It's not a bold claim, it's a trivial claim. No existing learning system can reason. If it could we could hand it axioms and it could do the same deductive reasoning that you can. By definition and how these systems work, all they do is generalize from particular examples, and you can't do maths by empirically looking for numbers in a set of data, because there's an infinite amount of them. That's why ChatGPT spits out nonsense if you give it two large numbers two multiply, but your TI-83 does it perfectly on a battery. We can program deterministic, deductive methods into machines, we have no machine that develops them.
Now is there some architecture that can at some point learn how to do more than statistical prediction? Sure but this isn't it. Passing the Turing test and making people feel excited has little to do with what actual intelligence a system has. The Mechanical Turk in the 18th century fooled people, but it wasn't a intelligent machine, it was an elaborate contraption that mimics human behavior. And people understandably conflate the latter with the former.