Bertrand Russell defined mathematics as “ not just an inflexible application of rubrics to pointless symbols but something much more creative and an art in itself (“Famous Mathematicians,” 2012, para 1).” He compared it to painting and how as painters make patterns with careful strokes of their brushes, mathematics can be described as a significant study of patterns as well. Like Bertrand, Blaise Pascal, Jakob Bernoulli, C.R Rao and Leonhard Euler felt passionate about mathematics and made great contributions to the mathematical world, particularly in the fields of probability and statistics.

Probability

“Probability had its origin in the study of gambling and insurance in the 17th century, and it is now an indispensable tool of both social and natural sciences”( Probability and statistics, examples and facts, n.d). Simply put it is the extent or likelihood of an occurrence. Most are familiar with the marbles in a bag example. There is a set number of marbles in a bag, there are four different colors, what is the probability of grabbing a yellow marble. This is probability. Two mathematicians that helped shape probability into what we know and use today are Blaise Pascal and Jakob Bernoulli.

Pascal was born June of 1623 in Clermont-Ferrand France. His mother died when he was just three years of age and his father, a presiding judge, was also a mathematician and devoted his time to teaching his children. He was the only formal educator of Pascal due to Pascal’s poor health that he suffered from most of his life. At sixteen he went on to create and write on Pascal’s Theorem and Pascal’s Line (three intersections on opposite sides of a single line, inscribed in a circle and in a hexagon). Pascal is best known for his work the Pascal Triangle. He used the triangle to later help solve problems in probability theory. At age twenty-four, Blaise Pascal could no longer tolerate food and gained nutrients only in liquid form drop by drop. His family moved often because of financial and political reasons. Much of Pascals early work was in natural and applied sciences. He has a physical law named after him as well as the international unit for pressure. He went on through life believing it was better to bet than not to. While living in Paris Pascal wrote Essai pour les coniques and in 1645 he developed a prototype of a calculating machine and began experiments with mercury barometers. After working and experimenting with mercury barometers Pascal went on to publish Expériences nouvelles touchant la vide in 1647. In 1654 Pascal was in correspondence with Pierre Fermat about calculating probabilities associated with gambling. He proposed to solve problems in terms of quantity. He summarized his finding in a book called Traité du triangle arithmétique, which was published after his death. In 1665 Pascal worked on the arithmetic triangle and showed how to calculate numbers of combinations and how to solve basic gambling problems. Unfortunately, Pascals contribution to probability theory wasn’t recognized until the eighteen century when it was used by another mathematician. His probability theory took place in 1654 and was designed to solve a gambling problem related to expected outcomes. He wanted to figure out the best time to bet on a dice game, and how to fairly divide the stakes if the game was stopped midway through.

Jakob Bernoulli was born January of 1655. He is known for introducing the first principals of calculus of variation and the Bernoulli numbers concept. Along with his brother, he was one of the pioneers of Leibnizian form of the calculus. He formulated and proved the weak law of large numbers (also known as Bernoulli’s theorem), the foundation of modern probability and statistics. He is of Swiss descent whose family were drug merchants. Originally, Bernoulli was interested in studying theology, but he soon became interested in mathematics. In 1690 and 1691 Bernoulli studied catenary, “the curve formed by a chain suspended between two extremities” (‘Jakob bernoulli,’ n.d). He then became the first to use the term integral when analyzing a curve of decent. In 1695 he used calculus to aid in the design of bridges. After he died, many of his theories were published in “The Art of Conjecturing.” The publication included his theory of permutations and combinations (‘Jakob bernoulli,’ n.d.), Bernoulli numbers, his treatment of mathematical and moral predictability and the Bernoulli Law of Large Numbers (‘Jakob bernoulli,’ n.d.).

Statistics

“Statistics, is the science of collecting, analyzing, presenting, and interpreting data” (statistics, n.d.) Statistics has been around since the beginning of civilization. Early empires often collated samples of the population or recorded trade in various commodities. The Roman Empire was among the first to extensively gather data to identify the size of the empire’s population, geographical area and wealth. The earliest writing on statistics was found in a 9th-century Arabic book called Manuscript on Deciphering Cryptographic Messages, written byAl-Kindi and the original scope of statistics may have been to use data for governance, it was extended to many other fields of a scientific or commercial nature during the 19th century. Two mathematicians that helped shape statistics into what we know and use today are C.R Rao and Leonhard Euler.

C.R.( short for Calyampudi Radhakrishna) Rao was born September of 1920 in Karnataka. Early on, Rao showed interest in mathematics. In 1940 he earned his master’s in mathematics and decided to pursue a research career. He later became a technical apprentice where he taught and researched at the same time. He established the Theory of Estimation not long after. C. R. Rao organized research and training programs for students in India, resulting in the country having one of the best statistical systems. He founded the Indian Econometric Society, which has been promoting quantitative studies and the Indian Society for Medical Statistics. He’s held multiple international positions and promoted applications such as supervising doctoral research of 50 students. Rao is the author of 14 books and over 300 research papers in high impact journals. After retiring he worked for 25 years as a university professor. First, he worked at the University of Pittsburgh, then at the Pennsylvania State University as a Professor of Statistics. He retired from teaching at the age of 80 but works currently as the Director of the Center for Multivariate Analysis at Pennsylvania State University and the founder of the C. R. Rao Advanced Institute of Mathematics, Statistics and Computer Science . On June 29th 2011, the at the time, 91 year old was awarded the Guy Medal in Gold of the Royal Statistical Society for his fundamental contributions in “statistical theory and methodology, including unbiased estimation, variance reduction by sufficiency, efficiency of estimation, information geometry, as well as the application of matrix theory in linear statistical inference’ (About C.R Rao, by Marianna Bolla,).

Leonhard Euler was born April 1707 in Basel Switzerland. He was one of the founders of pure mathematics making contributions to the subjects: geometry, calculus, and number theory, among many others. He developed methods for problem solving in astronomy and would demonstrate various mathematic applications in public affairs and technology. In 1727 he became an associate of the Saint Petersburg Academy of Science and developed the theory of trigonometric and logarithmic functions. Euler lost sight in one eye in 1735 and in 1748 developed the concept of function in mathematical analysis. Today he is known in elementary geometry for the Euler line through orthocenter, the circumcenter, and the barycenter of a triangle. He also discovered imaginary logarithms of negative numbers and found that complex numbers had an infinite number of logarithms. He is responsible for introducing may current notations that we use today. For example: e for the base of natural logarithms, a,b,c, for the sides of a triangle along with A, B, C for opposing angles, and (f) to stand for function. Years later he lost sight in his good eye and spent his remaining years of life in total blindness. Yet, one of his greatest discoveries occurred in 1783 with his discovery of the law of quadratic reciprocity. Euler made many contributions to many areas of mathematics, including a few that specifically relate to statistics. Much of his work laid the foundation for probability and statistic. An example would be his work on Graeco- Latin square which are sometimes known as Euler squares. Euler squares are created when two squares are overlaid to include two attributes in each cell of the array. The squares ensure that each and every possible pairing of the two attributes appears exactly once in the array. Towards the eighteen century he contributed to the concept of maximum likelihood.

All four of these individuals played monumental roles in the way we use and are taught mathematics today.

References

About C. R. Rao, by Marianna Bolla. (n.d.). Retrieved from https://mathematics.ceu.edu/rao

Blaise Pascal (Stanford encyclopedia of philosophy). (n.d.). Retrieved from https://plato.stanford.edu/entries/pascal/#FreWil

Famous mathematicians and statisticians. (2015, August 24). Retrieved from https://www.statisticshowto.com/probability-and-statistics/famous-mathematicians-and-statisticians/

Famous mathematicians. (2012, January 20). Retrieved from https://famous-mathematicians.com/

Jakob bernoulli. (n.d.). Retrieved from https://www.britannica.com/biography/Jakob-Bernoulli

Leonhard Euler. (n.d.). Retrieved from https://www.britannica.com/biography/Leonhard-Euler

Probability and statistics | History, examples, & facts. (n.d.). Retrieved from https://www.britannica.com/science/probability

Statistics. (n.d.). Retrieved from https://www.britannica.com/science/statistics