# Mathematical Treasure: Signature of Colin Maclaurin

Author(s):
Sidney J. Kolpas (Delaware County Community College)

Framed portrait and autograph from the collection of Dr. Sid Kolpas.

Colin Maclaurin (1698–1746), a Scottish mathematician, may be best known to calculus students for his series expansion of f(x) about x=0:

$f(x) = f(x) + f'(0) +\frac{f''(0)}{2!}x^2+\frac{f^{(3)}(0)}{3!}x^3+ \ldots +\frac{f^{(n)}(0)}{n!}x^n+ \ldots$

which is a special case of the Taylor Series. The first and second editions of his masterwork, the two-volume Treatise on Fluxions, may also be seen at Convergence.

Since at least the 19th century, it has been a common but unfortunate practice by autograph collectors to cut signatures from letters and documents. As a result, many letters whose content may have been significant have been lost forever. The undated, clipped signature shown here reads:

very affectionately you[rs]

Colin Mac Laurin

Edinburgh

March 31, 1730

(A previous owner of the signature has added “Mathematician”.)

The portrait was first created by the young astronomer James Ferguson (1710–1776), probably in the 1740s. The Earl of Buchan, David Steuart Erskine (1742–1829), used it to make a drawing circa 1795. The version shown here is a broadside drawn by R. Page and printed by G. Jones in 1814. Its caption reads:

Page Sculp

MACLAURIN

London Pubd as the Act directs Novr 1st 1814 by G Jones

The small drawing beneath the portrait depicts a woman with two globes, a telescope, a map, books, and a wall hanging covered with mathematical symbols. Other extant versions of this composition include a colored engraving now owned by the Wellcome Library as well as copies in the Dibner Library (part of the Smithsonian Institution Libraries), and the National Library of Scotland. A cropped, darker version of the Dibner's image is in Convergence's own Portrait Gallery.

Several other publishers also made engravings of the portrait, although they wrote different captions and did not add the image of the woman. Three of these printers, whose copies all appeared in 1798, included:

• Edward Harding
• John Smith, Iconographia Scotica (London)
• Thomas Trotter

Sidney J. Kolpas (Delaware County Community College), "Mathematical Treasure: Signature of Colin Maclaurin," Convergence (September 2019)