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I came across this in a math book:

Schon in der reellen Analysis ist es gelegentlich vorteilhaft, komplexe Zahlen einzuführen. Man denke beispielsweise an die Integration rationaler Funktionen, ...

I know that Subjunctive I can be used in mathematics to define something, but here there's no act of definition, just "One thinks, for example, of the integration of rational functions ...". Why subjunctive I?

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The subjunctive is here used in its archaic function to express commands or requests – sort of an imperative to the third person singular, which is the only person for which this still works in some cases, namely the following:

  1. Recipe-style instructions like manuals, mathematical definitions or exam tasks.
  2. In mostly fixed figures of speech. One such example is »man denke«, where the reader is addressed in the third person singular as man and which only works with this an similar verbs. Two examples:

    Man denke nur, jeder täte dies. – Just think about (what would happen) if everybody did that.
    Man stelle sich vor, die Bombe wäre nicht entdeckt worden. – Imagine the bomb had not been discovered.

Though in a mathematical text, your example is of the second kind and not the first – it is a motivatory text, no definitions or similar instructions are being made.

Using such a construction in a case that is neither covered by neither of the aforementioned cases is so over-the-top archaic, snobby and feudal, that it is only used ironically (and may not be understood by everybody):

Man reiche mir den Salzstreuer. – Can someone please hand me the salt cellar? [Not translating the archaic, snobby and feudal tone.]

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    I don't think there is a limitation to verbs. A lot of user manual (as the recipes you mentioned) use this subjunctive... "Man schneide, nehme, werfe, glätte, öffne, schäle..."
    – Emanuel
    Dec 21, 2013 at 21:05
  • @Emanuel: You are mixing up manual-like instructions (where this can be used with every verb) and constructs similar to »man denke«. We here have the latter case. Seeing that my answer was not very clear about this aspect, I reformulated it entirely.
    – Wrzlprmft ♦
    Dec 21, 2013 at 21:53
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Your translation is wrong. It's not "One thinks", because that would be "Man denkt". The meaning of "Man denke" is imperative. This imperative isn't addressed at "you", but at anyone who reads the sentence. I've got trouble thinking of an exact equivalent in English. Maybe "One shall think"? Notably, other languages have an exact equivalent. In Spanish, for instance: "Piénsese".

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  • This should rather be a comment (which I know, you cannot make yet).
    – Wrzlprmft ♦
    Dec 21, 2013 at 9:08
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    I would just suggest: “Think, for example, of …”
    – Wrzlprmft ♦
    Dec 21, 2013 at 9:10

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