It seems to me highly probable, for various reasons, that Mathematics was the first science developed by man. By science I mean a mode of reasoning which organizes a vast amount of disorganized phenomena in an understandable system.
If it is assumed that, at any rate, man is not born with a proper training in such science, it follows that he would be amazed by the complex scheme of things external to him, when not insulated by a developed culture (e.g. early man as a vagabond). He may fear and revere the uncomprehensible situation, but given the necessity he finds in survival, a part of him would certainly try to manipulate reality by making it comprehensible , ie, the emergency of survival would be the conquest of unknown reality.
Along with this emergency to simplify the world would be the ability of sense-experience and a computive mind (as scientists have us believe). They will see most clearly the presence of numbers (basic quantitative units) and sets (groups of similarities)- 10 fingers, 2 eyes, a group of 12 people, 4 men and 8 women, x no. of fruits, berries or animals hunted, n no. of positions of the sun all throughout the day, etc etc. They find these numbers consistent and trustworthy. With this ability to gauge the number of one kind of things, even if rudimentary, is satisfied the exigency mentioned earlier, ie, of simplifying the world. Slowly, by having to manage the numbers they have created, they would then understand the operations involved in Mathematics, they would find rules that can't be applied to different realities, and for these realities they would diascover newer rules. So, by the obvious presence of numbers, and by their consistency, Mathematics is, if I am not mistaken, the first science to be devloped by man.