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In English language there is a beautiful colloquial usage, which describes the way a proof is done ie a "handwavy proof". A handwavy proof is a kind of proof, in which you use no/very little mathematical rigour and motivate the theorem by physical assumptions. Wiktionary defines handwavy in the following way:

Of a demonstration, proof, or explanation, missing important details or logical steps, perhaps instead appealing to common sense, tradition, intuition, or examples.

One could always say non-rigorous proof ie nicht strenger Beweis but that doesn't seem to describe the situation as nice as handwavy proof.

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    How negative is this? Would it be used when someone is unable to write a proper proof, when someone is just too lazy to do it properly, or when the intention is to convey just the gist of the proof that might otherwise get lost below technical details?
    – chirlu
    May 15, 2015 at 22:58
  • @chirlu: It is not negative at all. It is very commonly used in physics. To answer your question in a more concrete way, the usage of the word is the last option that you presented in your comment: "when the intention is to convey just the gist of the proof that might otherwise get lost below technical details"
    – Gonenc
    May 15, 2015 at 23:01
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    Why is there a close vote?
    – Emanuel
    May 15, 2015 at 23:31
  • @Emanuel: Im Close-Dialog wird dir angezeigt, welche Schließgründe von wie vielen Nutzern ausgewählt wurden.
    – chirlu
    May 15, 2015 at 23:55
  • As we know, “proofs should only be communicated in private and to consenting adults”, and therefore hand-waving is to be preferred in most situations.
    – Carsten S
    May 16, 2015 at 6:34

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There seems to be no equally used German counterpart as I have often heard (and used) the English “hand waving” while conversing about mathematics in German.

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When I was studying maths at university, "Beweis durch Händewedeln" was in use, but that describes a very very vague "proof" in the sense of "it can be easily seen that theorem 1.2 applies together with lemma 2.3, and the details are left as an exercise for the reader".

For "proofs" the appeal to intuition or common sense, I'd use "Beweis durch Anschauung" or something similar. Don't confuse with "anschaulicher Beweis" (a (possibly rigourous) proof which is also very intuitive).

As always (translation is rarely one-to-one), the preferred German expression depends on context and the actual proof that is described as handwavy.

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  • „Händewedeln“ ist natürlich eine sehr schöne direkte Übersetzung. Wie treffend sie ist, ist eine andere Frage.
    – Carsten S
    May 17, 2015 at 8:05
  • @CarstenSchultz: Möglicherweise war es auch eine augenzwinkernde direkte Übersetzung (davon waren einige in Umlauf); zumindest war es in Gebrauch, und jeder wusste, was gemeint ist. Der englische Ausdruck direkt wurde dagegen nicht benutzt (es sei denn, man sprach sowieso Englisch).
    – dirkt
    May 17, 2015 at 16:32
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Depending on the nature of the handwaving, one of the following may fit:

  • Ein salopper Beweis – It’s what I prefer to use in such a situation, though I usually apply it to certain steps of a proof and not the proof as a whole. It particular fits proof that omit technical details and apply to intuition, visualisation or examples.
  • Ein formloser Beweis – A proof that is mainly lacking form, e.g., stuff isn’t clearly defined, logical steps are not spelt out and implied or the order does not correspond to the logically required one.
  • Eine Beweisskizze – A sketch of a proof. Contains only the central arguments and steps, but omits the details.
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    I often see Beweisidee used like Beweisskizze.
    – chirlu
    May 21, 2015 at 7:08
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I have seen the adjective hemdsärmelig used in this case.

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    That would surprise me.
    – Carsten S
    May 17, 2015 at 8:04
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Though it isn't a real equivalent to handwavy I think in some cases you might be able to use the expression über den Daumen gepeilt.

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