The Roman Number system:
The Roman system which uses six symbols to represent a base 10 numeric system (repeats every 10 digits) I,V,X,L,C, and M which referred to the numbers 1,5,10,50,100,and 1000 respectively, and the placement of the symbols determined their value. If a symbol with a smaller value came before a larger, it was subtracted from the larger; if it came after it was added, so IV meant 4 while VI meant 6.
However, these numbers quickly become cumbersome and are difficult to add: to add the numbers IVXLCMM and CMLXXXII, for example, one would first cancel out any numbers that are subtracted, then grouping like letters, then simplify from the highest to the lowest. Finally after a few minutes of effort it should end up with MMCMXXVI. Obviously, this is hard to do and takes a lot of time to add simple numbers (1944 and 982) and this process becomes even more complex when multiplying.
The second problem with Roman Numerals is that there are no fractions or decimals. Fractions cannot be easily written out as 1/4 instead they would have to be written out in words. These factors combine and create bulky and inefficient system that actually hampered the spread and development of mathematical concepts such as pi.
The Hindu/Indian Number System:In contrast the Hindu system, which was developed from around 2BC to 5AD in India, had three important innovations that would make it extremely useful. The first is that there was a 0. While this concept is not unique in the world, it did make it possible to do many new things. The second is the placement system: unlike the Roman system where numbers are not grouped, the Hindu system introduced the idea of columns and place values. Thus, by combining the 0 with the concept of base 10, we see the creation of a system where each column is 10 to a power (the 1’s column is 10^0, 10’s column is 10^1, 100’s column is 10^2 etc). To see the importance of this one can imagine a tower of champagne glasses, when the top is filed it over flows and fills the four below it, which in turn fill the 16 below them. Similarly when one column has a value of more than 9 the extra spills over into the next column making simple vertical addition possible. The third innovation that made the Hindu system unique is the decimal place. Unlike the roman system where you would have IV and twenty-two out of twenty-five the Hindu system allows a person to write 4.88. This idea is fundamental for calculating precise numbers, and the creation of many mathematical constants like pi could only be done with a decimal place.
Before the Western society was introduced to the “Arabic” — technically, the number system originated in India — numeral system,
Even though the mathematical benefits of the Hindu system are obvious, it did not just spread across the world immediately. The numbers were first introduced in the 7th century AD, but it wasn’t until the 12th century AD that the entire system spread to Western Civilization.
The first wave was the numbers themselves which allowed people to write much more succinctly and easily. The Hindu’s had several different number systems over the period where the number system was developed, but the one we are most familiar with, and was absorbed by the Arabs, is the Nagari number system which is very similar to ours. In the system however there are a few modifications from its original form over the years; for example, originally the 1 resembled a 9, the number 4 was represented by an 8, a 5 was represented by a 4, the 6, 7 and 8 were quite unlike any of our current numbers, and the 9 was backwards. The numbers first spread to the Arabs around the 7th century — the earliest and most complete records come from the writings of a man named al-Biruni from the 11th century.
However, the mathematical concepts didn’t follow until the 12th century. A 9th century Arab named “Al-Khwarizmi” is credited with introducing the concepts of the mathematical possibilities of the numbers through his treatise which was translated into Latin in the early 12th century. After this the numbers quickly spread throughout Europe and the rest is history
Information about Great Indian Mathematicians:
Aryabhatt (First) (490 AD)
He was a resident of Patna in India. He has described, in a very crisp and concise manner, the important fundamental principles of Mathematics only in 332 Shlokas. His book is titled Aryabhattiya. In the first two sections of Aryabhattiya, Mathematics is described. In the last two sections of Aryabhattiya, Jyotish (Astrology) is described. In the first section of the book, he has described the method of denoting big decimal numbers by the alphabets.
In the second section of the book Aryabhattiya we find difficult questions from topics such as Numerical Mathematics, Geometrical Mathematics, Trignometry and Beezganit (Algebra). He also worked on indeterminate equations of Beezganit (Later in West it was called Algebra). He was the first to use Vyutkram Zia (Which was later known as Versesine in the West) in Trignometry. He calculated the value of pi correct upto four decimal places.
He was first to find that the sun is stationary and the earth revolves around it. 1100 years later, this fact was accepted by Coppernix of West in 16th century. Galileo was hanged for accepting this.
Bhaskar (First) (600 AD)
He did matchless work on Indeterminate equations. He expanded the work of Aryabhatt in his books titled Mahabhaskariya, Aryabhattiya Bhashya and Laghu Bhaskariya .
Brahmgupt (628 AD)His famous work is his book titled Brahm-sfut. This book has 25 chapters. In two chapters of the book, he has elaborately described the mathematical principles and methods. He threw light on around 20 processes and behavior of Mathematics. He described the rules of the solving equations of Beezganit (Algebra). He also told the solution of indeterminate equations with two exponent. Later Ailer in 1764 AD and Langrez in 1768 described the same.
Brahmgupt told the method of calculating the volume of Prism and Cone. He also described how to sum a GP Series. He was the first to tell that when we divide any positive or negative number by zero it becomes infinite.
Mahaveeracharya (850 AD)
He wrote the book titled "Ganit Saar Sangraha". This book is on Numerical Mathematics. He has described the currently used method of calculating Least Common Multiple (LCM) of given numbers. The same method was used in Europe later in 1500 AD. He derived formulae to calculate the area of ellipse and quadrilateral inside a circle.
Shridharacharya (850 AD)
He wrote books titled "Nav Shatika", "Tri Shatika", "Pati Ganit". These books are on Numerical Mathematics. His books on Beez Ganit (Algebra) are lost now, but his method of solving quadratic equations is still used. This is method is also called "Shridharacharya Niyam". The great thing is that currently we use the same formula as told by him. His book titled "Pati Ganit" has been translated into Arabic by the name "Hisabul Tarapt".
Aryabhatta Second (950 AD)He wrote a book titled Maha Siddhanta. This book discusses Numerical Mathematics (Ank Ganit) and Algebra. It describes the method of solving algebraic indeterminate equations of first order. He was the first to calculate the surface area of a sphere. He used the value of pi as 22/7.
Shripati Mishra (1039 AD)
He wrote the books titled Siddhanta Shekhar and Ganit Tilak. He worked mainly on permutations and combinations. Only first section of his book Ganit Tilak is available.
Nemichandra Siddhanta Chakravati (1100 AD)
His famous book is titled Gome-mat Saar. It has two sections. The first section is Karma Kaand and the second section is titled Jeev Kaand. He worked on Set Theory. He described universal sets, all types of mapping, Well Ordering Theorems et-cetera.One to One Mapping was used by Gailileo and George Kanter(1845-1918) after many centuries.
Bhaskaracharya Second (1114 AD)He has written excellent books namely Siddhanta Shiromani,Leelavati Beezganitam,Gola Addhaya,Griha Ganitam and Karan Kautoohal. He gave final touch to Numerical Mathematics, Beez Ganit (Algebra), and Trikonmiti (Trignometry).
The concepts which were in the form of formulae in "Vedah" has also described 20 methods and 8 behaviors of Brahamgupt.
Great Hankal has praised a lot Bhaskaracharya's Chakrawaat Method of solving indeterminate equations of Beezganit (Algebra). This Bhaskaracharya's Chakrawaat Method was used by Ferment in 1667 to solve indeterminate equations.
In his book Siddhanta Shiromani, he has described in length the concepts of Trignometry. He has described Sine, Cosine, Versesine,... Infinitesimal Calculus and Integration. He wrote that earth has gravitational force.
Narayan Pundit (1356 AD)
He wrote the book titled Ganit Kaumidi. This book deals with Permutations and Combinations, Partition of Numbers, Magic Squares.
Neel Kanta (1587 AD)He wrote the book titled Tagikani Kanti. This book deals with Zeotish Ganit(Astrological Mathematics).
Kamalakar (1608 AD)He wrote a book titled Siddhanta Tatwa Viveka.
Samraat Jagannath (1731 AD)He wrote two books titled Samraat Siddhanta and Rekha Ganit (Line Mathematics)
Apart from the above-mentioned mathematicians we have a few more worth mentioning mathematicians. From Kerla we have
Madhav (1350-1410 AD). He wrote books on Geometrical Mathematics, Numerical Mathematics and Trignometry.
Sudhakar Dwivedi (1831 AD)
He wrote books titled Deergha Vritta Lakshan(which means characteristics of ellipse), Goleeya Rekha Ganit(which means sphere line mathematics),Samikaran Meemansa(which means analysis of equations) and Chalan Kalan.
Ramanujam (1889 AD)
Ramanujam is a modern mathematics scholar. He followed the vedic style of writing mathematical concepts in terms of formulae and then proving it. His intellectuality is proved by the fact it took all mettle of current mathematicians to prove a few out of his total 50 theorems.
Swami Bharti Krishnateerthaji Maharaj (1884-1960 AD)
He wrote the book titled Vedic Ganit.
