This article mentions a couple of recent studies on language change that seem to conclude that the core vocabulary in a language changes the slowest. Well, from what I understand, yes and no. It depends on what kind of change you're talking about, and the article doesn't make it clear if they're talking about phonology or morphology or both.
It seems like they're talking mostly about morphology, because they talk about verbs becoming regularized, but then they throw out the example of the word
three, which appears not to have changed much in most Indo-European languages. But it's a bad example, because the number four, which is presumably only slightly less frequently used than
three, has changed tremendously in those same languages.
More specifically, frequent words are subject to more phonological changes, but they're more morphologically stable. It's the opposite for less-frequently used words. The weird thing is that the conclusions they reach seem to be ones that linguists have known about for years. I don't quite understand why evolutionary biologists and applied mathematicians are researching the subject in the first place. Maybe I'll just chalk it up to a poorly written article.