During this decade, he wrote many treatises on various subjects, ranging from the color of the sky to the existence of God through the origins of languages (see e. g. references in Johann Christian Poggendorff, 1863).

After this polygraphic formation period, Tetens goes back to more fundamental enquiries: after having read David Hume's work, he popularized it throughout the German-speaking world.

His interest in polynomial algebra was influenced by his belonging to the German combinatorial school of Carl Friederich Hindenburg, Christian Kramp and others.

It contains an extensive synthesis of previous work on the subject, from Halley's mortality table to Richard Price's Observations on reversionary payments.

It is recognized by actuaries for featuring the first risk measure ever (the Risico der Casse);[6] moreover it offers some insights in mathematical statistics: by using an approximation of the binomial distribution, Tetens tried to compute the confidence level of a given sampling procedure.