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.

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