We're looking at the dawn of modern mathematics. Focus on connections between the 17th century and Indian mathematics when discussing the 17th century. Modern mathematics is modeled on Greek mathematics, with its axiomatic approach, and we often tend to overlook the contributions of other cultures.

Why is the seventeenth century so important in the history of mathematics? Discuss some of the major events that occurred. Now connect this to the fllowing related material. Discuss the major contributions and people from the time period.

Here is the related material :

  

The Hindu time period, which is generally considered to span from the five centuries 500-1000, was a time of great mathematical innovation in India. During this period, Indian mathematicians made significant contributions to fields such as algebra, geometry, and trigonometry, which have had a lasting impact on modern mathematics. One of the most significant contributions of the Hindu mathematicians was the development of the decimal system, which is the basis of modern mathematics. The decimal system, which uses the digits 0-9 to represent numbers, allowed for much more efficient calculations than earlier systems, which were based on Roman numerals or other systems.Aryabhata (6^th century AD), Brahmagupta and both Bhaskara's dedicated a portion of their works to explaining the decimal system and giving rules for computation (Berlinghoff & Gouvea).In addition, the Hindu mathematicians developed the concept of zero as a number, which was a revolutionary idea that allowed for the creation of the place value system. Mahavira recorded that adding zero to a number produces zero and subtracting it resulted in the same number and a few centuries later, Bhaskara II said that a number divided by zero is an infinite amount. A key to opening the door to mathematics was the Indians' understanding of 0 as a number.

Another important contribution of the Hindu mathematicians was the development of algebra. Indian mathematicians developed methods for solving quadratic equations and other higher-order equations, and they also developed a system for solving systems of linear equations. These methods were later transmitted to Europe, where they had a significant impact on the development of modern algebra. The Hindu mathematicians also made important contributions to geometry and trigonometry. They developed methods for measuring angles and distances, and they also discovered the properties of various geometric shapes, such as the circle and the ellipse. In addition, they developed trigonometric functions, which are used to calculate angles and distances in many branches of science and engineering.

Religious thought at this time had a significant impact, and Hindu mathematicians were motivated by astronomical issues to study a variety of mathematical issues. These mathematicians created a variety of subjects, such as arithmetic, algebra, trigonometry, and astronomy. They were also the first to understand and use negative values. Aryabhata, Varahamihira, Brahmagupta, and Mahaviracarya (Mahavira the Learned), were the most notable mathematicians throughout this time period, along with the Bakhshali Manuscript. There is also the Brahmasidhanta, is 21-chapter astronomical work written at age 30 by Brahmagupta, who flourished in the seventh century, and it contains to special chapters, the Ganitadhaya and the Kutakhadyaka.

The Panca Siddhantika, written by Varahamihira in the fifth century AD, is his best-known work. This work exhibits an advanced level of mathematical astronomy and contains the calculation required to determine the location of a planet. In addition, Varahamihira educated his people about the sphericity of the planet and urged them to respect the Greeks' contributions. Alberuni has translated two of his works into Arabic (c. 1000).

In the seventh century, Brahmagupta was a well-known mathematician who lived and worked at Ujjain or Ujjayini, the important astronomical center of Hindu knowledge.The first Indian author to use algebra to astronomy to any significant amount was Brahmagupta, who was also concerned in the solution of indeterminate equations. The total of an arithmetic progression was another thing he was able to calculate, and he also discovered procedures for calculating square and cube roots.

Written by Mahaviracarya (Mahavira the Learned) wasthe Ganita-Sara-Sangraha, a work that begins with Oriental treatises with a salutation of a religious nature (Dover Publications Inc.). His book has nine chapters and covers subjects including addition, subtraction, multiplication, division, and square roots to name a few. Only Mahaviracarya, a Hindu scholar of the native school, attempted to handle the ellipse seriously, albeit his work was wrong.

Another significant work in mathematics from this era is the Bakhshali Manuscript, which includes both arithmetic and algebraic content. The Hindu arithmetic and astronomy were written on by Isaac ben Salom. Nonetheless, modern mathematics has benefited greatly from the mathematical ideas that were created throughout the Hindu era. Two of the most significant contributions made by Hindu mathematicians are the decimal system and the acceptance of negative integers. Moreover, many of the contemporary mathematical ideas still in use today have their roots in the algebraic and trigonometrical work they did. Modern mathematics has benefited from their contributions to combinatorics, equations in many variables, and approximation computing.

To conclude, the Hindu era (500-1000 AD) was a crucial moment in the evolution of mathematics since it saw the introduction of a number of mathematical notions that continue to influence contemporary mathematics today. These mathematicians created a variety of subjects, such as arithmetic, algebra, trigonometry, and astronomy. They were also the first to understand and use negative values. Hindu mathematicians produced several major contributions to mathematics, two of which are the decimal system and the acceptance of negative numbers. Their work in algebra and trigonometry established the groundwork for many of the contemporary mathematical ideas that are still in use today. The Sanskrit poetry in which the Hindu mathematicians penned their works enabled them to explain mathematical ideas in a variety of ways, which was essential to their success. Also, I found it interesting that via Baghdad and the Arabic mathematical heritage, many of the findings from India found their way to the West.

  

References

Berlinghoff, W. P., & Gouvea Fernando Q. (2021). Math through the ages: A gentle history for teachers and others. MAA Press.

Dover Publications Inc. (1950, November 30). History of mathematics vol I : Eugene Smith david. : Free download, Borrow, and streaming. Internet Archive. Retrieved March 7, 2023, from https://archive.org/details/historyofmathema033304mbp/page/42/mode/2up?view=theater