Mathematician:James Gregory

Mathematician

Scottish mathematician and astronomer best known for designing the Gregorian telescope.

Made advances in trigonometry, discovering infinite series representations for several trigonometric functions.

One of the first to distinguish between convergent and divergent series.

Gave both the first published statement and proof of the Fundamental Theorem of Calculus, but only for a limited class of functions.

The uncle of David Gregory, who inherited his papers on his death.

Nationality

Scottish

History

• Born: November 1638 in Drumoak (near Aberdeen), Scotland
• Died: October 1675 in Edinburgh, Scotland

Theorems and Definitions

• Gregory Series (also known as Gregory's Series and Inverse Tangent Series)
  • Gregory's Series for $\pi$ (also known as Leibniz's Formula for $\pi$, for Gottfried Wilhelm von Leibniz)

• Gregory's Constant (possibly also named for Grégoire de Saint-Vincent), also known as:

Mercator's Constant, for Nicholas Mercator

the alternating harmonic series

• Gregory Coefficients

• The Gregory-Newton Forward Difference Formula (with Isaac Newton), also known as:
  • the Newton-Gregory Forward Difference Formula
  • Newton's Forward Difference Formula
  • the Forward Difference Formula

• The Gregory-Newton Backward Difference Formula (with Isaac Newton), also known as:
  • the Newton-Gregory Backward Difference Formula
  • Newton's Backward Difference Formula
  • the Backward Difference Formula

Results named for James Gregory can be found here.

Definitions of concepts named for James Gregory can be found here.

Publications

• 1668: Geometriae Pars Universalis, in which the Fundamental Theorem of Calculus appears

Also known as

James Gregory's surname was originally spelt in the Scots manner as Gregorie.

Sources

• John J. O'Connor and Edmund F. Robertson: "James Gregory": MacTutor History of Mathematics archive

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Gregory, James (1638-75)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Gregory, James (1638-75)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Gregory, James (1638-75)