What is History of mathematics: Definition and 16 Discussions

The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.
The earliest mathematical texts available are from Mesopotamia and Egypt – Plimpton 322 (Babylonian c. 2000 - 1900 BC), the Rhind Mathematical Papyrus (Egyptian c. 1800 BC) and the Moscow Mathematical Papyrus (Egyptian c. 1890 BC). All of these texts mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a "demonstrative discipline" begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. Although they made virtually no contributions to theoretical mathematics, the ancient Romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, creation of lunar and solar calendars, and even arts and crafts. Chinese mathematics made early contributions, including a place value system and the first use of negative numbers. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics through the work of Muḥammad ibn Mūsā al-Khwārizmī. Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. Contemporaneous with but independent of these traditions were the mathematics developed by the Maya civilization of Mexico and Central America, where the concept of zero was given a standard symbol in Maya numerals.
Many Greek and Arabic texts on mathematics were translated into Latin from the 12th century onward, leading to further development of mathematics in Medieval Europe. From ancient times through the Middle Ages, periods of mathematical discovery were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 15th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day. This includes the groundbreaking work of both Isaac Newton and Gottfried Wilhelm Leibniz in the development of infinitesimal calculus during the course of the 17th century. At the end of the 19th century the International Congress of Mathematicians was founded and continues to spearhead advances in the field.

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  1. matqkks

    Are there any really good resources on modelling with differential equations?

    I will have to teach a first course in differential equations. A good motivator might be to promulgate modelling with differential equations but I have seen some teachers have made polemic against modelling. Are there any really good resources on modelling with differential equations? I want...
  2. matqkks

    What to cover in a differential equations module?

    I will have to teach a first course in differential equations. What should I cover in this module? For example, in most books they have Laplace Transforms which is fine but I would not use LT to solve differential equations. I want to write a course that it motivates students and has an impact...
  3. matqkks

    Introduction to pure mathematics

    TL;DR Summary: education, history I need to devise a module for next academic year which is an introduction to pure mathematics. They need to use this module as a stepping stone module such as number theory, group theory, combinatorics, real analysis. What should I cover to make this an...
  4. Adesh

    I How did students manage to study the required Mathematics for Physics

    I will basically focus on 18th and 19th century, I got to know from the biographies of Max Planck and few other that there were no organized syllabus in Universities for studying. Students had to take classes that they could understand and it was less like a lecture and more like a private...
  5. nomadreid

    History Question about the history of mathematics

    Since this is on the history of philosophy linked to set theory, rather than set theory itself, I presume I can't put it into the Set Theory rubrik. First, for those who are unfamiliar with the Reflection Principles of Set Theory (or more properly model theory),there are several versions, but...
  6. Auto-Didact

    A Is QM Foundations Facing a Crisis?

    This thread is a shootoff from this post in the thread Summary of Frauchiger-Renner. The topics are related, but this thread offers a new perspective that diverges from the main subject of that thread. In QM foundations, the sheer amount of interpretations, disagreement among experts about what...
  7. nomadreid

    I "Laws of Form" by G. Spencer-Brown (1969)

    I have received (unasked) a digital edition of "Laws of Form" (1969) by G. Spencer-Brown; I have glanced at it, and also at the Wikipedia article https://en.wikipedia.org/wiki/Laws_of_Form. OK, another logical system; logical journals (e.g. by ASL) are full of them, and I am not sure whether...
  8. Cantor080

    Other Utility of a general math book introducing subjects not in historical order?

    I have Abstract Algebra Course, and my teacher is using the book, "Abstract Algebra" of David S. Dummit, and Richard M.Foote. This book, and other books which my teachers are using for the courses, seem to give definitions, theorems, and problems, in no historical order or are not mentioning the...
  9. matqkks

    Are there any resources for questions on primitive roots?

    Does anyone know of any resources on questions on primitive roots and order of a modulo n? They need to be suitable for elementary number theory course. (These could be interesting results and challenging ones).
  10. matqkks

    I What is the most motivating way to introduce primitive roots

    I am teaching elementary number theory to first year undergraduate students. How do introduce the order of an integer modulo n and primitive roots? How do I make this a motivating topic and are there any applications of this area? I am looking at something which will have an impact.
  11. H

    How did egyptian mathematical fractions evolve in antiquity?

    There are certain explanations on how integers might have evolved, like for example "the wings of a bird to symbolize the number two, clover--leaves three, the legs of an animal four, the fingers on his own hand five."1 Seeing all these, and making experience short--abstract, can be said to have...
  12. H

    The history of mathematics help with resources

    The history of mathematics...help with resources Hey guys I need help finding good resources to help me understand basic to advance math from a developmental point of view, the applied necessities of the inventors of math operations and concepts. For example the addition operation was...
  13. A

    History History of Mathematics: A Review of Steven Krantz's Book

    Hey I am looking for a book talking about history of mathematics Steven Krantz has one here Amazon Amazon.com: Customer Reviews: An Episodic History of Mathematics: Mathematical Culture through Problem Solving (Maa Textbook) (Mathematical Association of America Textbooks) who know this book...
  14. E

    Book: History of Mathematics since the 20th Century

    Hi all, Can anyone recommend a good book on the history of mathematics in very recent times (i.e. since the 20th century, specifically including the mathematical beginnings of computer science, game theory, chaos theory, complex systems, recent developments in stochastics etc.etc.)? Most...
  15. F

    History of Mathematics book

    I was wanting to learn about the development of mathematics and the mathematicians who helped with it. I was wondering if anyone knew of any book that was particularly well written and included a lot of information. Also, if it could go into detail about the mathematicians responsible for the...
  16. Astronuc

    History Discover the Fascinating History of Mathematics Across Cultures

    - http://aleph0.clarku.edu/~djoyce/mathhist/ Pick a region - http://aleph0.clarku.edu/~djoyce/mathhist/earth.html Maintained by David E. Joyce Department of Mathematics and Computer Science Clark University I picked up a thick paperback book on the history of mathematics...