rather have said*discover*instead of*invent*since I think mathematics exist*per se*, before we know them, in the platonic world.
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