A MATHEMATICIAN LOOKS AT LATIN CONJUGATION

It is perhaps only fitting that a mathematician should take a look at the Latin verb, as generations of mathematicians were first exposed to mathematical rigour when learning to conjugate the verb AMO. The Latin verb exhibits in general 90 inflected forms: 15 simple tenses x 6 persons. We disregard imperatives, infinitives, participles, gerunds and compound tenses. These 90 forms may more conveniently be arranged in three matrices displaying 30 forms each. Thus, to most verbs V we associate the matrices Cjj(V), C?j(V) and Cy(V), where the row index i ranges over the numbers 1 to 5 and represents three indicative and two subjunctive tenses, while the column index j ranges over the numbers 1 to 6 and represents the three persons singular and the three persons plural. The first matrix displays the present aspect of the active voice, the second matrix displays the perfect aspect of the active voice and the third matrix displays the present aspect of the passive voice. The perfect aspect of the passive voice is ruled out of consideration, as it is formed by means of compound tenses. Not all verbs admit all three matrices. Many verbs have no passive and consequently do not admit the third matrix. A few verbs, such as MEMINI, admit only the second matrix and a few, such as NASCOR admit only the third.