How about Hilbert‘s 16th problem, would that satisfy your conditions for a counterclaim to your assertion? For a short summary, see https://mathoverflow.net/a/116530/60775 or https://valentermz.github.io/documents/slides/olivetti-2013-... for instance.

In any case, there is still the foundational crisis in the late 19th and early 20th century that‘s worth a mention.