The Story Of The Banned Numbers - A whiteboard graphics style image showing the number 16 written in pink inside a black box on the left. This box and number combination is copied and rotated 180 degrees on the right to represent 91.

The story of the banned numbers is a fascinating one about the evolution of numbers in field of applied mathematics. When you think about it, it does sound strange that someone would ban certain numbers. “Why would anyone do that?!” is the first question that pops to the mind.

Throughout history, there have been several well-known instances of nations, governments, and societies banning certain numbers for various reasons. In this essay, I will presenting one such story.

On the one hand, this story sheds some light on some of the challenges we, as human beings, faced with numbers in applied mathematics. On the other hand, it also gives us a glimpse into the history of mathematical developments that enabled us to enjoy the technologies we have today. Without any further ado, let us begin.

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Applied Mathematics in the Middle Ages

One of the biggest applications of mathematics for folks in the middle ages was in trade and commerce (some things never change). In Europe, specifically, people were using Roman numerals.

However, the Arabians were using a more nuanced system known as the Hindu-Arabic numeral system. The biggest advantage they had in comparison with their European counterparts was the number zero.

The Story Of The Banned Numbers — An image showing the European form of Arabian digits.
European form of Arabian digits — Image from WikiCC

You see, the Roman numeral system did not feature the concept of zero. With their nuanced system, the Arabian traders were simply more efficient with their trade and commerce calculations.

Arabian Traders Visit Europe

When the Arabian traders landed on the Italian coasts to trade, the local traders and finance establishments immediately understood the advantage of adopting/using the Hindu-Arabic numeral system.

However, legal and political authorities proceeded with caution. For starters, the Hindu-Arabic numerals offered more freedom in the calligraphy department. Because of this, traders could easily write one number and claim later that they had meant some other number.

For instance, a trader could first say that some item costs 16 currency units, and later claim that the bill actually reads 91 currency units instead. The Arabian traders could make out the subtle differences, but the locals were not so familiar with them.

The Story Of The Banned Numbers — A whiteboard graphics style image showing the number 16 written in pink inside a black box on the left. This box and number combination is copied and rotated 180 degrees on the right to represent 91.
16 transformed to 91 — Illustrative art created by the author

Besides this issue, there was a bigger conceptual issue with the number zero.

Why was Zero Frowned Upon?

Until this point, the European locals had no exposure to the concept of zero. Not only did the locals not easily grasp the concept of zero, but they also were not morally ready to accept its applications.

For instance, zero was instrumental in the notion of using negative numbers to denote debt in trade and commerce. Back at this time, debt was still considered morally questionable. Combined together, these two factors did not work well for the Hindu-Arabic numeral system, especially for the number zero.

The Story of the Banned Numbers — The Ban Hammer Strikes!

Eventually, in the 13th Century, the regulatory authorities of Florence, Italy, banned the usage of Hindu-Arabic numerals in their territory for recording trade and commerce transactions. This just marked the beginning of a bunch of controversies that lasted centuries.

The Story Of The Banned Numbers — An image showing Roman numerals on the stern of a ship (left) Vs. Bakhshali manuscript with detail of zero (right)
Roman numerals on the stern of a ship on the left (source WikiCC) Vs. Bakhshali manuscript with detail of zero on the right (source WikiCC)

One group of practitioners and mathematicians saw the value and benefit of using the Hindu-Arabic numerals, especially zero. Another group expressed strong resistance to these concepts.

As far as negative numbers are concerned, mathematicians engaged in debates over their validity well into the 19th century. We know, with the help of hindsight, how that story ends.

This is Not the First Time in History

Although we take the concepts of zero, negative numbers, and the Hindu-Arabic numerals for granted these days, this story shows how counter-intuitive they were to new users back in the day. Similarly, the evolution of mathematics has been riddled with controversies.

An engraving of Hippasus by Girolamo Olgiati — image from WikiCC

Hippasus of ancient Greece, for instance, discovered the notion of what we refer to today as irrational numbers. He could not find any number known at that time to represent the diagonal of a square with unit side length.

The people of the time were so opposed to this notion of “imperfection” that legend says that Hippasus was exiled for publishing his doubts and thoughts on this topic!

The Story of the Banned Numbers — Will History Repeat Itself?

Even though hindsight renders our ancestors’ behaviour as “silly” to us, we cannot deny the brutality of history. Human beings have always been (and will always) be afraid of and resistant to change (and consequently, evolution).

And Mathematics is very much a human venture. Therefore, we could expect there to be controversial takes on topics that are at the periphery of mathematical state-of-the-art. In a way, such controversies are essential for the evolution of mathematics.

As a corollary, if we are currently not experiencing controversies in the field of mathematics, then it means that the field might not be evolving as much or as quickly as it used to. My perception is that this is indeed the case.

While there are a numerous controversial takes as far as subjects like physics and biology are concerned, Mathematics seems to be a field that is slowly moving away from controversies. I question whether this is a good thing in the context of its historical evolution thus far.

“Will history repeat itself?” I don’t know. But I certainly hope so!

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Reference and credit: Alessandra King.

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