An Early History of Mathematics

In the Greek tradition, mathematics was portrayed as having originated within the studies of early Egyptian philosophers. Although mathematics was more of an extrapolation from the other natural sciences which were based in a reality with which one could individually react, it developed its own internal cosmos. In “ Making Modern Science: A Historical Survey,” by Peter J. Bowler and Iwan Rhys Morus, “Philosophers talked of experiment and of mathematics as providing new tools and even a new language that could be used to understand nature” (Bowler and Morus, 25). Mathematics was a method of reformatting knowledge about the physical world so that it could be manipulated into providing extensive information into the unknown. Despite the conviction the Greek philosophers had about the origins of the field of mathematical inquiry, discrepancies arose. In “The Dialogue of Civilizations in the Birth of Modern Science,” by Arun Bala, “He [Historian Colin Ronan] counters the prevalent Greek view that their mathematics began in Egypt” (Bala, 17). Greek philosophers and mathematicians held this belief, excited by having the exotic terrain as the remote source of their area of study.

Mathematics was a skillset new to the ancient world and fairly useful to know, even to upper echelons of society which were capable of hiring mathematicians. “ Gentlemen landowners (and gentleman adventurers) increasing found themselves in need of the skills of practical mathematicians and even started acquiring a certain level of mathematical proficiency themselves”(Bowler and Morus, 40). Explorers needed to be able to navigate new environments, and being knowledgeable about measurement devices and visible astronomical features such as bright stars and planets enabled them to travel to new environments. “Practical mathematics was an activity built around the manipulation of different kinds of of mathematical instruments, such as sextants, quadrants, or calculating devices like the slide rule”(Bowler and Morus, 40). Until fairly recently, the slide rule was used by engineers designing all kinds of devices. Today, the modern calculator has taken its place, and unfortunately the last generation capable of easily using a slide rule has reached old age. It would be prudent for scientists and historians of science to work to keep this skill alive in both academia and industry. It would interesting to study the neural networks that mimic the slide rule and compare them to those that mimic a modern calculator.

Ronan highlights the dispute over the recipient of credit for the creation of early mathematical thought. Bala writes, “Although he [Colin Ronan] admits that Greek science is not the mathematical empirical science we have today, he is nevertheless prepared not to concede to the Greeks the achievement of having developed the foundations of modern science” (Bala, 15). The reason for this discrepancy is that a lot of “Greek” scientific culture had actually been invented in other areas, for example, in ancient Mesopotamia, before the birth of Hellan civilization. Tools for calculating correct farming techniques were established in older civilizations. According to some Greek intellectuals, mathematical methods were adopted from travelers to Egypt: “The Greeks claim to have received their mathematics from Egypt by way of Thales; Herodotus, Aristotle and his pupil Eudemos, who wrote a history of mathematics, all claim that Thales ‘after a visit to Egypt, brought this study to Greece’”(Bala, 17). Considering that Eudemos was able to compile a history of mathematics so early in Greek history, a modern day approach to the history of this scientific field could include loops. Let us say there are ten time frames during which enough mathematical methods were invented to write about, Time Period One, Time Period Two, etc., a modern historian can compile these histories in a manner mimicking the modern computational method of loops, by distributing the topics throughout time periods past. Perhaps the first chapter of each historical Time Period may be linked to each other first chapter of every other Time Period. This would require, of course, very thorough and detailed accounts of the invention of mathematical thought and overlaps in ideas such as those that occurred between Newton and Leibniz would add an extra layer of confusion to this approach to understanding the history of mathematics.

The irony of reading about early Italian science is that even today, the modern equivalent of “natural philosophy” is still considered to be a topic of greater importance than that of pure mathematics. There may today be a slight glorification of certain fields of science, however, philosophy, which is a very unscientific field, with the exception of course of the great work of the late Baruch Spinzo, is still considered to be a more realistic understanding of reality than that of pure mathematics. This hierarchy of the importance of thought, “[M]eant that astronomy occupied a different place from natural philosophy in university curricula, for example. It also meant that its practitioners, like mathematicians, were held to be of lower intellectual and social status that professors of natural philosophy. This was one of three reasons, as we shall see later, that Galileo was so pleased to have persuaded Cosimo de’Medici to engage him as court philosopher rather than court mathematician” (Bowler and Morus, 25). This tragic pattern is possibly caused by the fact that the modern philosopher often has a better grasp on rhetoric and public speaking, and the modern mathematician is often snubbed for both studying inaccessible ideas, and possessing weaker skills in typical human conversation. Bowler and Morus argue that this pattern changed over time, “ Increasingly, also many natural philosophers argued that the language in which the book of nature was written was the language of mathematics. This represented a major shift in the epistemological-and social-status of mathematics. As we have already seen, mathematics had traditionally been regarded as epistemologically inferior to natural philosophy”(Bowler and Morus, 40). The social status of mathematics is still entrenched by the ignorance and weak scientific vocabulary that the average person possesses today, limiting the ability of a mathematician to communicate their ideas to the global community. Unfortunately, the only solutions available are either to write mathematical research in a manner so simply that the modern mathematician spends an inordinate amount of time trying to translate complex ideas into simple, understandable language, or to leave their work written in cryptic scientific jargon, leaving their research unapplied to various other fields of science and impossible to comprehend by the average person.

Despite the issues encountered by both the ancient and modern scientific historian, some vital aspects of mathematical truth have apparently been understood and translated into normal human language, (a vocabulary lacking any scientific jargon). Baigrie writes, “We have next to consider how the mathematician differs from the physicist or natural philosopher; for natural bodies have surfaces and occupy spaces, have lengths and present points, all which are subjects of mathematical study” (Baigrie, 1). This description of provided by Baigrie, unfortunately demonstrates a slight ignorance of the clear difference between the study of physics and that of mathematics. His account is actually more along the lines of a summary of physics, and demonstrate a poor understanding of mathematics. There are slight exaggerations that demonstrate the ignorance in early records of science, “ Natural magicians like the Elizabethan courtier and mathematician John Dee or the Jesuit scholar and polymath Athenasius Kircher could produce spectacular phenomenon at will”( Bowler and Morus, 34). Although Bowler and Morus record early mathematicians as entertainers, rather than scientists, a good example of applied mathematical thought is the Foucoult Pendulum which behaves much in the way that Baigrie later describes: “ The hypothesis of spherical motion finds support also in the fact that on any other hypothesis save this one alone it is impossible that the instruments for measuring hours should be correct” ( Baigrie, 10). The Foucoult Pendulum, such as the one kept in Griffith’s Observatory, demonstrates the passage of time with regard to the movement of the planet Earth. This type of gigantic clock is perfect example of both “spherical motion” and “measuring hours”.

Peter Bowler and Iwan Rhys Morus, Making Modern Science: A Historical Survey, ISBN 978-0226068619

Arun Bala, “Why did Modern Science Not Develop in Civilization X?” and “The Eurocentric History of Science,” in The Dialogue of Civilizations in the Birth of Modern Science

Excerpts from Aristotle’s Physics and Ptolemy’s Almagest, from Scientific Revolutions: Primary Texts in the History of Science, Brian Baigrie