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Who Invented Math?

Apparently, Satan made us do it.

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Dr. Katie Spalding

author

Dr. Katie Spalding

Freelance Writer

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory.

Freelance Writer

Edited by Francesca Benson
author

Francesca Benson

Copy Editor and Staff Writer

Francesca Benson is a Copy Editor and Staff Writer with a MSci in Biochemistry from the University of Birmingham.

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Photo of a caveperson writing on a stone wall, modified to look like they're writing 2+2=4

A definitely very real etching of a mathematical sum...

Image Credit: Gorodenkoff/Shutterstock.com, Modified by IFLScience

“Mathematics,” Carl Friedrich Gauss is said to have claimed, “is the queen of the sciences.” Of course, as one of history's most famous and influential mathematicians, he was a little biased; ask a physicist, and she may well reply with the famous observation that “physics is to mathematics what sex is to masturbation.”

But whether or not math is the queen, she could certainly be called the doyenne of the sciences. The subject is way older than other forms of rational inquiry, stretching back tens of thousands of years at least; when Ibn al-Haytham was busy inventing science in the 10th century, he was already relying on millennia of mathematical knowledge and discovery to inform his inquiry.

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Which raises an intriguing question: who kicked it all off?

Lead us not into temptation

The earliest “mathematicians” – that is, the first people referred to by that name in English – were way more badass than today’s number-crunching nerds.


“Domicianus, the son of Vespasian, reignede xv. yere and v. monethes, the wife of whom was callede firste Augusta; and he commandede hym to callede god, and the lorde of all thynges […] puttenge in to exile mony mathematicions and philosophres.”

So wrote the anonymous translator of Ranulf Higden’s magnum opus of world history, the Polychronicon. It was somewhere in the second quarter of the 15th century, and as far as anyone has been able to tell, it was the first time the word “mathematician” had ever been used in English.

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It tells the story of Domitian, Emperor of Rome between 81 and 96 CE and, historians have generally agreed, a Not Very Cool Guy. Even today, when we’re usually all about the rehabilitation of maligned historical figures, the best we can say is that Domitian was “efficient” and “good at burying Vestal virgins alive”. In his own time, he was even less popular, with the Roman Senate damning his memory – essentially, formally writing him out of the history books – pretty much as soon as he popped his clogs (or, to be more accurate, had his clogs popped for him by a couple of assassins).

Most of the reason for that was due to Domitian’s approach to ruling – one traditionally summed up by the Latin phrase futue tu ipsum. The emperor’s philosophy on power was simple: he had it, and he could do what he liked with it, and everyone else could shut the hell up.

Anyone who refused to do so – such as philosophers, whom Epictetus had famously declared would “look tyrants steadily in the face” – would be expelled from Rome. We can only speculate as to why mathematicians supposedly provoked Domitian’s ire – but they joined not just philosophers, but also adulterers (harsh) and mimes (understandable) in their status as enemies of the Emperor.

While this level of controversy over sums might seem strange to us, it may not have been so odd to Higden. As an English monk writing in the 14th century, he would have been very familiar with the teachings of Saint Augustine of Hippo – a man whose views on math were something akin to a hyper-religious Malibu Stacy’s.

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“The good Christian should beware of mathematicians,” reads De Genesi ad litteram, a 4th-century exegetical text by the beatified megaherbivore. “The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell”.

Art in heaven

Now, in fairness to Augustine, he almost certainly meant astrologers rather than mathematicians – and despite frequently being confused for each other, math and hokum are different things. But in this imperfect translation lies a clue to an even earlier chapter in mathematical history.

Every ancient culture that studied math came to it via their own route: for the Greeks, it was harnessing geometry and logic to come up with theorems and proofs – concepts that there’s pretty much no evidence for before people like Pythagoras and Plato started teaching them after the 6th century BCE. In ancient China, on the other hand, math grew up primarily as a practical system for governance and provision; in India, texts as old as the 8th century BCE Shatapatha Brahmana used math as a way to commune with the gods.

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But for the Ancient Babylonians, working as far back as 1600 BCE, it was astronomy that set their mathematical tradition apart from all the others. Their observations form some of the earliest known examples of ancient math: “Scribes systematically began documenting celestial phenomena (e.g. eclipses) in about the eighth century BC,” wrote mathematician Chris Linton in his 2004 book From Eudoxus to Einstein: A History of Mathematical Astronomy. “In order to carry out their work, astrologers needed tables of the future positions of heavenly bodies […] and this desire was the driving force behind the production of such tables for over 2000 years.”

The oldest Babylonian math, such as that seen on Plimpton 322, is a weird mix of rudimentary and impressive. It’s incomplete and contains mistakes; there’s no evidence of any technique being applied, and it probably wasn’t even written by a mathematician at all. But at the same time, it’s evidence of an extremely ancient mathematical tradition that some say rivaled Renaissance Europe in its sophistication.

But were they the first?

The first named mathematician

In fact, we can go quite a bit further back than Plimpton 322 before we run out of examples of written math. Over in Egypt, people had been using – and, more importantly for our purposes, recording – mathematics for as long as they’d been writing at all, with evidence of a base-10 number system being found on artifacts from over five millennia ago.

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“By 3000 BC […] agriculture had been developed making heavy use of the regular wet and dry periods of the year,” wrote John Joseph O'Connor and Edmund Robertson, both researchers at the University of St Andrews School of Mathematics and Statistics. “Knowing when the rainy season was about to arrive was vital and the study of astronomy developed to provide calendar information.”

On top of that, “the large area covered by the Egyptian nation required complex administration, a system of taxes, and armies had to be supported,” they added. “As the society became more complex, records required to be kept, and computations done as the people bartered their goods. A need for counting arose, then writing and numerals were needed to record transactions.”

And for the best evidence of Egyptian mathematical prowess, look no further than the most iconic of the civilization’s achievements: the pyramids. 

“The Great Pyramid at Giza was built around 2650 BC and it is a remarkable feat of engineering,” the pair point out. “This provides the clearest of indications that the society of that period had reached a high level of achievement […] some of the measurements of the Great Pyramid […] make some people believe that it was built with certain mathematical constants in mind.”

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So, were the Ancient Egyptians the first mathematicians? Well, in one rather important way, yes, they were: the earliest known named author of a math textbook – known as the Rhind Papyrus, and containing some 84 practice problems covering arithmetic, geometry, and primitive algebra – came from the so-called Second Intermediate Period of Egypt. 

His name was Ahmes, and he almost certainly wasn’t actually a mathematician. The papyrus, according to his own introduction to the work, “was copied in the year 33, in the fourth month of the inundation season, under the majesty of the king of Upper and Lower Egypt, ‘A-user-Re’, endowed with life, in likeness to writings of old made in the time of the king of Upper and Lower Egypt, Ne-ma’et-Re” – in regular numbers, that translates to having been written in around 1650 BCE and copied from work dating roughly two centuries earlier than that.

Other than that, though, we know virtually nothing about Ahmes – a pretty much random scribe who probably never knew he’d end up such a seminal figure in the history of math.

In the beginning

We’ve gone back more than 5,000 years at this point – past the point where we can even put names to figures, even – and it’s tempting to think we must have found the first mathematician by now. 

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Honestly, though, we’re nowhere near. For that, we have to go back not a few thousand years, but tens of thousands – all the way back to the stone age.

“It is taking an unnecessarily restrictive view of the history of mathematics to confine [the] study to written evidence,” writes mathematician, and specialist in the history of math, George Gheverghese Joseph in his 2010 book The Crest of the Peacock: Non-European Roots of Mathematics

“Mathematics initially arose from a need to count and record numbers,” he explains. “If we define mathematics as any activity that arises out of, or directly generates, concepts relating to numbers or spatial configurations together with some form of logic, we can then legitimately include […] protomathematics, which existed when no written records were available.”

The first mathematician, by this metric, wasn’t some Roman or Greek writing down abstract theorems, and it wasn’t a Babylonian recording the stars. It wasn’t even Ahmes, or the students dutifully working through the problems he had set. It was whoever created the Ishango bone.

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It’s a small thing, only about 10 centimeters (3.9 inches) in length, and at first glance, you might not suspect it has anything to do with math at all. The key is in the notches that have been scraped into its sides: four groups in this row; four in that; eight in another; all in different amounts and with varying spacing between them.

The Ishango Bone on display at the Royal Belgian Institute of Natural Sciences
The Ishango Bone on display at the Royal Belgian Institute of Natural Sciences.
Joeykentin, CC BY-SA 4.0, via Wikimedia Commons


It sounds haphazard, but it’s not. “Certain underlying numerical patterns may be observed within each of the rows,” Joseph points out. “The markings on rows (a) and (b) each add up to 60 […] Row (b) contains the prime numbers between 10 and 20. Row (a) is quite consistent with a numeration system based on 10, since the notches are grouped as 20 + 1, 201, 10+ 1, and 10- 1. Finally, row (c), where subgroups (5, 5, 10), (8, 4), and (6, 3) are clearly demarcated, has been interpreted as showing some appreciation of the concept of duplication or multiplying by 2.”

Exactly why the Ishango bone was created is a mystery – some believe it was used for mathematical games; others that it functioned as a calendar for religious or meteorological purposes. There’s even speculation that the Ishango people eventually bequeathed their number system to the Egyptians – making the bone not just evidence of some ancient calculator, but the closest thing the math world has to a Last Universal Common Ancestor. 

With an age of between 20,000 and 25,000 years, it’s true that other potentially mathematical artifacts have been found that predate it – the Lebombo bone, for example, beats it by 20,000 years or so, and might be the earliest known period tracker. But for now, it’s the Ishango bone that takes the crown as the oldest confirmed mathematical object in existence – and its creator, whoever they were, is undoubtedly the world’s first known mathematician.


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