Mathematics: Numbers, Formulas, and Structures

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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?

Natural sciences, engineering, medicine, finance, computer science, and social sciences Signup and view all the answers

What are the fundamental truths of mathematics independent from?

Any scientific experimentation Signup and view all the answers

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

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

What is the significance of the word 'mathēmatikós'?

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

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

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

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

In Latin and English until around 1700, the term 'mathematics' more commonly meant 'astrology' (or sometimes 'astronomy') rather than 'mathematics'. 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?

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. Signup and view all the answers