The development of the decimal system, particularly the numerical system with a base of ten, is a significant milestone in the history of mathematics. This system, which includes the concept of zero as a placeholder and as a number, was largely developed by Indian mathematicians and later transmitted to the Islamic world, where it was further refined and disseminated to Europe. 

Here are key points about its development and impact:

1. Origins in India:
   • The decimal system, also known as the Hindu-Arabic numeral system, originated in India between the 1st and 6th centuries CE. Indian mathematicians like Brahmagupta (c. 598–668 CE) played a critical role in developing this system, including the use of zero.
2. Concept of Zero:
   • The introduction of zero as both a placeholder and a concept representing “nothing” was revolutionary. It enabled the development of the positional number system, which simplifies arithmetic operations significantly.
3. Transmission to the Islamic World:
   • The numeral system was transmitted to the Islamic world through translations of Indian mathematical texts. The scholar Al-Khwarizmi (c. 780–850 CE) was particularly instrumental in this regard. He wrote the book “Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala” (The Compendious Book on Calculation by Completion and Balancing), which introduced the system and algebra (a term derived from al-jabr) to a broader audience.
4. Refinement and Adoption:
   • Islamic mathematicians, fascinated by its efficiency compared to the cumbersome Roman numeral system, adopted and refined the decimal system. They played a key role in introducing it to Europe through translations into Latin and by way of the Moorish presence in Spain.
5. Introduction to Europe:
   • The system reached Europe through translations of Arabic texts into Latin in the 10th to 12th centuries. Fibonacci (Leonardo of Pisa) was pivotal in popularizing it through his book “Liber Abaci” in 1202, which illustrated the superiority of the Hindu-Arabic numeral system for commercial arithmetic.
6. Impact on Mathematics and Science:
   • The decimal system revolutionized mathematics by simplifying calculations, thereby fostering advances in various fields of science, engineering, and commerce.
   • It laid the groundwork for the development of algebra, calculus, and modern numeracy.
7. Enduring Influence:
   • Today, the decimal system is the standard numeral system used globally. Its simplicity and efficiency make it foundational to modern mathematics and day-to-day calculations.

In summary, the development of the decimal system was a transformative event in the history of mathematics, rooted in Indian innovation and carried forth by Islamic scholars, which profoundly shaped the scientific and mathematical advancements that followed.

Written by AI. A more correct, God given, explanation can be found here.