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Tools and instruments are integral features of the history of mathematics, aiding numerous pursuits such as navigation, description of the natural world, and regulation of commerce. The world's oldest scientific instruments were developed to aid calculation. For hundreds of years, ruler-like tools were the most common calculating devices and their use persisted alongside mechanical innovations that automated simple mathematical procedures.

The Whipple Museum is in possession of more than 700 'calculators', from sectors used by Early Modern astronomers to an impressive collection of handheld calculators of the sort used by twentieth-century astronauts. The articles in this section explain various aspects of the history of calculating devices.

Read more at: A Brief History of Calculating Devices
Chinese suanpan abacus

A Brief History of Calculating Devices

From the abacus to the EDSAC computer, humans have used physical apparatuses for counting to simplify and solve mathematical problems. Here you can read a brief overview of how certain devices developed over time and continued to be useful despite apparently superior developments.

Read more at: Tables
Beazley's curve tables


Perhaps the most important 'devices' for calculation throughout human history, mathematical tables standardise values for computation and come in a variety of shapes, sizes, and applications.

Read more at: The Sector
Sutton Gunter sector, folded

The Sector

All sorts of devices for measuring, weighing, and telling time were used in antiquity, and the revival of astronomy in Europe toward the end of the Middle Ages linked classical knowledge to developments from Arabic societies. New instruments came with new theories, most notably the sector, championed by Galileo.

Read more at: John Napier's Calculating Tools
Abacus and base and Napier's bones

John Napier's Calculating Tools

In the early 17th century, Scottish mathematician John Napier introduced the logarithm to speed up calculation by hand, along with other means of representing multiplication problems including the numbered rods or 'bones' for which he became known. These developments laid the foundation for mechanising calculation.

Read more at: Slide Rules
Detail from Gunter rule

Slide Rules

Undoubtedly the most widely used mathematical instrument from their invention in the late 17th century to the 1970s, slide rules are seen today as historic curiosities. But in their time they took on numerous shapes and were understood as 'universal' tools with limitless applications to any domain in which proportions and scaling were used.

Read more at: Mechanical Calculation
Brunsviga calculating device

Mechanical Calculation

18th-century Enlightenment fascination with clockwork generated designs for automatic calculating devices, many of which were built and some of which provided templates for later mass-produced machines. Though few of these early devices survive, later manifestations allow us to see what the actual practice of calculating was like.

Read more at: Charles Babbage's Difference Engine
Detail from the Babbage Difference Engine No. 1

Charles Babbage's Difference Engine

Acknowledged as the first architect of a general-purpose computer, Charles Babbage's first foray into automation was spurred by the problem of efficiently producing reliable sets of mathematical tables. He worked, unsuccessfully during his lifetime, to apply principles of computational labour division for humans to automated machines.

Read more at: Pocket Calculating Devices
Curta handheld calculator

Pocket Calculating Devices

While the 20th century saw grand designs for general-purpose computers, it also saw principles of precision engineering applied to earlier designs, allowing them to become portable.

Read more at: The EDSAC and Computing in Cambridge
Electronic Delay Automatic Storage Calculator (EDSAC) in Cambridge

The EDSAC and Computing in Cambridge

The Electronic Delay Storage Automatic Calculator was one of the earliest general-purpose computers. Built for Cambridge academics and students to run problems on, it was one of the first computers to be made a community resource.

Read more at: Handheld Electronic Calculators
The Decimo Vatman I, V.Sc. II, and Extra S electronic calculators

Handheld Electronic Calculators

Developed in the 1970s, handheld electronic calculators facilitated some essential advances in the history of computing, including the development of microprocessors and freestanding exchangeable software.