Picturing science: teaching maths

Cross-posted from The H Word blog.

Detail from of a portrait of Thomas Weston

Seeing Alex Bellos’s ‘sconic sections’ in his post on combining baking and geometry, made me think of this lovely early 18th century mezzotint, recently acquired by the National Maritime Museum.

Sadly no foodstuffs are involved, but there is a prominently placed dissected cone, with ready-cut conic sections, in the left foreground. Alongside are some of the other essentials of the mathematical teacher: drawing instruments (today’s ‘geometry set’ known to all kids heading back to school in the autumn), diagram, textbook and writing materials. It is less pencil and squared paper, of course, and more quill and ink.

The portrait is of Thomas Weston, who from 1712 headed Weston’s Academy in Greenwich, which, in taking some pupils who were sons of pensioners at Greenwich Hospital, was one of the forerunners ofGreenwich Hospital School. The portrait was the frontispiece to his book, “A copy-book written for the use of the young-gentlemen at the Academy in Greenwich” (1726).

The text in the picture is a lecture, clearly titled Lectiones Astronomicae Lectio 12. Astronomy and mathematics were Weston’s specialty, especially as the basis to learning navigation. Before setting up his school, Weston had been an assistant to the Astronomer Royal, John Flamsteed. At that time, he lived and worked at the Royal Observatory, an institution founded to help improve astronomical methods for finding longitude at sea.

There is another portrait of Weston, on the ceiling of the Painted Hall at Greenwich Hospital. Here he looks with admiration at Flamsteed, both in front of the mural arc that was, by the 1690s, the most significant instrument at the Observatory. Placed on a wall aligned north-south, it defined a Greenwich Meridian.

Portrait of Thomas WestonWhile I love the mathematical details in the foreground of this image, perhaps the most splendid thing about it is Weston, wearing a formal wig and, best of all, a striped dressing gown or banyan.

However, if the combination of food and science is more your thing, have a read of this post by Melanie Keene on the objects used to teach elementary astronomy. There are blueberries and oranges that might stand in for the relative sizes of planets but, even better, in the early 19th-century children’s book, Tom Telescope:

the movement of the earth around the sun was best explained as like that of a rotisserie chicken. This “common occurrence in a kitchen” showed how it was “far better for the bird [the earth] to turn round before the fire [the sun], than the fire to turn round the bird”.

Melanie will be saying more about the use of familiar objects in teaching science in the 18th and 19th centuries in her paper at the International Congress for the History of Science, Technology and Medicine (iCHSTM) in Manchester next month.

Leonhard Euler, longitude winner

Cross-posted from The H Word blog, first appeared 15 April 2013.

18th century mathematician Leonhard Euler
Leonhard Euler, the influential Swiss mathematician, has had the 306th anniversary of his birth honoured by a Google doodle. Photograph: Google. Photograph: Kunstmuseum Basel/Wikimedia Commons

I was delighted to spot today’s Google doodle, celebrating the Swiss mathematician, Leonhard Euler. The Guardian’s brief piece today states that:

Euler was arguably the most important mathematician of the 18th century and one of the greatest of all time. He introduced most modern mathematical terminology and notation and was also renowned for his work in mechanics, fluid dynamics, optics, and astronomy.

What is not noted, but is well-known to those of us working on the history of the Board of Longitude project, is that Euler is one of those who received a financial reward from the Board in 1765.

In the aftermath of a sea trial of three possible approaches to solving the problem of finding longitude at sea, two emerged as worthy of further investment. One was John Harrison’s sea watch, for which the maker received £7500 in October 1765. Any further reward would depend on his showing that this was a machine that could be replicated.

Back in May 1765, however, the Board also worked out how to reward and support the lunar distance method. This, much more obviously than Harrison’s work, was a method produced through the work of many individuals, several already deceased. However, as well as setting up the future publication of digested astronomical data in the form of theNautical Almanac, they opted to flag up some key contributions.

Tobias Mayer’s widow, Maria was paid £3000 as a posthumous reward to her husband “for his having constructed a Set of Lunar Tables” and to her for making them property of the Commissioners.

Catherine Price, Edmond Halley’s daughter, was paid £100 for handing over several of Halley’s manuscripts, which the Commissioners believed “may lead to discoveries useful to navigation”.

Still living, however, was Leonhard Euler, who received £300 “for Theorums furnished by him to assist Professor Mayer in the Construction of Lunar tables”.

Euler’s important mathematical work had very practical applications, of which he and the Board were well aware. It was this work, building on that of Johann Bernoulli and Gottfried Leibniz that allowed Mayer to do what had always eluded Isaac Newton: produce a usable theory of the moon.

Histories of mathematics

Although I am currently writing a chapter on biographical portrayals of Newton “as a mathematician”, I am, by no stretch of the imagination, an historian of mathematics. The reason is, in large part, because I am not a mathematician. Now, I am also not a physicist, or a geographer, or a chemist or an astronomer, or a scientist (or woman of science) of any other description, having finished my formal scientific education with Higher Chemistry (a Scottish qualification, for those unsure, taken around the age of 16/17), yet I have written about aspects of the history of all of those disciplines.

I get away with it because history of science has long since moved away from focusing entirely on the content of the science and has embraced approaches that consider science in its widest social and cultural contexts. The battles between ‘internalists’ and ‘externalists’ in history of science are (mostly) behind us, and the subject is the richer for being able to take lessons from both spheres, and for including individuals with a range of backgrounds. History of mathematics, though, was one of the last remaining bastions of internalism.Read More »