What is the grammatical term for a verb form that expresses action or existence without reference to person, number, or tense?

The term that describes a verb form expressing action or existence without reference to person, number, or tense is indeed the infinitive. An infinitive is typically formed with the word "to" followed by the base form of a verb (e.g., "to run," "to eat," "to be"). This verb form does not indicate who is performing the action or when it occurs, making it neutral in terms of person and tense.

In many contexts, infinitives can be used as nouns, adjectives, or adverbs, which allows them to function in a variety of grammatical roles. For example, one might say, "To learn is to grow," where "to learn" serves as the subject of the sentence.

Understanding this term is essential as it differentiates the infinitive from other verb forms such as participles, gerunds, and modals, which each have their own specific grammatical rules and usages.