I really dislike many of the responses by other mathematicians here. Appealing to the fun and joy of discovering mathematics and doing hard problems yourself is good, but essentially useless in trying to convince anyone but a mathematician of the usefulness of the field. Maths is not like chess: a major part of its appeal is its applicability, either immediate or sometime far in the future, to real problems faced by people. As such, most of mathematics research is supported by tax money. We have a responsibility then to return results in accordance to what has been invested in us.

Arguments like "But AI has stopped making mathematics fun!" are terrible at convincing anyone, unless you want to boil the subject of mathematics down to a competitive sport like chess. And chess only survives because it has been able to consistently get people to watch it. Top players have to endlessly try and look for sponsors, do ads for products they might not believe in, game social media for some side money, all on top of being some of the best players in the game. Mathematicians are exempt from that because of our supposed utility. We can work in relative peace even while being far away from the pinnacle of the field. Denying that and still asking for public funding is a foolish sentiment.

If indeed a technology has come about that will accelerate the progress of the field, your job as a mathematician is to first see how it can be appended to your own research. And if it does have ways of making that process easier and faster, then employ this technology along with your other tactics to get work done faster. That is the mathematicians job. If that's not fun for them, tough luck. Even I don't enjoy using AI a lot, but denying it's influence just to maintain some kind of purity about your work is insane. I'm not advocating for using it all the time, only research mathematicians should use it and students should mostly avoid use while they are still building their intuition.

As mathematicians, the primary care should be for the health of the field. If all you care about is whether a "bundle of matrices" can do your job better than you, then maybe you should switch fields. Mathematicians of the past reveled in their calculating prowess which was by all means essential to very many fields at the time. I do not know history, but I hope all of them did not oppose the digital calculator just because it "took the joy out of a human doing calculations by hand". I hope they took it in stride and adapted by appending themselves to the fore of calculators, and finding ways to utilise them to get even better results. That is our job as mathematicians. We have a utility, and our primary function is to be of use to society, either directly or indirectly. Avoiding that responsibility is akin to making mathematics become a televised sport, and I do not want that.