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I see that in mathematics text, “Prove that” is translated to German as “Man beweise, dass”, and “Determine” is translated as “Man bestimme”. What kind of construction is this? It reminds me of the imperative, but this is not quite the same. For imperative it would be “Beweise, dass …” (du form) or “Beweisen Sie, dass …” (Sie form).

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As an aside, zeigen is a common synonym for beweisen in mathematics. –  chirlu Aug 29 '13 at 5:45
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This construction uses a form of subjunctive (Konjunktiv I) in the main clause and expresses a request, more or less equivalent in meaning to a sentence using the imperative. The imperative form is actually used in some mathematical texts as well, particularly more recent texts.

The imperative can be perceived as quite blunt; on the other hand, man + subjunctive is obsolescent, but has the advantage that no decision about du or Sie is required.

Formerly, the man + subjunctive construction was commonly used in recipes and similar instructional texts. A well-known advertising slogan for a company producing baking powder, instant pudding etc. is derived from this: Man nehme Dr. Oetker.

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Klare Erklarung. Danke schön, chirlu! –  Mika H. Aug 29 '13 at 20:30
    
Statt zw. Du und Sie muss man zwischen Du und Sie und man wählen - die Situation ist also komplexer geworden, nicht einfacher. –  user unknown Aug 30 '13 at 4:03
    
@user unknown: "Du beweisest, daß ..."? Das halte ich für völlig ungrammatisch. –  chirlu Aug 30 '13 at 5:31
    
Du hast geschrieben but has the advantage that no decision about du or Sie is required, nicht mit Du fällt mir nur die häßliche Form "Du beweisest, daß ..." ein. Das man wäre ja keine Alternative, wenn es eine Du- oder Sie-Form gar nicht gäbe. Beide sind in der Frage nachzulesen. –  user unknown Aug 31 '13 at 16:28
    
@user unknown: Es gibt noch ungezählte andere Möglichkeiten, weit mehr als zwei. Z.B. "Der Leser möge beweisen", "Es werde bewiesen". In der Frage ging es nur um die zwei verbreitetsten Konstruktionen (Imperativ und "Man beweise"), nur die beiden habe ich verglichen. –  chirlu Aug 31 '13 at 20:10
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You are right, it's not an imperative, it's a subjunctive. The same form is often used in recipes, for example, "Man nehme 3 Eier".

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