16 Questions
What are the major subdisciplines of modern mathematics as mentioned in the text?
Number theory, algebra, geometry, and analysis
What is the essential activity in most mathematical work according to the text?
Discovery of properties of abstract objects
What do proofs in mathematics consist of?
A succession of applications of deductive rules to already established results
In what areas is mathematics essential according to the text?
Natural sciences, engineering, medicine, finance, computer science, and social sciences
Are the fundamental truths of mathematics dependent on scientific experimentation?
No, the fundamental truths of mathematics are independent from any scientific experimentation
What do most mathematical objects consist of in modern mathematics?
Entities that are stipulated to have certain properties called axioms
What is the narrower and more technical meaning of the word 'mathematics' in Classical times?
The study of arithmetic and geometry
What does the word 'mathēmatikós' (μαθηματικός) mean?
Related to learning or studious
Which school of thought in Pythagoreanism was known as the mathēmatikoi (μαθηματικοί)?
Learners
What did the term mathematics more commonly mean in Latin and English until around 1700?
Astrology
What did Saint Augustine's warning about mathematici mean in his context?
Astrologers
Which area of mathematics had no practical application before its use in the RSA cryptosystem?
Integer factorization
What led to a correlated increase in the development of both mathematical innovations and scientific discoveries?
Interaction between mathematical innovations and scientific discoveries
Where did the concept of a proof and its associated mathematical rigour first appear?
Greek mathematics
What was mathematics primarily divided into until the 16th and 17th centuries?
Geometry and arithmetic
What did the foundational crisis of mathematics lead to?
Systematization of the axiomatic method
Explore the diverse topics of numbers, formulas, shapes, and quantities in mathematics, along with its major subdisciplines such as number theory, algebra, geometry, and analysis. Delve into the ever-evolving nature of mathematical activity and the absence of a universal definition for this academic discipline.
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