A Huge Problem with the Popular History of Science and Mathematics

Is that it is often presented by scientists and mathematicians. And they often don't give a hoot about what the actual facts were. E.g., I just saw mathematician Bruce Edwards claim, in a lecture on proofs, that Hudalrichus Regius found that 2^11 - 1 was not a prime 'using Roman numerals.'

Immediately I wrote my friend Thony to check out what appeared to me to be a far-fetched claim. I heard back:
European university mathematicians were already using Hindu-Arabic numerals in the 12th century. They were introduced into commercial arithmetic by Fibonacci in the 13th century. By the 16th century they were in common use. As Ulrich Rieger (his real name) published his results in his Rechenbuch, which was a textbook for teaching the use of Hindu-Arabic numerals I very much doubt (being polite) that he did his calculations in Roman numerals.
So, Edwards was roughly four centuries off in his wild guess about when a European mathematician would still have been using Roman numerals, and the proof in question actually appeared in a book for teaching Hindu-Arabic numerals!

I've seen this frequently: scientists and mathematicians just don't take history seriously, and appear to simply make up whatever "facts" they want to suit the story they wish to tell.

And note: This is pretty clearly not a case of deliberate distortion of history for ideological purposes.  It is a case of just not bothering to check the facts.

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