This is about Muslims, more generally rather than Arabs particularly. They were the people who preserved the ancient Greek knowledge when in the West we were scraping their parchments and using them to write Christian religious texts. They were a scientific light in the world during the dark ages - like China. That was our dark age but the Islamic golden age, from the eighth century onwards. They introduced Arabic notation (the notation we all still use for numbers) and algebra to mathematics. They developed the astrolabe and other navigational aids. Made maps. Were amongst the oldest surviving universities in the world. Probably our industrial revolution would never have happened if it wasn't for Muslims preserving the ancient Greek knowledge and then adding to it and improving it and passing it back to the West.

"Muslims have always been eager to seek knowledge, both religious and secular, and within a few years of Muhammad's mission, a great civilization sprang up and flourished. The outcome is shown in the spread of Islamic universities; Al-Zaytunah in Tunis, and Al-Azhar in Cairo go back more than 1,000 years and are the oldest existing universities in the world. Indeed, they were the models for the first European universities, such as Bologna, Heidelberg, and the Sorbonne. Even the familiar academic cap and gown originated at Al-Azhar University.

"Muslims made great advances in many different fields, such as geography, physics, chemistry, mathematics, medicine, pharmacology, architecture, linguistics and astronomy. Algebra and the Arabic numerals were introduced to the world by Muslim scholars. The astrolabe, the quadrant, and other navigational devices and maps were developed by Muslim scholars and played an important role in world progress, most notably in Europe's age of exploration.

"Muslim scholars studied the ancient civilizations from Greece and Rome to China and India. The works of Aristotle, Ptolemy, Euclid and others were translated into Arabic. Muslim scholars and scientists then added their own creative ideas, discoveries and inventions, and finally transmitted this new knowledge to Europe, leading directly to the Renaissance. Many scientific and medical treatises, having been translated into Latin, were standard text and reference books as late as the 17th and 18th centuries."

That's from Muslim Science. Which then goes on to look into achievements individually in various fields. It's not exaggerated. I'm especially interested in the history of mathematics myself, and for sure our modern maths would have developed much later if it wasn't for Islam. See also the Wikipedia article Science in the Islamic world

I can answer best on mathematics. From the preserved writings of the Persian Muhammad ibn Musa al-Khwarizmi, and other Islamic mathematicians of the ninth century onwards, they were expert mathematicians, especially in the field of algebra.

A page from Muhammad ibn Musa al-Khwarizmi's book on algebra

It's the maths that I know most about, being a mathematician myself with a long term interest in the history of maths. The Greeks did do a lot, the Chinese too, and many other cultures such as the Sumerians and the Egyptians all contributed to modern maths. But the Islamic contributions were huge also. Amongst their achievements:

• Development of modern ideas of algebra - bringing together lots of separate problems into a unified field
• Freed algebra from reliance on geometry, to a pure abstract discipline
• First to use the bar notation for fractions which we all use today
• Introduced place notation for decimals e.g. 0.5342 etc

This is from the MacTutor history of maths under Arabic mathematics : forgotten brilliance?

On algebra:

"Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.

"Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject."

They were also very important in the development of the astrolabe

"The astrolabe, whose mathematical theory is based on the stereographic projection of the sphere, was invented in late antiquity, but its extensive development in Islam made it the pocket watch of the medievals. In its original form, it required a different plate of horizon coordinates for each latitude, but in the 11th century the Spanish Muslim astronomer az-Zarqallu invented a single plate that worked for all latitudes. Slightly earlier, astronomers in the East had experimented with plane projections of the sphere, and al-Biruni invented such a projection that could be used to produce a map of a hemisphere. The culminating masterpiece was the astrolabe of the Syrian Ibn ash-Shatir (1305-75), a mathematical tool that could be used to solve all the standard problems of spherical astronomy in five different ways."

Two pages from a book on the astrolabe by Nasir al-Din al-Tusi

This is in the field of maths. As I said above there were many other fields they excelled in. And - their science and maths shone out as a bright light in the history of maths and science at this time more so because in the West then there were few who were interested at all and they even scrubbed the writing from ancient texts on maths and science to reuse them to make copies of the Christian sacred texts.

This is an example, the only remaining copy of a work by the famous Greek mathematician Archimedes, which was erased by Christian monks in the thirteenth century to write prayers on.

The Greek text is faint, running left to right and the writing by the medieval Christian monks runs top to bottom.

This shows how in the dark ages most Christians just weren't interested in science and maths while the Islamic scholars of course were. Many Christians of course did develop a keen interest in the subject later on. But without the Islamic scholars much of the Greek learning would have been lost and they also made substantial contributions themselves.