16 Questions
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 do proofs in mathematics consist of?
a succession of applications of deductive rules to already established results
In which disciplines is mathematics essential?
natural sciences, engineering, medicine, finance, computer science, and social sciences
What are the fundamental truths of mathematics independent from?
any scientific experimentation
What are the topics included in mathematics?
numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes
What is the etymology of the word mathematics?
The word mathematics comes from Ancient Greek máthēma (μάθημα), meaning 'that which is learnt', 'what one gets to know', hence also 'study' and 'science'.
What is the meaning of the adjective mathēmatikós (μαθηματικός)?
The meaning of the adjective mathēmatikós (μαθηματικός) is 'related to learning' or 'studious', which likewise further came to mean 'mathematical'.
What did mathēmatikḗ tékhnē (μαθηματικὴ τέχνη) mean in Ancient Greek?
The term mathēmatikḗ tékhnē (μαθηματικὴ τέχνη) meant 'the mathematical art' in Ancient Greek.
What did the term mathematics commonly mean in Latin and English until around 1700?
In Latin, and in English until around 1700, the term mathematics more commonly meant 'astrology' (or sometimes 'astronomy') rather than 'mathematics'.
What was the first practical application of the problem of integer factorization?
The first practical application of the problem of integer factorization was its use in the RSA cryptosystem, now widely used for the security of computer networks.
In Ancient Greek, what did the word máthēma (μάθημα) mean?
In Ancient Greek, the word máthēma (μάθημα) meant 'that which is learnt', 'what one gets to know', hence also 'study' and 'science'.
What were the two main schools of thought in Pythagoreanism known as?
The two main schools of thought in Pythagoreanism were known as the mathēmatikoi (μαθηματικοί).
Who was likely the first to constrain the use of the word 'mathematics' to just the study of arithmetic and geometry?
The Pythagoreans were likely the first to constrain the use of the word 'mathematics' to just the study of arithmetic and geometry.
What appeared first in Greek mathematics, most notably in Euclid's Elements?
The concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements.
What led to a correlated increase in the development of both mathematical innovations and scientific discoveries?
The interaction between mathematical innovations and scientific discoveries led to a correlated increase in the development of both.
Explore the foundational topics and subdisciplines of mathematics, including numbers, formulas, structures, shapes, and quantities. Delve into number theory, algebra, geometry, and analysis to gain a deeper understanding of this diverse academic field.
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