In the cases you listed you aren't really seeing a number. You're seeing legs. That there happen to be four, or eight, or two, or six, or however many legs centipedes have, doesn't mean that you are seeing the numbers. Indeed, there are some tribes (I think, I vaguely remember this from some TV show) that don't even recognise numbers higher than three. So that their count would go "one, two, three, many." Another tribe has no words for numbers at all:
https://en.wikipedia.org/wiki/Pirahã_people
Things are either "few", or "many". I think this does suggest that maths was invented to suit our needs, or the needs of our ancestors -- because if those needs (which are going to be related to farming) never exist, then neither it seems do the numbers or the concepts to go with them.
I'm not enough of an anthropologist to know more about this, about the development of languages and cultures. But it seems worth mentioning.
The more I think about it, the harder it is to say that maths was discovered. Sometimes the invented concepts may lead us to places we would never have considered. But even then that discovery is going on inside our heads.