# Which mathematical fact is most important?

I don’t want to make a decision on that.Here are a few that non-mathematicians are mostly unknown or at least unaware.

- Mathematics can also do without arithmetic.

Look at geometry and topology.

It works perfectly even without it.

Mathematics describes structures and patterns. Some are surprising, but not by chance.

A few axioms are enough. No one can even guess beforehand how big the newly created world is.

Deep truths are beautiful when they are simple. The four-color set, the large Fermatsche set, and most importantly: [mathe-

(Gödel’s incompleteness, already mentioned in another answer)

*an*“infinity”.

(Bolzano, Cantor)

It is enough to have a mathematical world that cannot even be touched.

So far, no one has been able to define a coherent, multi-valued logic.

Mathematician wonders this: comic world.

Every farmer understands this, but not a philosopher. He still rushes turtles and runners at each other.

However, they are often unpredictable or even predictable.

We prefer to talk about homomorphisms, which are harmless and often even productive.

Everything is definition.

This is astonishing, because mathematics requires accuracy.

If you just don’t define, it’s not math.

It is the only real humanities.

If he wanted to intervene in an illogical way, don’t deceive anyone. Otherwise, there is no contradiction. The question of God is one that arises outside of mathematics.

It just exists, in itself.

And it will probably remain so.

On the contrary, all mathematical ambiguities follow from language.

Mustard is nothing mathematical.

*a*sub-range of mathematics.

In this sub-range, the 0 and the 1 are special. The 2, of course. And 561 or 1729. Of course, also [math[/math, [math_pi[/math and [mathi[/math.And in general. The most boring of all numbers has not yet been found. Maybe none exists.

You can prove that.

There is probably no similar solution in the three-dimensional. There is no proof (m.W.). Whether there is an adequate problem at all in higher dimensions is still unknown in my day.

The original hypothesis has been worked out, proved to be insoluble, and thus irrelevant today. Once upon a time, it was the biggest problem of mathematics. To be one again, a new formulation would be needed.

Conversely, not.

n-iken; already at n=8 there are still questions open, for larger n anyway.)

But if there were nothing, there would still be mathematics. That is not a contradiction. It is enough if there is anything.Its existence has thus been proven.

The necessary axioms promise only no advantage over the usual one.

Only in this way can their mathematics be beautiful. And that often involves a lot of work.

Still, many mathematicians love Douglas Adams.

…

*ad infinitum, but not q.e.d.*