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I've read this article, and I know that he made lenses but it's not clear what tools he used to build them. Specifically, if he used mathematical tools of if he did that only by trial and error. I was unable to find a copy of the references in the end of the article.

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  • $\begingroup$ I do not know the answer to your question, but note that the Dutch Wikipedia page says: "His scientific status was completely dependent on his exclusive knowledge of lens production, and he took great care to keep his methods a secret. Perhaps he made his lenses from the little bit of glass that remains on the end of the blowpipe after glassblowing." (translation mine). $\endgroup$ – Danu Jan 23 '16 at 18:24
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The same Wikipedia article only mentions that he "attended school" for a short time. After that he became a bookkeeper's apprentice. So he probably learned some mathematics at school and as a bookkeeper's apprentice. Then we learn that he was appointed a land surveyor, which certainly requires more mathematics. This implies that he learned somehow the necessary mathematics for this job. Either at school or (more likely) by self-education.

There is not so much mathematics a lens maker has to know, besides what a land surveyor has to know.

Most 17s and 18s and 19s century craftsmen who made important inventions had no formal mathematical training (I mean at the university level). They were self-educated, and they knew enough mathematics for their trade. I mean people like Jost Burgi (one inventor of logarithms), James Watt, or John Harrison (chronometer), and many others. They obtained the necessary mathematical knowledge in the process of training for the trade and self-education.

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