There's an old children's story about making Stone Soup.
In it, a penniless begger offers to teach people how to make his favorite recipe: soup, made from a stone!
He boils some water and drops a stone in, and while it's "cooking", keeps mentioning offhand things like
"It'd go great with some carrots" or "Celery would be lovely in this".
The townspeople rush off and get celery, carrots, potatoes, onions, and the like to add to the soup, until eventually, they've made proper soup in his pot along with the stone.
So basically, the whole "stone soup" thing was a clever con game by which the begger can eat for free (or, in kinder versions than the one I recall, to trick the townspeople into learning a lesson about sharing).
The stone adds nothing to the soup.
cooking.stackexchange.com/users/6317/Yamikuronue
The version of the story that many Americans know comes from the book Stone Soup , in which three weary soldiers enter a village and convince the suspicious villagers to share their supplies by showing them how to make soup from stones.
A big pot, some water, and three smooth stones is all you need for the soup, but it's much better if you add vegetables, meat, some milk, salt and pepper, etc.
In the book, the villagers end up putting on a great feast and having a wonderful time, and the implied lesson for children is that it's more fun to share what you have for everybody's benefit than to keep your cabbages and barley hidden in the cellar.
cooking.stackexchange.com/users/5505/Caleb
I learned this trick from an old friend of my Grandmother more than 50 years ago.
She put three rounded stones in the pot when cooking soup so they would move about and stop the vegetables and grains from settling and burning on the bottom of the pot.
Molly did all of her cooking on a wood/coal fired oven.
Many people of my Mother's generation used to put glass marbles in the pan when making Jams or conserves for the same reason.
cooking.stackexchange.com/users/9081/Jerome B Newell
There is also a french dish called "potée" that take a stone in the pot, this is suppose to mash ingredients with the boiling movement and provide a particular texture.
So maybe it's the original mixer
cooking.stackexchange.com/users/47578/rm-ass
I grew up being told a stone was used in the soup or stew while the food was being cooked.
This was a method used to keep the food in the pot hot for a while longer.
cooking.stackexchange.com/users/47518/Cheryli VanAlstine
I came to the question from trying to find the best kinds of soup stones to add minerals to stews etc.
I know that Italians have a tradition of putting marble into their wells to add minerals to the water, and I know that cooking vegetables releases acids from the old habit of putting bicarbonate of soda in with peas etc.
I have observed the disintegration of bones used to add body to stews.
It is plausible that sea shells would perform this function, and I know that granite dust is used to provide trace elements in agriculture.
So stones may do more than tell you when your pot has gone dry.
cooking.stackexchange.com/users/21146/Leo
Have you ever heard of the trick to cook a potato faster by pushing a nail into the center of it before placing it in the oven?
The nail gets hot and so the potato gets cooked from the inside while also being cooked from the outside..
I've never heard of using stones in soup, but it immediately reminded me of the nail trick
so my reaction was "ohh, that's a really good idea."
Lol.
Some stones (maybe all stones?)
retain heat very very well.
In fact, I once ate at a restaurant called"The Stone Grill" who's signature dish was bringing you a hot flat stone slab along with raw steak
\ chicken
\ pork and
you would cook your own meat on the rock.
I was full after I finished eating all the steak and pork
so I threw my raw chicken on the stone to cook so I could take it home, and even after 40 minutes the stone was hot enough to cook the chicken.. Soo
yes, old wives tales and stories aside, stones cooked in soup would most certainly keep the soup hot long after it was removed from the stove.
And might even help it cook slightly faster..
cooking.stackexchange.com/users/67456/Ant
In Utah sometimes in elementary school teachers encourage students to bring stones for a soup.
The teacher then shows the children how to identify what kinds they brought and adds all the stones that have a high mineral content.
The result is a drink which is warm and tastes more like the water you get from the mountain springs and the teacher explains that the reason the mountain springs taste the way they do is the minerals from underground stones.
However I don't think this kind of stone soup is common elsewhere.
cooking.stackexchange.com/users/80975/Jaq
I was surprised by the added stone in the soup of  this question :   "Also, for irony, a large (cleaned) stone is always left in the pot"  What would be the reason for this? For the minerals in the stone? As far as I know, minerals do not infuse water directly out of a stone.
Why put a stone in the soup?
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<soup><nutrient-composition>
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cooking.stackexchange.com/users/641/BaffledCook
There is a children's story where a stone is used to make soup, but stones are sometimes used to stop food from burning on the bottom of the pot, as a way to mash the food or in order to help the pot retain its heat. It might come from an old tale about making stone soup. There is definitely a practice of putting stones in with food to stop it sticking to the bottom of the pan. It would also keep the food hot for longer.
It might come from an old wives' tail about making stone soup. Putting stones on the bottom of the pan stops things from burning on the bottom of the pot. The stones keep the food hotter for longer.