31 Questions
What are the major subdisciplines of modern mathematics according to the text?
Number theory, algebra, geometry, and analysis
What are the fundamental truths of mathematics independent from, according to the text?
Scientific experimentation
What does most mathematical activity involve, according to the text?
Using pure reason to prove properties of abstract objects
What does a proof in mathematics consist of, according to the text?
A succession of applications of deductive rules to already established results
What are the entities in modern mathematics stipulated to have certain properties called?
Axioms
In which fields is mathematics essential, according to the text?
The natural sciences and engineering
What is the word 'mathematics' derived from?
Greek word máthēma (μάθημα)
What did the Pythagoreans initially use the term 'mathēmatikoi' to refer to?
Learners
What was the common meaning of the term 'mathematics' in Latin and English until around 1700?
Astrology
Which mathematical concept had no practical application before its use in the RSA cryptosystem?
Integer factorization
What was primarily divided into geometry and arithmetic until the 16th and 17th centuries?
Mathematics
What appeared in Greek mathematics, notably in Euclid's Elements, as the concept of a proof and its associated mathematical rigour?
Proofs
What did the foundational crisis of mathematics at the end of the 19th century lead to?
Systematization of the axiomatic method
What did Saint Augustine's warning about mathematici mistranslate as?
'Astrologers'
What was primarily developed independently from any application and often later found practical applications?
'Pure mathematics'
'The mathematical art' is known as what in Latin?
'Ars mathematica'
What is the primary focus of mathematics, according to the text?
Proving abstract mathematical properties
Which of the following fields is NOT mentioned as essential areas where mathematics is extensively used?
Agriculture
What is the term used in modern mathematics for entities stipulated to have certain properties?
Axioms
What did the foundational crisis of mathematics at the end of the 19th century lead to?
Reevaluation of basic mathematical principles
What does a proof in mathematics consist of, according to the text?
Logical reasoning and deduction
What are the major subdisciplines of modern mathematics according to the text?
Number theory, algebra, geometry, analysis
What does the word 'mathematics' come from?
Greek word máthēma, meaning 'that which is learnt'
What did the Pythagoreans initially use the term 'mathēmatikoi' to refer to?
Learners
What did mathematics primarily involve until the 16th and 17th centuries?
Geometry and arithmetic
What led to the systematization of the axiomatic method at the end of the 19th century?
Foundational crisis of mathematics
What did Saint Augustine's warning about mathematici mistranslate as?
Astrology
What appeared in Greek mathematics, notably in Euclid's Elements, as the concept of a proof and its associated mathematical rigour?
Arithmetic and geometry
What are the major subdisciplines of modern mathematics according to the text?
More than 60 first-level areas
'The mathematical art' is known as what in Latin?
Mathematicus ars
Which mathematical concept had no practical application before its use in the RSA cryptosystem?
'Integer factorization'
Test your knowledge of mathematics with this overview quiz covering topics related to numbers, formulas, structures, shapes, and quantities. Explore major subdisciplines such as number theory, algebra, geometry, and analysis.
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