Today, mention of the word Islam can, to some, conjure up images of terrorists flying planes full of people into buildings, all in the name, they say, of God.

In an equally sad vein, the word Baghdad brings to mind Saddam Hussein. Both images are as unrepresentative as they are understandable, a sad reflection on the ease with which a handful of fanatics can hijack not just a plane but an entire cultural heritage and its associated religion.

For those of us in mathematics, the sadness is even greater. For the culture that these fanatics claim to represent when they set about trying to destroy the modern world of science and technology was, in fact, the cradle in which that tradition was nurtured.

For all present-day mathematicians and scientists are children of Islam. Following the advent of Islam in the seventh century, Islamic forces attacked and conquered all of North Africa, most of the Middle East, and even parts of Western Europe.

The capital of this empire, Baghdad, was established on the Tigris River. Its location made it a natural crossroads, the place where East and West could meet. Baghdad quickly became a major cultural centre. With the emergence of a new dynasty, the Abbasids, in the 8th century, the Islamic Empire started to settle down politically, and conditions emerged in which mathematics and science could be pursued.

Early in the 9th century, the Abbasid caliphs adopted a deliberate approach to the cultural and intellectual growth of the empire. They established the House of Wisdom, an academy of science, and gathered manuscripts in Greek and Sanskrit, and scholars who could understand them.

Important Greek and Indian mathematical books were translated and studied, leading to a new era of scientific creativity that was to last until the 14th century. One of the first Greek texts translated was Euclid's classic geometry text Elements.

This had a huge impact; Arabic mathematicians then adopted a very Greek approach, formulating theorems precisely and proving them formally in Euclid's style. Like Greek mathematics, which was defined more by the common language in which it was written and carried out than the nationality of the practitioners, Arabic mathematics was determined largely by the common use of Arabic by scholars of many nationalities, spread throughout the Islamic Empire.

One of the earliest and most distinguished of the Arabic mathematicians was the 9th century scholar Abu Ja'far Mohammed ibn Musa Al-Khwarizmi, an astronomer to the caliph at Baghdad. His full name can be translated as "Father of Ja'far, Mohammed, son of Moses, native of the town of Al-Khwarizmi".

Al-Khwarizmi wrote several enormously influential books. One, in particular, describes how to write numbers and compute with them using the place-value decimal system we use today, which had been developed in India some time before 600 AD.

This book would, when translated into Latin 300 years later, prove a major source for Europeans who wanted to learn the new system. Today, we know it as the Hindu-Arabic system. It is taught to schoolchildren worldwide.

Many translations of the book began with the phrase " dixit Algorismi " ("so says Al-Khwarizmi"), a practice that led to the adoption in medieval times of the term "algorism" to refer to the process of computing with the Hindu-Arabic numerals.

"Algorithm" is an obvious derivation. Another of Al- Khwarizmi's manuscripts was called Kitab al jabr w'al-muqabala , which translates roughly as "restoration and compensation".

The book is essentially an algebra text. It opens with a discussion of quadratic equations, then goes on to some practical geometry, followed by simple linear equations, and ends with a long section on how to apply mathematics to solve inheritance problems. The Englishman Robert of Chester translated the algebra book from Arabic into Latin in 1145. Such was the influence of this work that the Arabic phrase al jabr in the book's title gave rise to our modern word "algebra". After Al-Khwarizmi, algebra became an important part of Arabic mathematics.

Arabic mathematicians learned to manipulate polynomials, to solve certain algebraic equations and more. For modern readers, used to thinking of algebra as the manipulation of symbols, it is important to realise that the Arabic mathematicians did not use symbols. Everything was done in words. It was largely through translations of the Arabic texts into Latin that western Europe, freshly emerged from the Dark Ages, kick-started its mathematics in the 10th and subsequent centuries, paving the way for the scientific revolution in the 17th century and thence to the scientific and technological world we now take for granted.

Without the dedication of the Islamic scholars of the 9th to the 14th century, it is not clear that Western Europe would have become the world leader in science and technology. And it is also unlikely that the United States would have inherited that leadership role.

I suspect that Osama bin Laden, as an educated man from a wealthy family, is fully aware of the crucial role played by Islam in the development of the West's scientific tradition. I doubt the same is true for his supporters in the streets of Iraq and Pakistan.

Ignorance, we used to say, is bliss. Maybe that was once the case, although I doubt it. The clear message of September 11 and the events that have unfolded since then, is that ignorance is dangerous, leaving gullible individuals open to manipulation by evil men. It is also deeply sad, particularly for mathematicians and scientists.