# 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.

• 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.