15 Questions
What are the major subdisciplines of modern mathematics as mentioned in the text?
Number theory, algebra, geometry, and analysis
What is the primary activity in mathematics according to the text?
Discovery of properties of abstract objects and use of pure reason to prove them
What do proofs in mathematics consist of?
A succession of applications of deductive rules to already established results
What are the fundamental truths of mathematics independent from according to the text?
Any scientific experimentation
In which fields is mathematics essential according to the text?
Natural sciences, engineering, medicine, finance, computer science, and social sciences
What do mathematicians not have a general consensus about according to the text?
A common definition for their academic discipline
Which of the following best describes the relationship between applied mathematics and pure mathematics?
Applied mathematics is developed independently from any application, while pure mathematics is developed in close correlation with applications.
What did the problem of integer factorization, dating back to Euclid in 300 BC, have no practical application before?
Its use in the RSA cryptosystem
When did algebra and infinitesimal calculus become introduced as new fields of mathematics?
16th and 17th centuries
What does the word 'mathematics' come from?
Ancient Greek máthēma (μάθημα)
What did the term 'mathematics' more commonly mean in Latin and English until around 1700?
Astrology
What does the word mathēmatikḗ tékhnē (μαθηματικὴ τέχνη) refer to?
'The mathematical art'
What did one of the two main schools of thought in Pythagoreanism, known as the mathēmatikoi (μαθηματικοί), mean at the time?
'Learners' rather than 'mathematicians' in the modern sense
What did Saint Augustine's warning about mathematici mean?
'Astrologers'
'Mathematical study' had what meaning even in Classical times?
'That which is learnt', 'what one gets to know', hence also 'study' and 'science'
Explore the foundational concepts of mathematics, including numbers, formulas, shapes, and quantities, as well as major subdisciplines such as number theory, algebra, geometry, and analysis. Delve into the diverse areas of study within mathematics and gain insights into the academic discipline's multifaceted nature.
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