That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math?

I suggest if one looks at the history of funding for mathematics and science, the product of these efforts is not understanding, but rather power. Funding went way up after WW2 when the war demonstrated that power flows from them. Math not only contributed to the scientific weapons of the way, but was directly used in operation planning (the birth of the field of Operations Research) as well as in cryptography.

The reason this matters is that AI is also a quintessential power-oriented technology. From the point of those providing the monetary lifeblood on which modern mathematical practice depends, the current math-AI discussion presents no issue worthy of concern.

Power depends on understanding - Seeing a larger scale view of what is happening as opposed to an arbitrary sequence of manipulations.

The foundations of the WW2 technologies you cite were dependent on previous theoretical efforts (ex:relativity) to develop a good understanding.

Without understanding, you get brittle demos which fail as the environment or problem description changes.

> That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math?

Yes, and your examples are exactly examples of what the GP quote is talking about.

Of course people paying money want applications, which includes "power" in your kind of reductive framing (applications to war being only one of many types of applications, or we could redefine any gradient provided by expanded understanding as "power", in which case the choice of word just seems melodramatic).

What we've also learned over the centuries, a lot more clearly in the last few, is that seemingly pointless or applicationless understanding can very quickly become useful. This is why it's clearly worth still funding pure math.

There is more to math, than input (money) and output (power). Sure, there is some relation between applied sciences and how knowlegde can assist effecting world events.

But for the most part, math discovery relied more on human curiosity than on resources to "do math". Conversely, if people allocate lots of money to developing AI, that doesn't mean mathematicians have an obligation to take the money provide ROI to investors.