Reviewer Contents

• The pythagorean theorem ax2 + bx2 = cx2 was first discovered in Greek Mathematics by Pythagoras.
• In 16th century, the cubic formula ax3+bx2+cx+d=0 was developed.
• Sexagesimal system was originated with the Sumerian then passed down by Babylonians - is also known as 60 base, which could be counted physically using the twelve knuckles on one hand and the five fingers on the other hand
• The Gupta numerals became popular when the Gupta dynasty ruled over the Magadha state in Northeastern India from the early 4th century to the late 6th century. Subsequently, they changed and turned into a new version called the Nagari numerals in the 7th century but still continuously evolving until the 11th century.
• The name Nagari suggests the writing of the gods and was considered as the most beautiful among other variations developed. As depicted in the figure 4, zero is already included. Mayans and Americans already had a symbol of zero and it was believed that it was adopted by the Arabs. They later on spread this from different parts of the world such as Devangari, West Arab Gobar, and Spain.
• The Greeks extended their numeric system using the first ten letters of the alphabet,with each subsequent letter representing increments of 10. Beyond 100, each subsequent letter denoted multiples of 100. This method proved more efficient for writing numbers. To represent larger values, lines were drawn over or under the letters. However, these systems were impractical for complex calculations, unlike the more advanced Indian number system, developed around 600 AD, which forms the basis of the modern system we use today.
• Today, Greek numbers or letters are primarily employed to symbolize unknowns in algebra.
• Hieratic numerals allowed numbers to be written in a far more compact form yet using the system required many more symbols to be memorised. There were separate symbols for 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 20, 30, 40, 50, 60, 70, 80, 90,100, 200, 300, 400, 500, 600, 700,800, 900,1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000
• Belgian geologist Jean de Heinzelin de Braucourt focused most of his research efforts in Africa. He was employed by the universities in Brussels and Ghent. After discovering the Ishango Bone in 1950, he became well-known throughout the world.

  
• Archimedes - known as the Father of Mathematics.

  
• Rene Descartes was a French physicist, mathematician, and philosophers regarded as the founder of modern philosophy.

  
• Rene Descartes was born to a political father and had an interest in science, philosophy, and mathematics while in school. After Graduating from law school, Rene spent the most of his time traveling across Europe,studying the greats' scientific, philosophical, and mathematical writings.
• Rene Descartes also communicated with some of the best minds of his day and continued to broaden his knowledge base. In the realm of mathematics, he is most known for developing analytic geometry, which demonstrated that algebra and geometry may be studied concurrently.
• Blaise Pascal was a French mathematician and physicist who laid the foundation for the modern theory of probabilities.

  
• A multi-faceted personality, Blaise Pascal was also a Christian philosopher, inventor, and writer. Born as the son of a talented mathematician, he received his primary education from his father, who through his unorthodox curriculum, wanted to ensure that his bright young son grew up in an intellectually stimulating environment. The boy started displaying signs of brilliance at an early age and was regarded as a child prodigy.
• Blaise Pascal was just 16 when he wrote a significant treatise on the subject of projective geometry and started working on other serious mathematical concepts as well.
• Pierre de Fermat was a 17th-century French mathematician, made fundamental contributions to the creation of infinitesimal calculus. He conducted groundbreaking research into number theory and uncovered various new patterns in numbers that had confused mathematicians for ages.

  
• Born into an affluent family of high social standing, Pierre de Fermat chose to pursue a legal career, as was required of young men of his social standing at the time, despite his strong interest in mathematics. However, the young man's decision to pursue a career in a subject unrelated to mathematics did not prevent him from becoming an amateur mathematician.
• Sir Isaac Newton was a brilliant and accomplished physicist, mathematician,astronomer, and alchemist, is often regarded as the greatest and most influential scientist of all time.

  
• One of the most importantcontributors to the 17th century Scientific Revolution,' Isaac Newton developed the principles of modern physics, which he laid out in his book, 'Philosophiae, Naturalis, Principia Mathematica. Popularly known as Principia,' the book highlighted the concepts of universal gravitation and laws of motion, which remained at the forefront of scientific theories for centuries
• Gottfried Wilhelm Leibniz was a distinguished German polymath, philosopher, metaphysicist, historian, lawyer, and political counselor. Born in the same era as Isaac Newton, he was accused of plagiarizing Newton's work during his lifetime, but researchers have recognized that he created differential and integral calculus independently of Newton since 1900.

  
• Today, Gottfried Wilhelm Leibniz has a significant place in the history of mathematics, having invented Leibniz's notation, the Law of Continuity, and the Transcendental Law of Homogeneity. Furthermore, his work on the binary system is the foundation of contemporary computers.
• The Riemann Integral was developed by a mathematician named Bernhard Riemann. He was a German mathematician born on September 17, 1826, in Breselenz, Kingdom of Hanover (now in Germany).

  
• Bernhard Riemann made significant contributions to various areas of mathematics,including analysis, differential geometry, number theory, and mathematical physics. Riemann studied at the University of Göttingen under mathematicians such as Carl Friedrich Gauss and Johann Dirichlet
• The Poincare conjecture asserts that the same is true for 3-dimensional spaces. Originally conjectured by Jules Henri Poincaré in 1904.

  
• Jules Henri Poincare, 1854-1912, was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed during his lifetime.