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The Crusaders per se did not take any mathematical achievements back to Europe from the Arabs. Europeans in general would receive numerous advancements in mathematics from Islamic Civilization primarily through the translators in Toledo, Spain after 1038. Most of the advancements in mathematics were not made by Arabs but by Persians who wrote in Arabic such as Omar Khayyam, al-Khwarezmi, al-Beiruni, at-Tusi, etc. These individuals wrote on numerous subjects such as algebra, trigonometry, geomtric proofs, and basic physics. Arguably the most prolific Arab contributor to math was Thabit ibn Qurra who expanded on al-Khwarezmi's discussions of algebra and who invented the physics discipline of statics.

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Q: What specifically have the crusaders taken from Arabs in the field of Mathematics for their benefit along the time line?
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