# Which areas of maths are from which fundamental areas

1. Dec 5, 2014

### samgrace

Hello,

I am a physics student and have catagorised most of physics, e.g classical mechanics, relativistic mechanics, quantum mechanics and quantum field theory, and have also identified all the mathematics involved in each of these catagories.
For example classical mechanics involves Calculus, Differential Equations, Vector Analysis, Calculus of variations and Linear algebra (matrcies and tensors). So on a so forth for each catagory. (large/small, fast/slow).

Now I am looking for a flow or web diagram of how mathematics developed. To elaborate, I need a diagram that starts with the fundamentals of mathematics such as set theory, catagory theory, and shows that these lead onto algebra and topology, and that these with real analysis and geometry lead to differential geometry etc.

I am not confident with this order and thus don't know where to start to have a full appreciation/understanding, for example, using matrices to solve simultaneous equations does mean I understand linear algebra.

Thanks

P.S Here is a TED talk on the beauty and truth of physical theory (provided you know the fundamentals)
https://www.ted.com/talks/murray_gell_mann_on_beauty_and_truth_in_physics

2. Dec 5, 2014

### SteamKing

Staff Emeritus
It's not clear if you are looking for the historical development of mathematics or something else. Arithmetic and geometry are two of the oldest branches of mathematics, but things like set theory and topology are relatively recent developments. For example, no one started with set theory and said to himself, "I'll invent algebra now!" Although mathematics appears to be built on an orderly structure, it definitely did not evolve that way. Even our number system has evolved in fits and starts over the centuries, starting with positive integers, then fractions, negative numbers, etc. The concept of zero as a number was a great innovation and not only for making calculations.

3. Dec 6, 2014

### samgrace

The history slash evolvement of mathematics is what I am looking for, however now that you've said that, it seems that I should get a book on the material I want to learn, and then back track to other books that cover the material that I don't understand in that book.

4. Dec 6, 2014

### SteamKing

Staff Emeritus
If you are interested in a good technical and historical survey of the development of mathematics, I recommend Mathematical Thought from Ancient to Modern Times, by Morris Kline (3 vol.)

https://www.amazon.com/Morris-Kline/e/B001H6MNLK

This work discusses the historical development of mathematics and gives some descriptions of the mathematics involved. Some of his other works may interest you as well. You should be able to find Mathematical Thought in your college library or a public library if you don't want to purchase it.

You can also use Amazon to search for other books dealing with the development of particular mathematical topics of interest.