In the 2007 bubble, economists but even mathematicians had their reputations stained somewhat, especially "financial mathematicians". Because they knew what was going on, and they didn't really give the world a full-throated warning about the bubble and the damage it was going to do to the economy. They knew better, and were too busy making money (or their reputations) off the bubble to worry about broader ethical implications. The reason mathematicians got stained by the event was that much of the reason for the bubble was the cloaking of the deception in an intellectual cloud that made it difficult for outsiders to really understand what was going on. The intellectual cloud involved some mathematics, or perhaps the more appropriate thing to say is it involved a mis-understanding of some mathematics.
To add a caveat to the above paragraph, I would say the stain is largely a stain by association. There of course were some people pointing out the systemic problems in the economy. People sounding a warning often get far less press than people enthusiastically discussing making mountains of money, and so are drowned-out.
Most other bubbles haven't been like this. The dot-com bubble didn't really involve mathematicians in as significant a way -- mainly employing some of our graduates. But this AI bubble does involve mathematicians, and ideas from mathematics. There are of course many other issues with the current economic bubble: it involves relatively few decision-makers. The automotive boom with the start of automation was fueled largely by the high demand for vehicles like the model-T, i.e. large consumer demand. AI's development hasn't been fueled by "ground level" consumer interest. It is largely fueled by a small cluster of companies investing in each other. Moreover, while automobiles had clear applications to the general population, AI (to put it skeptically) is a technology largely based on trying to fake human interactions, so one of the leading clear applications people are aware of is the automation of fraud. You could make a similar argument about mathematics involvement in crypto currencies, but here it is more general financial crimes. That would be a bit of a digression.
Should mathematicians start trying to balance-out the hype about AI with an appropriate amount of informing skepticism?
Comment on if this thread should be here: I started this on meta, to get a sense for if MO was an appropriate location for this thread. It seems like there is some cautious support, so let's see how it goes. Original meta inquiry is here: Do mathematicians have an ethical role to play, regarding the AI bubble?