I would like to know where to start, i.e papers/books/video conferences and conceptions/misconceptions, with the history of mathematics before it was really considered mathematics. I'm talking about very primitive notions or tricks that would have a mathematical meaning/explanation today. For example:

  1. A sheep keeper makes a mark in his cane, or adds a pebble to a pile for each sheep that enters the stables. When taking them out, he/she crosses the mark or removes the pebbles one by one. In this way, the sheep keeper doesn't need to know how many sheep he/she has, or even to count how many enter/get out of the stable. If at the end one or more marks/pebbles remain, then there are missing sheep.
  2. Almost any somewhat "developed" animal has at least a vague sense of "few vs lots" of things. A mother knows if one of its cubs is missing without having to count them or using marks/pebbles. I'm talking about notions that go further than basic perception: a bird knows its altitude "instinctively" and not because it has a notion of "my distance to the ground is greater here than there".
  3. Humans always have had a sense of causality. A thunder must be caused by something (be it the rage of some god, or a modern explanation). We have this intrinsic notion of logical implication

Would you say that there are some necessary requirements that make mathematics and logic "developable" in a mind? For example, vague notions of missing/not missing, bigger/smaller, similar/not similar could evolve into a basic arithmetic and then into more advanced maths

Thanks in advance! (Please, let me know if the question can be made more precise)

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    $\begingroup$ Off-hand, I don't know anything particularly focused on what you want, but if no one else offers much then my suggestion is to look over the first few pages of history of mathematics books -- such as those by Kline, Stillwell, Evans, Boyer/Merzbach, Smith, Grattan-Guinness, Kramer, etc. -- which you can do quickly at a university library, if a university is close enough to you to be worth travelling to ("worth" being dependent on how motivated you are to seek out this information). Some of these books may begin with prehistoric speculations and possibly also mention some relevant literature. $\endgroup$ Apr 14, 2023 at 10:19
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    $\begingroup$ See Abraham Seidenberg, The Ritual Origin of Counting, AHES (1962) and The Ritual Origin of Geometry, AHES (1961) $\endgroup$ Apr 14, 2023 at 15:22
  • $\begingroup$ Example 3 has little to do with mathematics. I like your phrasing of example 2 though, I agree that notions of topology and continuity and measurements (order too) are sitting somehow deeper in the human mind than e.g. arithmetic, but it took us longer to describe them mathematically. One somehow has to dig deeper to unearth these basics which are intuitive to children already before they start counting (or to animals who might never start counting). $\endgroup$ Apr 16, 2023 at 4:27


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