## Abstraction (mathematics) |

**Abstraction** in ^{[1]}^{[2]}^{[3]} Two of the most highly abstract areas of modern mathematics are

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Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as

Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract. Take the historical development of geometry as an example; the first steps in the abstraction of geometry were made by the ancient Greeks, with ^{[4]} In the 17th century

The advantages of abstraction are :

- It reveals deep connections between different areas of mathematics.
- Known results in one area can suggest conjectures in a related area.
- Techniques and methods from one area can be applied to prove results in a related area.

One disadvantage of abstraction is that highly abstract concepts can be difficult to learn.^{[5]} A degree of ^{[6]}

*The Scientific Outlook* (1931), writes that "Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say."

Other Languages

العربية: تجريد (رياضيات)

català: Abstracció (matemàtiques)

فارسی: تجرید (ریاضیات)

Bahasa Indonesia: Abstraksi (matematika)

עברית: הפשטה (מתמטיקה)

Bahasa Melayu: Pengabstrakan (matematik)

português: Abstração (matemática)

русский: Математическая абстракция

தமிழ்: கருத்தியல் தன்மை (கணிதம்)

Türkçe: Matematiksel soyutlama

ייִדיש: אבסטראקציע (מאטעמאטיק)