HISTORY OF MATHEMATICS
QUESTIONS AND ANSWERS WITH
SOLUTIONS 2024
Explain what the history of mathematics is(as a subject). - ANSWER The area of study known as the
history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to
a lesser extent, an investigation into the mathematical methods and notation of the past.
Which are the oldest mathematical texts available? - ANSWER The most ancient mathematical texts
available are Plimpton 322 (Babylonian c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian c. 2000-
1800 BC) and the Moscow Mathematical Papyrus (Egyptian c. 1890 BC).
How did the study of mathematics begin? - ANSWER The study of mathematics as a demonstrative
discipline begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from
the ancient Greek μάθημα (mathema), meaning "subject of instruction".
Explain the origins of mathematical thought. - ANSWER The origins of mathematical thought lie in the
concepts of number, magnitude, and form. Such concepts would have been part of everyday life in
hunter-gatherer societies.
How did the concept of "number" evolve over time? - ANSWER The idea of the "number" concept
evolving gradually over time is supported by the existence of languages which preserve the distinction
between "one", "two", and "many", but not of numbers larger than two.
What was Babylonian mathematics? - ANSWER Babylonian mathematics was any mathematics
developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall
of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited.
How are Babylonian mathematical texts classified? - ANSWER Regarding time, they fall in two distinct
groups: one from the Old Babylonian period and the other mainly Seleucid from the last three or four
centuries BC.
Were there any differences between the two groups of Babylonian mathematics? - ANSWER In respect
of content there is scarcely any difference between the two groups of texts. Thus Babylonian
mathematics remained constant, in character and content, for nearly two millennia.
, Where does our knowledge of Babylonian mathematics come from? - ANSWER Our knowledge of
Babylonian mathematics is derived from some 400 clay tablets unearthed since the 1850s. Written in
Cuneiform script, tablets were inscribed while the clay was moist, and baked hard in an oven or by the
heat of the sun. The majority of recovered clay tablets date from 1800 to 1600 B.C.
What numerals did the Babylonians use? - ANSWER The Babylonian system of mathematics was
sexagesimal (base 60) numeral system. From this we derive the modern day usage of 60 seconds in a
minute, 60 minutes in an hour, and 360 degrees in a circle.
Explain how the sexagesimal (base 60) helped the Babylonians. - ANSWER The number 60 is a superior
highly composite number, having factors of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, facilitating calculations
with fractions.
Did the Babylonians have a place-value system? - ANSWER The Babylonians had a true place-value
system, where digits written in the left column represented larger values much like our base ten system.
What did the Babylonians use as a tool for doing correct arithmetic? - ANSWER The Babylonians used
pre-calculated tables to assist with arithmetic. For example, two tablets found at in 1854, dating from
2000 BC, give lists of the squares of numbers up to 59 and the cubes of numbers up to 32. The
Babylonians used the lists of squares together with the certain formulas to assist in multiplication.
Did the Babylonians have algebra? - ANSWER As well as arithmetical calculations, Babylonian
mathematicians also developed algebraic methods of solving equations. Once again, these were based
on pre-calculated tables.
What is the Plimpton 322? - ANSWER A Babylonian clay tablet, notable as containing an example of
Babylonian mathematics. This tablet, believed to have been written about 1800 BC, has a table of four
columns and 15 rows of numbers in the cuneiform script of the period.
What does Plimpton 322 contain? - ANSWER This table lists what are now called Pythagorean triples, i.e.,
integers a, b, c satisfying a^2+b^2=c^2. From a modern perspective, a method for constructing such
triples is a significant early achievement, known long before the Greek and Indian mathematicians
discovered solutions to this problem.
QUESTIONS AND ANSWERS WITH
SOLUTIONS 2024
Explain what the history of mathematics is(as a subject). - ANSWER The area of study known as the
history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to
a lesser extent, an investigation into the mathematical methods and notation of the past.
Which are the oldest mathematical texts available? - ANSWER The most ancient mathematical texts
available are Plimpton 322 (Babylonian c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian c. 2000-
1800 BC) and the Moscow Mathematical Papyrus (Egyptian c. 1890 BC).
How did the study of mathematics begin? - ANSWER The study of mathematics as a demonstrative
discipline begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from
the ancient Greek μάθημα (mathema), meaning "subject of instruction".
Explain the origins of mathematical thought. - ANSWER The origins of mathematical thought lie in the
concepts of number, magnitude, and form. Such concepts would have been part of everyday life in
hunter-gatherer societies.
How did the concept of "number" evolve over time? - ANSWER The idea of the "number" concept
evolving gradually over time is supported by the existence of languages which preserve the distinction
between "one", "two", and "many", but not of numbers larger than two.
What was Babylonian mathematics? - ANSWER Babylonian mathematics was any mathematics
developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall
of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited.
How are Babylonian mathematical texts classified? - ANSWER Regarding time, they fall in two distinct
groups: one from the Old Babylonian period and the other mainly Seleucid from the last three or four
centuries BC.
Were there any differences between the two groups of Babylonian mathematics? - ANSWER In respect
of content there is scarcely any difference between the two groups of texts. Thus Babylonian
mathematics remained constant, in character and content, for nearly two millennia.
, Where does our knowledge of Babylonian mathematics come from? - ANSWER Our knowledge of
Babylonian mathematics is derived from some 400 clay tablets unearthed since the 1850s. Written in
Cuneiform script, tablets were inscribed while the clay was moist, and baked hard in an oven or by the
heat of the sun. The majority of recovered clay tablets date from 1800 to 1600 B.C.
What numerals did the Babylonians use? - ANSWER The Babylonian system of mathematics was
sexagesimal (base 60) numeral system. From this we derive the modern day usage of 60 seconds in a
minute, 60 minutes in an hour, and 360 degrees in a circle.
Explain how the sexagesimal (base 60) helped the Babylonians. - ANSWER The number 60 is a superior
highly composite number, having factors of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, facilitating calculations
with fractions.
Did the Babylonians have a place-value system? - ANSWER The Babylonians had a true place-value
system, where digits written in the left column represented larger values much like our base ten system.
What did the Babylonians use as a tool for doing correct arithmetic? - ANSWER The Babylonians used
pre-calculated tables to assist with arithmetic. For example, two tablets found at in 1854, dating from
2000 BC, give lists of the squares of numbers up to 59 and the cubes of numbers up to 32. The
Babylonians used the lists of squares together with the certain formulas to assist in multiplication.
Did the Babylonians have algebra? - ANSWER As well as arithmetical calculations, Babylonian
mathematicians also developed algebraic methods of solving equations. Once again, these were based
on pre-calculated tables.
What is the Plimpton 322? - ANSWER A Babylonian clay tablet, notable as containing an example of
Babylonian mathematics. This tablet, believed to have been written about 1800 BC, has a table of four
columns and 15 rows of numbers in the cuneiform script of the period.
What does Plimpton 322 contain? - ANSWER This table lists what are now called Pythagorean triples, i.e.,
integers a, b, c satisfying a^2+b^2=c^2. From a modern perspective, a method for constructing such
triples is a significant early achievement, known long before the Greek and Indian mathematicians
discovered solutions to this problem.
