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.

1. Mathematics can also do without arithmetic.

Look at geometry and topology.

Mathematics is practically never taught at school.

Mathematics does not need an application, no world.

It works perfectly even without it.

There are no coincidences in mathematics.

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

Mathematics creates worlds.

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

Beauty is abstract, but easily recognizable.

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

Nothing can ever be fully described.

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

There is not only an “infinity”.

(Bolzano, Cantor)

The fact that something exists does not depend on whether it has a name.

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

We do not know whether there is only true and false.

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

When all unresolved mathematical questions (if solvable, see Gödel) are solved, we know only one thing: our ability to find open questions is not sufficiently developed.

It seems that some things in the real world around us are mathematically described.

Mathematician wonders this: comic world.

Getting close to a border as you like is the same as reaching it.

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

Results of mathematical questions are either non-existent or necessarily unambiguous (mathematically even often ambiguous).

However, they are often unpredictable or even predictable.

Analogies and beliefs can greatly disturb mathematics.

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

There are no predetermined characters or axioms.

Everything is definition.

A clearly defined and controlled inaccuracy can increase accuracy or make some problems solvable (e.g.: non-standard analysis).

This is astonishing, because mathematics requires accuracy.

The world becomes larger when you remove an axiom (e.g.: non-euclidean geometry).

What cannot be defined mathematically is definitive and by definition no mathematics.

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

Also objects that cannot be arranged have an order (e.g.: complex numbers).

Mathematics is creative, inductive.

It is the only real humanities.

Mathematics does not depend on whether there is life at all.

Mathematics does not need god.

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.

Mathematics doesn’t need people.

It just exists, in itself.

More than half of all meaningful lyrism has not yet been discovered.

And it will probably remain so.

There is no male or female mathematics, no poor or rich, dependent on skin colors or “races”, nor any that differs in the same way as humans.

Mathematics uses human language, but it does not need it.

On the contrary, all mathematical ambiguities follow from language.

Where there is a pattern or some order, there is also mathematics.

Mathematicians never give their mustard to anything.

Mustard is nothing mathematical.

It is the trauma of mathematics that the “natural sciences” use it.

Numbers are only 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.

There are only five Platonic bodies!

You can prove that.

You only need at most two different “plate shapes” to “patch” a level without gaps and non-periodic.

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.

It is not clear whether there is any continuum problem at all.

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.

Mathematics works without a computer.

Conversely, not.

Many easy-to-formulate problems quickly become unmanageable and often cannot be completely solved (e.g. structures such as quadrixs or

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

Many simple disciplines of mathematics are practically incomprehensible to laymen (e.g. set theory or topology).

If there was no mathematics, there would be nothing.

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.

There is no reason why [math1+1=3[/math could not apply.

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

Mathematicians are lazy.

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

One of the most beautiful ideas of mathematics is incomunability.

The 42 does not play a special role in any mathematical discipline.

Still, many mathematicians love Douglas Adams.

…

ad infinitum, but not q.e.d.