Goldbach’s Celestial Atlas

Christian Goldbach, Prussian mathematician. Probably most famous for the Goldbach conjecture, one of the oldest unsolved problems in mathematics:

Every even integer greater than 2 can be expressed as the sum of two primes.

The story goes that he scribbled this conjecture in the margin of a letter he wrote to Euler. In fact, he wrote two versions of the conjecture in that letter — one in the body, and one in the margin. The statement above, which is how we know the Goldbach conjecture today, actually came from a subsequent letter, in which he and Euler continued the original conversation.

But less known is the fact that Goldbach also dabbled — very briefly — in astronomy. In 1799 he published Neuester Himmels – Atlas zum Gebrauche für Schul und Akademischen Unterricht, nach Flamsteed … [et.al.], in einer neuen Manier, mit doppelten schwarzen Stern-Charten bearbeitet; durchgehends verbessert, und mit den neuesten astronomischen Entdeckungen vermehrt [The Newest Celestial Atlas for the use of School and Academic Education, according to Flamsteed …[et.al.], in a new Style, edited with double black Star-Charts; improved and expanded with the latest astronomical Discoveries].

NewImageThe constellation Leo, with figures
Thumbnail image from The Linda Hall Library

The atlas was printed with white stars on a black background in two pressings: the first pressing had the stars only, as you would see them in the night sky. On the second pressing, annotations and figures of the constellations were added, as seems to have been customary with star-charts of the time.

Neuster Himmels was Goldbach’s only astronomical publication. The Linda Hall Library of Science, Engineering, & Technology in Kansas City, Missouri has plates from the first edition of the atlas viewable online. You can see the charts as fairly large images both with and without the figures.

Enjoy.

Mathematics versus Computer Science

…until the development of computers the possibility of dealing successfully with the complex itself was never really envisaged. Perhaps the most successful substitute for such a possibility, as well as the nearest approach to it, came in mathematics. … To find the simple in the complex, the finite in the infinite — that is not a bad description of the aim and essence of mathematics.

That’s Jacob “Jack” Schwartz, writing in 1969. He goes on to say:

In this quest for simplification, mathematics stands to computer science as diamond mining to coal mining. The former is a search for gems. Although it may involve the preliminary handling of masses of raw material, it culminates in an exquisite item free of dross. The latter is permanently involved with bull-dozing large masses of ore — extremely useful bulk material. It is necessarily a social rather than an individual effort. Mathematics can always fix its attention on succinct concepts and theorems. Computer science can expect, even after equally determined efforts toward simplification, only to build sprawling procedures, which require painstaking and extensive descriptive mapping if they are to be preserved from dusty chaos.

Actually, I’ve always thought that mathematics is also a social effort (and data science, too).

The essay is “Computer Science,” from Jacob T. Schwartz, Mark Kac, and Gian-Carlo Rota, Discrete Thoughts: Essays on Mathematics, Science, and Philosophy, 1992.

Bon Mots from Professor Rota

As I’ve posted previously, we are writing a data science book. The preview of the first chapter of our book should come out in about a month or so. We are almost finished with the revisions to the first four chapters, and we’ve started refining the outline of the next three. Exciting!

It happens that I’ve been rereading mathematician Gian-Carlo Rota’s collection of essays, Indiscrete Thoughts, and I’ve found a few passages that really speak to me, now that I’m in book-writing mode. Enjoy.

NewImageFrom Augustin Hirschvogel’s Geometria, 1543

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