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According to Wikipedia the Lebombo bone (age 35 KY) and the Ishango bone (age at least 20 KY) presently are believed to show the first evidence for application of mathematics by humans. (Possibly African women, constructing a moon calendar, were the first mathematicians.) Is this the present state of the art? Or are there newer discoveries of older mathematical artifacts?

Remark: This question is not asking for some examples but for the present state of historical research in paleo-mathematics.

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Just a hint to literature concerning the Ishango Bone (or rather the difficulty to say something about it): reunion.iufm.fr/recherche/irem/IMG/pdf/… –  user15817 May 5 '13 at 12:00
    
in this connection, see mathoverflow.net/questions/106848/… –  Carlo Beenakker May 5 '13 at 12:44
    
@Carlo: Thank you, but I saw it already some time ago (and upvoted your answer). According to Wikipedia there could be prime numbers involved in the interpretation of the Ishango text. But I think that is not very probable. Anyhow would like to know more about these earliest origins of mathematics. –  Rhett Butler May 5 '13 at 13:14
    
@unknown: Thank you very much for that interesting source. –  Rhett Butler May 5 '13 at 13:15
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That depends heavily on what you mean by "mathematics". It underwent a sharp transition from the descriptive science to the deductive science sometimes somewhere in the Ancient Greece (it is believed that Thales of Miletus was the first to apply the deductive argument to a geometric problem about 600 BC but we have no proof that nobody did it earlier. Most likely, Thales just was influential enough to get it noticed and followed). This transition was so drastic and had so many implications that I would call everything that preceded it "pre-mathematics". As to mere counting, crows can do it. –  fedja May 5 '13 at 14:41
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