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Let's suppose AI models aren't so great for mathematics and it's Terence Tao doing most of the work.
The primary commercial usecase for AI isn't mathematics, it's coding, as you say.
I cannot code beyond the most basic Khan Academy beginner sense, my actual end to end abilities are completely worthless. And yet I can make useful AI tools for work, processing documents in various ways that saves lots of human time. In a certain sense, I'm providing most of the 'secret ingredient' since you cannot just tell an AI to do these fiddly tasks and expect them done properly in oneshot. It will usually not work the first time. So I give it some counsel and tell it what to troubleshoot, errors, differences from expected output, clarify my intentions and ultimate usefulness. Eventually it works and then I refine it to work better and better by getting AI to handle all these edgecases and Word-induced BS.
And how could I make a (still under development) 4X game with AI if I can't code? There's a fair bit going on. Space battles, ground battles, culture, technologies, buildings, resources, goods, markets, map generation, turn order, trade between provinces (intra faction), trade between factions, freighters, pops and social classes, loans, diplomacy and war plotting, coalition building... Some things are not well fleshed out but there is quite a bit there.
I was just now getting it to make an evolutionary testing system to refine ship designs and fleet compositions and so define the meta. First time it worked OK, then when trying to make it better (too many bad mutations!) it broke, then I overhauled it and now it works great and with multicore processing too. Apparently the dominant strategy is getting hundreds of incredibly cheap and terrible warships to act as chaff for a small core of high-tech warships to exploit the targeting and reinforcement logic. So clearly I need to change how reinforcement and targeting works, raise minimum costs for ships.
It was my idea to make this tool, my idea behind the overhaul and my ideas behind every mechanic but I could never have done it myself. The secret ingredient is clearly the AI.
I don't know, my experience is kinda the opposite, but I have been programming since childhood. I find AI very frustrating to use, and rarely consult it.
Keep in mind that it has all of Github in its training data. It can go a long way by basically feeding you an existing project and not mentioning where it got it. I don’t mean to oversimplify and say that this is all models do and that there’s no reasoning, but I think people underestimate just how much is memorised: you can get mainstream models to recite entire books like Harry Potter almost word-for-word, with upwards of 95% accuracy, and to the extent that you can't, it's usually due to active sabotage by the model vendor to prevent people from getting free Harry Potter, not because the model doesn't have Harry Potter memorised. Vendors really do not want it to look like everything is getting memorised, but to a large extent it is. I just tried it with some random books I'm reading now and… yeah, they definitely have every book I'm trying memorised, even though they're very coy about it. And some of these are quite obscure books that I'm confident less than 1% of people would even recognise the name of. I then tried it on a snippet from a random library I published ten years ago on Github and… yeah, it has it memorised, down to the exact word. Amusingly, unlike the books, it does not go out of its way to tell me where this quote is from and lecture me about the importance of copyright. When I explicitly ask it where it got that, it just says it made it up—that it’s not a quote from any published book.
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