The provided example directly shows ability in mathematical reasoning by coming up with a novel concept and example case, it is just poor in arithmetic.
Math is not simply arithmetic abilities, you seem unable to comprehend this.
"I want it to come up with a new idea. Its first attempt was to just regurgitate the definition of the set of zero-divisors (a very basic concept), and (falsely) asserted that they formed an ideal (among other false claims about endomorphism rings)."
"I tried a few more times, and it gave a few more examples of ideas that are well-known in ring theory (with a few less-than-true modifications sometimes), insisting that they are new and original."
"This in particular is quite an interesting failure. "
"So there we have it. A new definition. One example (of a 4-cohesive ring) extracted with only mild handholding, and another example (of a 2-cohesive ideal) extracted by cherry-picking, error-forgiveness, and some more serious handholding."
"Some errors (being bad at arithmetic) will almost certainly be fixed in the fairly near future." - and this opinion is based on absolutely nothing.
The provided example directly shows ability in mathematical reasoning by coming up with a novel concept and example case, it is just poor in arithmetic.
Math is not simply arithmetic abilities, you seem unable to comprehend this.