Probably where and/or how trade started.
And mathematics, because agriculture went hand-in-hand with documenting the ownership of a certain amount of land. And writing, because the farmer needed a durable record of the output of his fields, and of the amount of agricultural product he was trading. Not surprisingly, many of the oldest surviving cuneiform documents are records of agriculture and other forms of trade.
The early civilizations all were completely dependent on cereal grains and domesticated livestock. Cereal grains were especially important because they could be stored for long periods, even with the primitive technologies then available, which was not only a hedge against drought, floods and famine, it also could be shipped considerable distances to be traded or stored.
If domesticated livestock was raised on grain it could be kept in small feed lots instead of large pastures. Small feed lots could be set up closer to settlements, which allowed the meat to be slaughtered closer to the point of sale. So the development of domesticated cereal gains supported the keeping of domesticated livestock.
And all of this was important to the advancement of civilization because a developing culture needed people who "thought" for a living. You couldn't have people whose principal occupation was "thinking" (mathematicians, scientists, doctors, etc) unless they had some means of trading their services for the necessities of life. And there'd be no one to trade with for those necessities unless you had farmers who were able to raise in excess of what they and their family needed for their own sustenance. And this never would have been the case in a hunter-gatherer society.
Getting back to the topic of SunkenCiv's OP, and why all this is relative to the farmers splitting from the hunter-gatherers, is that this wouldn't have been possible before the lower mesolithic/upper paleolithic period because there were no cereal grains. Before that, all grasses had seeds that were too small and too few in number to be a practical food source. Then by purest chance, a number of natural hybridizations occurred in a relatively short timeframe creating three different cereal grains; emmer wheat (bread flour), einkorn wheat, and barley. In each case a variety of wild grass was pollinated by a wild goat grass. The miracle was that these chance cross-pollinations created fertile offspring with large numbers of big, fat seeds.
All three occurred naturally (and still do) in the Fertile Crescent and/or down into where modern Israel is, and all three have been found to have been domesticated and farmed by about 10,000 BC to 8,000 BC. So the first cities quite literally owed their existence and the timing of their creation to hunter-gatherers who decided to settle down and try their hand at domesticating and farming the "new" cereal grains.
Which also explains why Homo Sapiens had been around since about 200,000 BC but failed to establish a civilization for the first 190,000 years. Civilization requires specialists, and specialization of that sort would never have been possible without the chance hybridization of cereal grains.
Barley was important not just as livestock feed, it also was used to make beer. Beer then was a soupy nutritious mess, not a recreational beverage. It also was one of the earliest forms of food preservation by alcohol. The first great age of exploration ran on barley beer because clay jars of the stuff could be lashed to donkeys and you could explore without needing to scrounge for either food or water so long as the beer held out. Pay for the workers on the pyramids of the Giza plateau included a gallon of beer a day.
Dr Jacob Bronowski gets into this in his 1973 BBC series, The Ascent of Man, and I just geek out on that stuff.