# What are some things that mathematics students know, but others don't

Someone asked it on Quora and I answered to my best. What other things I can add to it, as it is well received there and carries nice information to non-mathematics people. Here is my answer

Obviously I don't mean technical definition and higher maths. Things with real life applications or math at the most comprehensible to school students.

• You going to start by adding the list you compiled so far? :) makes it easier for posters to check here. Commented Jan 20, 2015 at 17:11
• "Things that mathematics students know, but others don't"? Well, most mathematical results. Just like I don't know most of other areas of research. This question seems somewhat silly.
– Eff
Commented Jan 20, 2015 at 17:19
– AvZ
Commented Jan 20, 2015 at 17:19
• Smooth Infinitesimal Analysis
– user117644
Commented Jan 20, 2015 at 17:25

Mathematicians can make everything a problem to solve.

Move a sofa — problem.
Climb a mountain — problem.
Have you got any change? — you have got a problem.
Fold a napkin — problem.
Want to mix a cocktail — problem.

You can also say about ham sandwich theorem.

That you cannot comb the ball properly.

The Banach fixed point theorem implies that when you put a map of your country into the ground there will always be a point on the map that is lying on itself.

It is possible to divide a ball into finiteley many pieces so that you can make out of them tho balls identical with the first one. (Banach-Tarski decomposition of the ball)

There are theorems in math that you cannot proof or disproof them. You can assume that they are true or not and in both case there would be no contradiction.

etc.

There many theorems in math that have interesting application in real life or are just really interesting. Once I heard that Krein-Millman theorem implies that you can cut a pizza with $k$ ingredients for $n$ persons so that everyone would have the same amount of each topping.

• You mean Brouwers fixed point theorem? Commented Jan 20, 2015 at 19:18
• In example with the map I mean Banach fixed point theorem but I think Brouwer's fixed point theorem should work as well if the country do not has an enclave like Italy or South Africa. Commented Jan 20, 2015 at 20:53