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The title is drawn from a sentence in a Jim Holt article, "The Dangerous Idea of the Infinitesimal," now a chapter in his book collection.1 I found this a striking claim, and perhaps true, as the ancient Greeks did not have the algebraic means to formulate "scientific laws" as we know them today.

Q. To what extent is it in some sense true that the ancient Greeks did not discover a single scientific law? Are there counterexamples, cases where they did discover "laws," even if not phrased in equations?

The full sentence is: "The Greeks might have amassed much particular knowledge of nature, but their love of rigor held them back from discovering a single scientific law." Of course it is unfair to Holt to extract this from the surrounding context, but I do think the Q above can be discussed outside of Holt's context.

1 Jim Holt. When Einstein Walked with Gödel: Excursions to the Edge of Thought. Farrar, Straus and Giroux, 2018. Chp.13, pp.146-156. Quote p.153. (NYTimes Review.)

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It is a strange idea that scientific laws can be only expressed with algebraic means. The Greek did discover several scientific laws. The oldest one is attributed to Pythagoras himself: it relates the length of the string to its pitch. This seems to be the oldest scientific law ever discovered. More laws were discovered in Hellenistic times: the law of reflection, for example. Everyone knows the Archimedes laws about floating bodies and the laws of lever.

All these are genuine scientific laws, and we still learn them in our schools and universities in the same form as they were discovered. It does not matter how you express them: with equations or with words or with pictures.

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Euclid wrote an Optica (300 BC) — surely “Visual rays proceed in a straight line indefinitely” ranks with the best physical laws. So did Ptolemy (160 AD), and Hero wrote a Catoptrica (50 AD).

Aristotle knew the principle of virtual work.

Jim Holt’s physics don’t seem to fare much better than his math.

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Snell's law was discovered in the 16th century or even earlier, whereas the algebraic notation is a post-Viete thing and a product of the 17th century. Holt seems to be influenced by the ideology that "mathematics is the language of the sciences" which is an idea apparently first popularized by Galileo. While useful as a heuristic principle, this may not be exactly correct.

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    $\begingroup$ So Snell was Greek, now? Nor was Ibn Sahl, who had the law in 984 AD, per wiki. $\endgroup$
    – Francois Ziegler
    Commented Jul 29, 2018 at 19:09
  • $\begingroup$ @FrancoisZiegler, the OP seemed also interested in the more general question of whether scientific laws can be discovered without having an algebraic apparatus to express them (contrary to what is apparently Holt's claim, though I haven't read this particular piece by Holt). $\endgroup$
    – Mikhail Katz
    Commented Jul 30, 2018 at 7:01

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