[anonymous325]

Notice all the hand-waving in the article about mathematics. Mathematics proper, as in the derivation of theorems from axioms by means of proof, was discovered by the Greeks, and unless the residents of Benin City, or the Maya, or any other non-Western society that biased academics seek to rehabilitate were similarly deriving theorems from axioms by means of proof as did Euclid, speaking of their supposed mathematical prowess is extremely disingenuous and misleading.

[apalmer]

Mathematics as far as it being a branch of logic was pretty much invented by the greeks as you say.

And the mathematics mentioned in this article are definitely 'tenuous' at best. I clicked on the 'African Fractals' and didn't really see anything that I would consider mathematics, although I did see some organizing principals I guess.

However the claim that mathematics is either 'theorems' or bust is not really valid standpoint in general... seeking one must by a practical definition of mathematics include at least Egyptians (at least in practical geometry), early South American (at least in practical geometry). Neither of which had any strong belief in the necessity or ideal of 'proving' theorems. Further one should include without doubt early Indian contributions which covered both practical and theoretical mathematics and early Chinese contributions although they seem grounded in theorem based approach

[anonymous325]

> However the claim that mathematics is either 'theorems' or bust

The theorems of mathematics are what distinguishes it from other enterprises and provides us with a degree of certainty of the correctness of our conclusions that would otherwise be unavailable. No number of (Euclidean) triangles measured, however great, would convince us equally well that their interior angles always sum to 180 degrees, nor would any exhaustive search of pairs of integers convince us equally well that the square root of two really is irrational.

By exaggerating the accomplishments of Africans to a lay audience, the article is minimizing the accomplishments of Europeans.

[apalmer]

Seems like this viewpoint is based on preconceived views of 'europeaness'. However agree in general that this articles claim of African fractals doesn't seems to be based more on geometric patterns that please they eye more than mathematical principles

[yongjik]

Echoing other comments, the importance of "proof" in math has not been universal even in West. For example, the rigorous definition of derivatives[1] was not given until 1817, 130 years after Newton's Principia was published.

[1] https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of...

[RangerScience]

What? No. There's way more examples, but the ones that most come to mind are the calendars of the Mayan and Incan civilizations. If that's not mathematics, what is it?

[parennoob]

> Mathematics proper, as in the derivation of theorems from axioms by means of proof

That is an extremely narrow definition [1]. It is acceptable to me as someone who works in the intersection of technology and mathematics -- but for the general public the word implies a wide field of study, exploration and usage.

For example, on Wikipedia "Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change."

So all the author is saying that the residents of Benin City seem to have studied fractal patterns in some form and used them in art.

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[1] Although, reading your comment more carefully, you did qualify it with "mathematics proper". I guess my comment's whole point is that it's often "mathematics improper" when used by a popular columnist.