A lot of modern technical marvels were built on top of the leisurely work done by people who were just playing.

"I wonder what would happen if the square root of -1 existed"

"I wonder what happens if numbers were cyclic"

"Can you actually cross all the bridges of Köningsberg without walking any of them twice"

The impetus to solve these problems was that they were fun to think about, not that they a century or several centuries later would enable us to do harmonic analysis, invent the basis for cryptosystems or spectral graph theory. Which are billion or even trillion dollar inventions.

I don't think this is accurate. For example square root of -1 was motivated by clear applications in mathematics, it was definitely not just idle leisurely math. Most of important pure math has not been leisurely or recreational in any sense in its origin

Before the 19th and 20th century, much of the basis of modern math was entirely leisurely and recreational. Even today that still rings true. I recommend reading Barry Mazur's "Number Theory as Gadfly" to add some context to that claim.

> And -let me get this right- you want society to keep paying you, so you can play with your imagination?

No, pure mathematics is almost never completely recreational. No serious paper gets published in a decent journal without having some motivation and connection to the rest of mathematics.

It is of course valid to ask why we should fund research in pure mathematics, which is not directly related to any "real" applications.

Same question applies to things like niche art, literary studies, history, etc. One answer is that these things are relatively cheap, and our culture would be poor without these things.

With pure maths the advantage is also that it is cheap, and the payoff in applications (if and when they happen) is high.

Note well that the article makes a strong point that any practical benefits of mathematics are, essentially, a side-effect, and even a distraction:

It would be bad enough if the culture were merely ignorant of mathematics, but what is far worse is that people actually think they do know what math is about— and are apparently under the gross misconception that mathematics is somehow useful to society! This is already a huge difference between mathematics and the other arts. Mathematics is viewed by the culture as some sort of tool for science and technology. Everyone knows that poetry and music are for pure enjoyment and for uplifting and ennobling the human spirit (hence their virtual elimination from the public school curriculum) but no, math is important.

Also see the first two stanzas of the dialogue between "SIMPLICIO" and "SALVIATI" that follow the above paragraph. I think, in other words, that the author would say that the "motivation" in pure mathematics papers is more of a pretext to be able to get published and continue one's work unobstructed, than something that the mathematicians themselves really care about.

It is not always clear what will turn out to be useful or not, even in terms of morale. Witness Richard Feynman’s curiosity about a wobbling plate that someone threw in the air, that he credits with solving his burnout with science: https://pubs.aip.org/aapt/ajp/article/75/3/240/1056339/Feynm...

Riemann was 'just playing' with non-Euclidean geometry. Einstein used it as the basis for the modern theory of Relativity. Of course Galileo had 'played' with Relativity three centuries earlier. Now we have GPS navigation systems that depend utterly on the mathematics that they and an unknown number of other 'playful' mathematicians worked out over the centuries, much of it with no obvious immediate benefit to society.

My career was in practical physics and engineering, much of it with immediate effect on the world. Without all the groundwork done by people without any aim other than working out intellectual problems none of my modest achievements would have been possible.

Or was your point that we should pay people only to work on things that we know we need now?

My own work has been dismissed as too theoretical and impractical. I'm just pointing out the reaction that this language of "playing" can elicit in those strata of society that want to see "results". And, more importantly, to the people who do all the work that is needed to keep people like me alive: those who make the food I eat, who keep the trains running, who keep the sewers unclogged, the streets clean, the houses from falling, etc.

There is a certain arrogance in the article above, and I felt it should be pointed out. When we set out on a grand adventure of the mind, we should not forget who it is that's footing the bill.

One of the most surprising things about mathematics is how useful it can turn out to be even when the mathematicians involved don't think that it will ever apply outside of their obscure domain of e.g. boolean logic.