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# Mathematics: Numbers, Formulas, and Structures

Explore the diverse topics of mathematics including numbers, formulas, shapes, spaces, and quantities. Delve into major subdisciplines such as number theory, algebra, geometry, and analysis.

Created by
@MagicalBlackberryBush

### What are the major subdisciplines of modern mathematics?

Number theory, algebra, geometry, and analysis

### What does most mathematical activity involve?

The discovery of properties of abstract objects and the use of pure reason to prove them

### What does a proof in mathematics consist of?

A succession of applications of deductive rules to already established results

### In which fields is mathematics essential?

<p>Natural sciences, engineering, medicine, finance, computer science, and social sciences</p> Signup and view all the answers

### What are the fundamental truths of mathematics independent from?

<p>Any scientific experimentation</p> Signup and view all the answers

### What is the etymological origin of the word 'mathematics'?

<p>The word 'mathematics' comes from the Ancient Greek máthēma, meaning 'that which is learnt' or 'study'.</p> Signup and view all the answers

### What is the significance of the word 'mathēmatikós'?

<p>The word 'mathēmatikós' means 'related to learning' or 'studious', and further came to mean 'mathematical'.</p> Signup and view all the answers

### Who constrained the use of the word 'mathēmatikoi' to just the study of arithmetic and geometry?

<p>The Pythagoreans were likely the first to constrain the use of the word 'mathēmatikoi' to just the study of arithmetic and geometry.</p> Signup and view all the answers

### In Latin and English until around 1700, what did the term 'mathematics' more commonly mean?

<p>In Latin and English until around 1700, the term 'mathematics' more commonly meant 'astrology' (or sometimes 'astronomy') rather than 'mathematics'.</p> Signup and view all the answers

### What historical event led to the use of integer factorization in the RSA cryptosystem, thus giving it a practical application?

<p>The use of integer factorization in the RSA cryptosystem, giving it a practical application, was a result of the foundational crisis of mathematics at the end of the 19th century.</p> Signup and view all the answers

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