Multiple foundational and contemporary linguistic studies support the theoretical and formal consensus that natural human language employs recursive systems capable of generating an infinite array of structures.
The claim that human language is mathematically infinite is a standard theoretical consensus in linguistics, rooted in formal language theory and the property of recursion. Papers such as [2], [4], and [7] explicitly discuss how recursive operations (like Merge) allow natural language to generate unbounded or infinite arrays of hierarchical expressions. No provided papers refute this core mathematical property of generative grammar.