Mathematics MCQ Question Pool
Here is a collection of multiple-choice questions designed to cover a broad range of topics
relevant for a bachelor's level mathematics degree. The correct answer for each question is in
bold.
Famous Mathematicians
1. Who is credited with the development of the Cartesian coordinate system?
a) Isaac Newton
b) Gottfried Wilhelm Leibniz
c) René Descartes
d) Blaise Pascal
2. Which ancient Greek mathematician is known for his work on the geometry of conic
sections (ellipses, parabolas, hyperbolas)?
a) Euclid
b) Apollonius of Perga
c) Archimedes
d) Thales of Miletus
3. Leonhard Euler's famous identity, eiπ+1=0, connects five fundamental mathematical
constants. Which of the following is NOT in this identity?
a) Euler's number (e)
b) Pi (π)
c) The imaginary unit (i)
d) The Golden Ratio (ϕ)
4. Who is known as the "Father of Algebra" for his systematic approach to solving linear and
quadratic equations?
a) Omar Khayyam
b) Muhammad ibn Musa al-Khwarizmi
c) Carl Friedrich Gauss
d) Diophantus
5. Which mathematician laid the foundations of group theory and died tragically in a duel at
the age of 20?
a) Niels Henrik Abel
b) Évariste Galois
c) Augustin-Louis Cauchy
d) Joseph-Louis Lagrange
6. Emmy Noether is renowned for her groundbreaking contributions to which field of
mathematics?
a) Calculus
b) Geometry
c) Abstract Algebra
d) Probability Theory
7. David Hilbert proposed a famous list of 23 unsolved problems in 1900 that greatly
influenced 20th-century mathematics. In which city did he present this list?
a) Berlin
b) Paris
c) Göttingen
d) London
8. The "Sieve of Eratosthenes" is an ancient algorithm for what purpose?
a) Calculating square roots
b) Solving linear equations
c) Finding all prime numbers up to a specified integer
d) Approximating the value of Pi
9. Which mathematician is famous for his work on number theory and for mentoring the
brilliant Srinivasa Ramanujan at Cambridge?
a) David Hilbert
b) Bertrand Russell
c) G. H. Hardy
d) John Littlewood
10.Who is credited with inventing logarithms, a tool that greatly simplified calculations?
a) Leonhard Euler
b) John Napier
c) Henry Briggs
d) Blaise Pascal
11.Sophie Germain was a pioneering female mathematician who made significant
contributions to which area?
a) Number theory (especially Fermat's Last Theorem)
b) Set theory
c) Topology
d) Computer science
12.The term "prince of mathematicians" is often used to describe which of the following?
a) Isaac Newton
b) Leonhard Euler
c) Carl Friedrich Gauss
d) Srinivasa Ramanujan
13.Who developed the theory of transfinite numbers, which for the first time allowed
mathematical sets of infinite size to be compared?
a) Richard Dedekind
b) Georg Cantor
c) Kurt Gödel
d) Leopold Kronecker
14.The development of non-Euclidean geometry is primarily attributed to which pair of
mathematicians, who worked independently?
a) Riemann and Klein
b) Lobachevsky and Bolyai
c) Hilbert and Poincaré
d) Descartes and Fermat
15.Who was the first woman to win the Fields Medal (in 2014)?
a) Emmy Noether
b) Sophie Germain
c) Maryam Mirzakhani
d) Karen Uhlenbeck
16.Which mathematician is known as the "Father of the Computer" for his concept of a
programmable machine?
a) Alan Turing
b) John von Neumann
c) Charles Babbage
d) Blaise Pascal
17.Who is known for his "Incompleteness Theorems," which had a major impact on the
philosophy of mathematics?
a) Alan Turing
b) Kurt Gödel
c) Bertrand Russell
d) George Boole
18.The Fibonacci sequence is named after Leonardo of Pisa, who was also known by what
name?
a) Tartaglia
b) Cardano
c) Fibonacci
d) Pacioli
19.Who is credited with the first rigorous proof of the Fundamental Theorem of Algebra?
a) Leonhard Euler
b) Joseph-Louis Lagrange
c) Carl Friedrich Gauss
d) Jean-Robert Argand
20.Which mathematician's work on logic formed the basis for modern digital computer
circuits?
a) John von Neumann
b) George Boole
c) Augustus De Morgan
d) Charles Peirce
Books & Movies
21.The movie "The Imitation Game" chronicles the life of which mathematician and his work
on breaking the Enigma code?
a) John von Neumann
b) Alan Turing
c) John Nash
d) Kurt Gödel
22.The book "Flatland: A Romance of Many Dimensions" explores a world of two dimensions
to help readers imagine higher dimensions. Who wrote it?
a) Lewis Carroll
b) Edwin A. Abbott
c) George Gamow
d) Martin Gardner
23.The film "Good Will Hunting" features a janitor who is a self-taught mathematical genius.
What is the name of the fictional university where the movie is primarily set?
a) Harvard
b) Caltech
c) MIT
d) Princeton
24."Principia Mathematica," a three-volume work on the foundations of mathematics, was
written by Alfred North Whitehead and who else?
a) David Hilbert
b) Bertrand Russell
c) Ludwig Wittgenstein
d) Kurt Gödel
25.The movie "The Man Who Knew Infinity" is based on the life of which mathematician?
a) Aryabhata
b) Srinivasa Ramanujan
c) Harish-Chandra
d) C. R. Rao
26.What is the title of the foundational text on geometry written by Euclid?
a) The Elements
b) The Almagest
c) Arithmetica
d) Disquisitiones Arithmeticae
27.The 2016 film "Hidden Figures" focuses on the contributions of African-American female
mathematicians at which organization?
a) Jet Propulsion Laboratory (JPL)
b) NASA
c) Bell Labs
d) Los Alamos National Laboratory
28.Which book by Douglas Hofstadter explores themes of mathematics, art, and music
through the works of Gödel, Escher, and Bach?
a) The Emperor's New Mind
b) Gödel, Escher, Bach: an Eternal Golden Braid
c) I Am a Strange Loop
d) Metamagical Themas
29.The film "Pi" (1998) directed by Darren Aronofsky is a psychological thriller about a
mathematician who searches for what?
a) A proof of the Riemann Hypothesis
b) A numerical pattern in the stock market and the universe
c) The largest prime number
d) A solution to the P vs NP problem
30.Simon Singh's book "The Code Book" primarily deals with the history of what?
a) Computer programming
b) Cryptography
c) Mathematical logic
d) Accounting
31.The movie "A Beautiful Mind" is a biographical drama about the life of which Nobel
laureate?
a) Alan Turing
b) John Nash
c) Stephen Hawking
d) Richard Feynman
32.Which book, written by Carl Friedrich Gauss, is a cornerstone of modern number theory?
a) Arithmetica
b) Disquisitiones Arithmeticae
c) Liber Abaci
d) Geometriae
33.The film "Stand and Deliver" is based on the true story of which high school math
teacher?
a) Jaime Escalante
b) Sal Khan
c) John Saxon
d) Marva Collins
34."Liber Abaci," a 1202 book, was instrumental in spreading the Hindu-Arabic numeral
system in Europe. Who was its author?
a) Gerolamo Cardano
b) Niccolò Fontana Tartaglia
c) Leonardo of Pisa (Fibonacci)
d) Luca Pacioli
35.The movie "Agora" (2009) depicts the life and death of which female mathematician from
ancient Alexandria?
a) Theano
b) Hypatia
c) Maria Gaetana Agnesi
d) Elena Cornaro Piscopia
Mathematical Constants & Figures
36.The value 1.6180339887... is known as the Golden Ratio. By which Greek letter is it
commonly represented?
a) Alpha (α)
b) Sigma (σ)
c) Phi (ϕ)
d) Gamma (γ)
37.What is the value of the imaginary unit, i, when squared (i2)?
a) 1
b) -1
c) 0
d) i
38.The number e (Euler's number) is the base of which type of logarithm?
a) Common logarithm
b) Natural logarithm
c) Binary logarithm
d) Complex logarithm
39.Which of the following numbers is an example of a transcendental number?
a) 2
b) 5
c) π
d) 1/3
40.A shape with infinite perimeter but finite area is a characteristic of a:
a) Circle
b) Polygon
c) Fractal
d) Polyhedron
41.A Möbius strip is a surface with how many sides?
a) One
b) Two
c) Infinite
d) Zero
42.The square root of 2 (2) is what type of number?
a) Rational
b) Integer
c) Irrational
d) Transcendental
43.Which constant is defined as the limit of (1+1/n)n as n approaches infinity?
a) π
b) e
c) ϕ
d) γ (Euler-Mascheroni constant)
44.A Klein Bottle is a famous mathematical object that is a one-sided surface with what
property?
a) It has a large volume
b) It can hold exactly one liter
c) It has no boundary (no edge)
d) It is made of glass
45.The Mandelbrot set is a famous example of what type of mathematical object?
a) A polyhedron
b) A knot
c) A fractal
d) A vector space
46.The value of the Euler-Mascheroni constant (γ) is approximately:
a) 3.141
b) 2.718
c) 1.618
d) 0.577
47.In the context of complex numbers, what is the modulus of 3+4i?
a) 3
b) 4
c) 5
d) 7
48.The number 'g' (giga) in computing represents 109. What does a googol represent?
a) 1010
b) 1030
c) 10100
d) 101000
49.Which of the following constants is proven to be irrational but is not known to be
transcendental?
a) π
b) e
c) Apéry's constant ζ(3)
d) eπ
50.A tesseract is the four-dimensional analogue of what shape?
a) A sphere
b) A triangle
c) A cube
d) A circle
Mathematical Terms
51.A number that can only be divided evenly by itself and 1 is called a:
a) Prime number
b) Composite number
c) Rational number
d) Integer
52.What is a "derivative" in calculus a measure of?
a) The area under a curve
b) The instantaneous rate of change of a function
c) The sum of an infinite series
d) A type of matrix
53.In statistics, what does "standard deviation" measure?
a) The average of a dataset
b) The most frequent value in a dataset
c) The amount of variation or dispersion of a set of values
d) The middle value of a dataset
54.A "matrix" in mathematics is a:
a) Type of logical proof
b) Rectangular array of numbers
c) Geometric shape
d) Type of number
55.The "integral" of a function in calculus is most commonly associated with finding the:
a) Slope of a tangent line
b) Area under the curve
c) Maximum value of the function
d) Rate of change
56.In set theory, what is the "union" of two sets?
a) The set of elements that are in both sets
b) The set of all elements that are in either set (or both)
c) The set of elements that are in the first set but not the second
d) The set of all possible subsets
57.A "conjecture" is a mathematical statement that is:
a) Proven to be true
b) Proven to be false
c) Believed to be true but has not been formally proven
d) An axiom
58.What is a "vector" in mathematics?
a) A single number
b) A matrix with only one row
c) An object that has both magnitude and direction
d) The solution to an equation
59.The branch of mathematics concerned with the properties of space is called:
a) Algebra
b) Geometry
c) Analysis
d) Number Theory
60.An "isomorphism" in abstract algebra is a:
a) Subgroup of a larger group
b) Structure-preserving mapping between two algebraic structures
c) Type of mathematical proof
d) A group with only one element
61.What does the term "topology" refer to in mathematics?
a) The study of maps and map-making
b) The study of prime numbers
c) The study of properties of geometric objects that are preserved under continuous
deformations
d) The study of algorithms
62.A "proof by contradiction" is a method where one assumes a statement is:
a) True and shows it leads to a known truth
b) False and shows this leads to a logical contradiction
c) True and proves it directly
d) False and finds a counterexample
63.The "cardinality" of a set refers to its:
a) Largest element
b) Number of elements
c) Smallest element
d) Order of elements
64.What is an "eigenvalue" of a matrix?
a) The determinant of the matrix
b) A scalar by which an eigenvector is scaled when the matrix is applied to it
c) The inverse of the matrix
d) The sum of the diagonal elements
65.The "continuum hypothesis" is a famous problem in which area of mathematics?
a) Number Theory
b) Set Theory
c) Geometry
d) Calculus
Awards, Events & History
66.Which of these is often considered the "Nobel Prize of Mathematics"?
a) The Abel Prize
b) The Fields Medal
c) The Wolf Prize
d) The Chern Medal
67.The Fields Medal is awarded to mathematicians under the age of:
a) 30
b) 35
c) 40
d) There is no age limit
68.The International Congress of Mathematicians (ICM), where the Fields Medal is awarded,
is held every:
a) Year
b) Two years
c) Four years
d) Five years
69.The Abel Prize is awarded by which country?
a) Sweden
b) Norway
c) Denmark
d) Switzerland
70.The Clay Mathematics Institute's Millennium Prize Problems consist of how many
unsolved problems?
a) 5
b) 7
c) 10
d) 23
71.Which of the Millennium Prize Problems was solved by Grigori Perelman?
a) The Riemann Hypothesis
b) P vs NP
c) The Poincaré Conjecture
d) The Hodge Conjecture
72.The ancient Babylonians used a number system based on what number?
a) 10
b) 20
c) 60
d) 12
73.The development of calculus in the 17th century was a major event. Who are the two
mathematicians independently credited with its discovery?
a) Euclid and Pythagoras
b) Newton and Leibniz
c) Fermat and Pascal
d) Gauss and Euler
74.The Rhind Mathematical Papyrus is an important historical document from which ancient
civilization?
a) Greek
b) Babylonian
c) Egyptian
d) Chinese
75.Andrew Wiles received widespread fame in 1994 for proving what long-standing
conjecture?
a) Goldbach Conjecture
b) Twin Prime Conjecture
c) Fermat's Last Theorem
d) Riemann Hypothesis
76.The "Bourbaki" group, which began publishing in the 1930s, is a collective of
mathematicians from which country?
a) Germany
b) Russia
c) France
d) United States
77.The concept of zero as a number and its use in calculations was a major contribution
from which mathematical tradition?
a) Greek
b) Roman
c) Indian
d) Egyptian
78.The "Four Color Theorem," which states that any map can be colored with only four
colors, was the first major theorem to be proved using what tool?
a) A slide rule
b) A computer
c) A compass and straightedge
d) Set theory
79.The Wolf Prize is a prestigious international award granted in Israel. In which fields is it
awarded?
a) Mathematics only
b) Mathematics and Physics
c) Agriculture, Chemistry, Mathematics, Medicine, Physics, and Arts
d) Peace, Literature, and Economics
80.The Nevanlinna Prize is awarded for outstanding contributions in:
a) Mathematical aspects of information sciences
b) Abstract algebra
c) Applied mathematics
d) Geometry and topology
Current Affairs & Modern Concepts
81.The "Langlands Program" is a far-reaching web of conjectures that connects which two
major branches of mathematics?
a) Number Theory and Representation Theory
b) Topology and Geometry
c) Logic and Set Theory
d) Calculus and Differential Equations
82.In recent years, which field has seen a surge of interest and application in mathematics,
particularly in areas like optimization and pattern recognition?
a) String Theory
b) Machine Learning / Artificial Intelligence
c) Knot Theory
d) Game Theory
83.The ABC conjecture, for which a proof was proposed by Shinichi Mochizuki, is a problem
in what area of mathematics?
a) Number Theory
b) Topology
c) Logic
d) Combinatorics
84.The use of computers to formally verify mathematical proofs is a growing field known as:
a) Numerical analysis
b) Proof assistants / Interactive theorem proving
c) Computational geometry
d) Algorithmic game theory
85.What is the name of the problem that asks whether every problem whose solution can be
quickly verified by a computer can also be quickly solved by a computer?
a) The Halting Problem
b) The P versus NP problem
c) The Riemann Hypothesis
d) The Collatz Conjecture
86."Topological Data Analysis" (TDA) is a modern approach that uses concepts from
topology to:
a) Solve differential equations
b) Analyze the 'shape' of complex data sets
c) Prove theorems in number theory
d) Design faster algorithms
87.The 2022 Fields Medal was awarded to Maryna Viazovska for her proof of the optimal
sphere packing in which dimension?
a) 4
b) 8
c) 16
d) 24
88."Quantum computing" is a new paradigm of computation based on the principles of:
a) Classical mechanics
b) Quantum mechanics
c) General relativity
d) Thermodynamics
89.The concept of a "blockchain," which underlies cryptocurrencies like Bitcoin, relies
heavily on what mathematical field?
a) Calculus
b) Cryptography
c) Topology
d) Linear algebra
90.The "Collatz Conjecture" is a famous unsolved problem that is simple to state but
appears very difficult to prove. It concerns a sequence involving what basic operations?
a) Addition and subtraction
b) Multiplication and division by 2
c) Squaring and taking square roots
d) Exponentiation and logarithms
91.The "Navier-Stokes existence and smoothness" problem is a Millennium Prize Problem
related to what field?
a) Computer Science
b) Fluid Dynamics
c) Number Theory
d) Quantum Physics
92.Terence Tao, a Fields Medalist, is known for his wide-ranging contributions to many areas
of mathematics, including:
a) Harmonic analysis, PDEs, and combinatorics
b) Logic and set theory
c) Abstract algebra and category theory
d) Financial mathematics
93.The recent proof of the "Geometric Langlands Conjecture" is considered a major
achievement in unifying different areas of mathematics. This work involved a large team
and a proof spanning hundreds of pages. The program is named after which
mathematician?
a) Andrew Wiles
b) Robert Langlands
c) David Hilbert
d) Henri Poincaré
94.What is "tropical geometry"?
a) The study of geometry in tropical climates
b) A field that replaces standard arithmetic with min-plus or max-plus algebra
c) A branch of recreational mathematics
d) The geometry of curved spaces
95.In game theory, the "Prisoner's Dilemma" is a classic example of a game where:
a) Both players always cooperate
b) Rational individuals might not cooperate, even if it appears that it is in their best
interests to do so
c) One player always wins
d) The outcome is completely random
96.The "Birch and Swinnerton-Dyer conjecture" is a Millennium Prize Problem concerning
what mathematical objects?
a) Prime numbers
b) Elliptic curves
c) Matrices
d) Knots
97.The "Yang–Mills existence and mass gap" problem is a Millennium Prize Problem that
originates from what field?
a) Quantum Field Theory
b) Economics
c) Biology
d) Computer Science
98.The study of "random matrices" has found surprising applications in diverse fields, from
nuclear physics to:
a) Number theory (related to the Riemann zeta function)
b) Classical art
c) Political science
d) Culinary arts
99."Homotopy type theory" is a relatively new field of mathematics that connects logic,
computer science, and:
a) Topology
b) Number theory
c) Financial modeling
d) Fluid dynamics
100. A recent trend in pure mathematics is the use of AI and machine learning to do what?
a) Replace human mathematicians entirely
b) Suggest new conjectures and find patterns in complex data
c) Solve all unsolved problems automatically
d) Generate artistic mathematical visualizations
