A Concise History of Mathematics; The Final Post!

Summary: This last section of my reading was extremely small (15 pages in total). Though, it was 15 pages, it had as much information as the other sections I've read in the past. This section of the book begins to talk about the first half of the twentieth century. In the 20th century mathematics was in flourished. The leading countries in their mathematical advancements at the time were France and Germany. The book also mentioned how mathematicians earned their income in educational institutions, especially those engaged in research to be found on university faculties.

Quotation: "...mathematics was in flourishing conditions, although creative mathematics was still in the main confined to one section of the world, was in most cases an academic profession, and was restricted with few exceptions, to white males of European stock" (Struik 204).

Reaction: As creative mathematics began to grow, more properties to math were found. As I mentioned already, France and Germany were the leading countries when this period of mathematics flourished. In addition, distinguished mathematical work also came out of Russia, Great Britain, Italy, Switzerland, Scandinavia, Belgium, and the Netherlands.

A Concise History of Mathematics; Pages 151-200

Summary: This section on the book is still on 19th century mathematics. It mentions a few great minds which contributed to the study of mathematics, such as: Riemann, Weirstrass, Cantor, Steiner, Cayley, Lobscevkii, Sylvester, and Hamilton. It was because of these men that democratic ideas invaded academic life. With it, criticism rose against antiquated forms of thinking. Then, schools and universities had to be reformed and rejuvenated.

Quotation: "The mathematicians of the nineteenth century were no longer at royal courts or in the salons of the aristocracy" (Struik 165).

Reaction: The chief occupation of the mathematicians no longer consisted in membership in learned academy; they were usually employed by universities or technical schools and were teachers as well as investigators. This is important because now the mathematicians will not only know how to compute complex things, but they will have the chance to teach others what they have learned at the universities.

A Concise History of Mathematics; Pages 101-150

Summary: The book began to talk about more recent mathematics; mathematics that was being invented, and used during the 18th century. The book mentions many of the great mathematicians during the 18th century, for example, Leibniz, Euler, Lagrange, Laplace, and the Bernoulli brothers. For the most part, mathematical productivity in the eighteenth century concentrated on the calculus and its application to mathematics. The book also mentions the 19th century, and how the French Revolution and the Napoleonic period help further the growth of mathematics. Many of the great minds of the 19th century are: Friedrich, Legendre, Monge, and Galois.

Quotation: "To the France of the Age of Enlightenment belongs the first comprehensive history of mathematics, a very readable narrative, not just a catalog of names and titles like those of the past" (Struik 137).

Reaction: The Age of Enlightenment was one of the most important eras in dealing with how far France has improved scientifically and mathematically. It is important to understand that it was during the Age of Enlightenment that the first comprehensive history of mathematics belonged to France.

A Concise History of Mathematics; Pages 50-100

Summary: The more I read, the more about the history of mathematics the book talks about. I keep learning new things, like how most of our knowledge of Egyptian mathematics derived from mathematical papyri. The book does not only mention the papyri that it talks about in great detail, but it shows images of them as well. Great civilizations like the Babylonians, Mayans, and Incas are mentioned for their great mathematical achievements. The Mayans constructed a well understood counting system, where numbers from one through four are represented as dots, and a five is a horizontal bar. So, if a Mayan wanted to represent a 9, they will draw four dots and one horizontal bar. The book also mentions how the Mayans had a different base number because they will use all their fingers and toes. As a result, instead of having a base of 10, they had a base of 20.

Quotation: “The best-known achievement of Hindu mathematics is our present decimal position” (Struik 67).

Reaction: The fact that Hindu mathematics provided us with the decimal system is very important. In fact, many of the mathematics that has been studied in the Eastern Hemisphere have great importance. The book mentions how many of the great thinkers like Pythagoras have come from the East, and how many of the ideas that we use in math have come from the East as well. Much of the great ideas we use today are credited to Egyptian, Chinese, Hindu, and Europeans mathematics.

A Concise History of Mathematics; Pages 1-50

Summary: Though math has been around for many years, little progress was made in understanding numerical values and space relations until more modern times. It was went the transition occurred from the mere gathering of food to its actual production, from hunting and fishing to agriculture. The book has a great deal of information, for example it talks about the old Fiji Island language. It mentions how ten boats were called bola, and ten coconuts were called koro, and a thousand coconuts were referred to as saloro. Actually, the first occurrence of numerical terms began to come into play as a quantitative meaning, rather than a qualitative. They were used to make distinctions between one thing, to two things, and many of something.

Quotation: “The development of the crafts of commerce stimulated this crystallization of number concept. Numbers were arranged and bundled into larger units, usually by the use of the fingers of the hand or of both hands, a natural procedure in trading” (Struik 10)

Reaction: As explained in the quote, trading actually had a great significance in mathematics. With trading, the individuals were able to build on their math knowledge of differentiating amount from one another. And what is silly now, was sure not humorous back in the early times. I’m talking about counting with fingers. The men doing the trading might have needed to count with their fingers on a daily bases, and now-a-days we laugh when someone pulls out the finger count. The novel is told in first person, is very much limited. The narrator is just explaining a great deal of events, and the significance/importance math related topics.