The first is whether something can be said to be numerate. Is a working calculator numerate? Would an infinite machine with an infinite lookup table be numerate? Are the rules of math learned by modeling language sufficient to be considered numerate or does it require something more?
Whether any LLM is numerate probably depends heavily on the specific criteria an individual uses to define numerate. For some that might include the ability to actually reason mathematically (i.e., to understand mathematical rules and apply them). For others, it might only be to return a reasonable answer.
The second is usefulness for purpose. Whether something is numerate is effectively irrelevant for usefulness. We don't care how a tool gets its math answers if the answers are correct. A working calculator is useful. A broken one probably isn't (but could be, if, say, all the answers it returned were too low by one). But we don't really care whether a calculator is numerate by whatever definition when we're trying to get an answer.
Whether any LLM is useful for calculations probably depends more on how accurate it is and what you are trying to accomplish.
I would expect numeracy to be the same: a numerate agent would be one that understands that amounts and relationships can be modelled by numbers. That numbers are abstract concepts that exist separately from the symbols used to represent numbers. That there are an infinite number of them, but without identity, and without canonical representation (2 "is" 5 - 3). That you therefore must assign properties not to individual numbers, but to the sets of numbers that obey certain rules — and so you must recognize what rules a number obeys when you see it. And so forth.
If I teach you to do an "increment" operation, or a "less than" comparison, in Arabic numerals; and then I teach you how to represent numbers in Roman or Chinese numerals; then you should now be able to do an increment operation or a less-than comparison using those numerals. Likewise for e.g. base 10 vs base 2 numbers. Your understanding of numbers should not depend on the symbols themselves, but should instead be an understanding embedded in something more like an abstract, non-quantized visual field, where numbers can be above or below or between other numbers in an abstract visual sense; intervals can overlap other intervals in an abstract visual sense; etc.
(I would expect a hypothetical "fully" numerate system to be able to "imagine" any algebraic structure described to it, to see the properties it has, and to use that structure to "do math". I shouldn't have to teach arithmetic to the agent all over again just because it's now e.g. modular arithmetic. It should be able to derive — and perform! — all the operations of "modular arithmetic", just because it 1. knows regular arithmetic, and then 2. hears a description of a modular ring.)
so, no then
if it was in the training set maybe you'll get lucky though
