Calculating without a machine
Long before anyone built a calculating machine, people had ways to keep track of numbers. Tally marks on bones and sticks are among the oldest known records of counting. A well-known bone from central Africa carries groups of notches, and researchers have debated whether it was a simple tally, a calendar or something more complex, so it should be treated as an uncertain example.
Counting boards and the abacus were more systematic. Beads or stones moved in columns represented tens, hundreds and so on, and a skilled user could add, subtract, multiply and divide quickly. Different forms of abacus were used in the ancient Mediterranean, China, Japan and elsewhere. These are aids, not machines: the person does the reasoning, and the device only holds the intermediate numbers.
Hand-held calculating aids continued into the early modern period. In 1617, the Scottish mathematician John Napier described a set of rods, later called Napier’s bones, that turned multiplication into a series of additions. His work on logarithms, published a few years earlier, made it possible to replace multiplication with addition in another way, and within a few decades slide rules, which are scales sliding against each other, were in use. These helped with estimation but could not carry digits automatically or give exact results.
A separate thread is the ancient geared device known as the Antikythera mechanism, which calculated astronomical cycles. It was not a calculator in the ordinary sense, but it shows that complex gearing for calculation existed in antiquity.
Schickard and the calculating clock
The first mechanical device designed to perform arithmetic on its own is usually credited to Wilhelm Schickard, a professor in Tübingen, Germany. In letters to the astronomer Johannes Kepler from about 1623, he described a “calculating clock” that could add and subtract six-digit numbers, with a way of carrying a digit from one column to the next. A version of Napier’s rods was included to help with multiplication.
Much of what is known comes from those letters and from sketches found centuries later. Schickard wrote that a machine had been destroyed in a fire, and he died in 1635. The device was little known until the twentieth century, when modern builders constructed working models from his drawings. Opinions differ over how well the original would have functioned, but the reconstructions suggest the design was workable.
Pascal’s machine
In the 1640s, the French mathematician and philosopher Blaise Pascal began building a machine to help his father, who worked as a tax official and spent long hours on sums. The device, usually called the Pascaline, used a set of toothed wheels linked so that when one wheel passed nine, the next advanced by one. This is the carry mechanism, the central problem in a mechanical adder.
Pascal built a number of versions over several years, and some of his machines survive. They could add and subtract directly, and multiplication or division meant repeating those operations. The machines were costly to make, finicky and not widely adopted, and they were seen more as remarkable curiosities than as practical tools. Even so, Pascal’s work gave mechanical calculation public attention.
Leibniz and the stepped drum
The German mathematician and philosopher Gottfried Wilhelm Leibniz knew of Pascal’s machine and wanted something that could also multiply and divide. In the 1670s, he designed a calculator using a cylinder with teeth of different lengths, now called the Leibniz wheel or stepped drum. Depending on the digit set on the dial, the drum engaged a different number of teeth on a counting wheel, so that one turn of a crank could add a number several times.
He showed a model to the Royal Society in London in the 1670s, and a later version was finished in the 1690s. Historians generally report that the carry mechanism did not work reliably, which limited what the machine could do. Despite these problems, the stepped drum was influential; variations of it appeared in mechanical calculators for roughly two centuries.
Leibniz also became a strong advocate for binary arithmetic, using only zeros and ones, which later became the basis of electronic computers.
Why none of these was “the first”
If a title is to be awarded, it depends on how the question is framed.
- If the question is the first tool for calculation, the answer lies in prehistory, with tally marks and counting devices.
- If it is the first machine designed to add automatically, Schickard is the usual answer, with the caveat that the evidence is thin.
- If it is the first calculating machine of which examples were built and survive, Pascal’s machine is a strong candidate.
- If it is the first design able to multiply and divide by a mechanism, Leibniz’s drum is commonly cited.
Other inventors worked in the same period, and some of their efforts are lost or poorly documented.
Why they stayed rare
These early machines were not widely used for reasons that go beyond engineering. Clock-making skills, the same craft behind mechanical clocks, were needed to make accurate wheels, which made each machine very expensive. Parts wore, carries could jam, and there was no mass production. Meanwhile, accountants and astronomers could rely on tables, rods and trained clerks. A machine had to be both reliable and cheaper than a clerk to catch on, and for around two hundred years it was neither.
The path to practical, commercial calculating machines in the nineteenth century, and the route from there to electronic pocket calculators, is a separate story. What these early inventors left behind were the central ideas: the carry, the stepped drum and the possibility that arithmetic could be built into gears.