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As it is globally known that set theory as a foundation of mathematics, although in the beginning we didn't call it "Set" rather group of elements. For example - set of [1(banana) + 2(apple)+1(cow)] => contains 4 elements. Of course, counting objects as 1,2,3,4,5,... was the basis and earliest example of set theory though at that time we didn't give it the name "Sets".

So counting as sets was foundation of mathematics.

After this developing basic "operations" like addition/subtraction seems like a logical development of foundation in mathematics. I can be wrong also I would assume multiplication/division as complex operations

then what did we developed after this and why and how?

Did we invented geometry right after this foundation and then number system to make mathematics more concrete? Did we invented/discovered negative number / decimal / fraction / rational / irrational / Integers after geometry as mathematical foundation?

In what order of mathematical foundation we invented/discovered trigonometry? In what order of mathematical foundation we invented/discovered Algebra? When did we started using complex mathematical operations (multiplication/division)?

Few points: 1. I don't need dates as when it was invented rather "after what" it was discovered/invented. 2. What would be the logical timeline you will decide if just keep the history aside? 3. What is the actual timeline of mathematical foundations? And why did we discovered/invented them?

P.S: Please don't mark it as broad question because it is a broad question and all kind of example, references,links, study material is welcomed.

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    $\begingroup$ Why not start with a book on the History of mathematics ? $\endgroup$ – Mauro ALLEGRANZA Nov 21 '17 at 14:11
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    $\begingroup$ "What would be the logical timeline you will decide if just keep the history aside? " It makes little sense... $\endgroup$ – Mauro ALLEGRANZA Nov 21 '17 at 14:12
  • $\begingroup$ This question is indeed very broad. Please narrow it down further. $\endgroup$ – Rory Daulton Nov 22 '17 at 1:30
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    $\begingroup$ @RoryDaulton Yes, I know. The reason I keep it broad because I am preparing to teach maths as its origin so that people understand its logic and need of discovery/invention. Also the course is going for the non-STEM people who have basic understanding of number and operation but they hate maths because as maths levels up, its difficulty levels up too. Basically "Word power made easy" for Mathematics so that people understand concepts, its need, its origin, its application, its context etc. $\endgroup$ – ΛBHINΛV Nov 22 '17 at 2:17
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    $\begingroup$ Talking about the foundations of mathematics before the last 19th century (Russell, Whitehead, Hilbert, Bernays, etc) is arguably anachronistic. $\endgroup$ – Peter Taylor Nov 22 '17 at 9:13

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