# 251 Math Trivia Questions and Answers

The topic of mathematics varies greatly, and the history of math dates back to prior to 2000 B.C. Below you will find over 250 Math trivia questions and answers. These questions range in difficulty and were written for the true math enthusiast.

When it comes to math, the fields of math vary greatly. If you are interested in the topic, a great way to delve into it is by understanding the different fields and theorems that spawned them. With these 251 math trivia questions, you will find answers that will provide insight into areas of math, that many people may not even know about. This is a great way to possibly learn something new as a lover of math, but an even better way to deepen your general knowledge of the subject.

So, if you are looking for challenging math trivia questions, you have come to the right place. These questions and answers can give you a great framework for the topic of math for your next trivia night. If you happen to be a trivia enthusiast, you will find these questions challenging, varied, and rich with information on a variety of math related topics. Use them to challenge your friends, yourself, and possibly, even learn some new facts you haven’t known of before.

## 251 Math Trivia Questions

1. What is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena called?

Abstraction

2. What is the ” ∇ ” symbol called in calculus?

A Del or Nabla

3. What is the name for a symmetrical plane curve that forms when a cone intersects with a plane parallel to its side, with an example being, a u-shaped graph of a quadratic function?

The Parabola

4. In mathematics, what is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables called?

A Polynomial

5. Which theorem describes the algebraic expansion of powers of a binomial where, it is possible to expand the polynomial  (? + ?)n  into a sum involving terms of the form  ??b?c, where the exponents  ?  and  ? are non-negative integers with  ? + ? = ?, and the coefficient  ?  of each term is a specific positive integer depending on  ?  and  ? ?

The Binomial Theroem

6. What does the blackboard bold ” ℤ ” symbol denote a set of?

Integers

7. What is the mathematical term for the number that sits above the line in a fraction?

A Numerator

8. Which theorem states that you will have ? roots for an ??ℎ degree polynomial, including multiplicity?

The Fundamental Theorem of Algebra

9. What is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms, or on the basis of previously established statements in mathematics called?

A Theorem

10. What kind of equation is an equation that equates a quartic polynomial to zero, of the general form ??⁴ + ??³ + ??² + ?? + ? = 0 where ? ≠ 0 ?

A Quartic Equation

11. What does the ” ≤ ” symbol mean in mathematics?

Less Than or Equal To

12. What German mathematician and physicist, who made significant contributions to a number fields in mathematics and science said, “Mathematics is the queen of the sciences—and number theory is the queen of mathematics”?

Carl Friedrich Gauss

13. Which theorem states that, if  ƒ (?, ?)  is an analytic germ in two variables, then the solutions  ? = φ (?)  of the equation  ƒ = 0  can be expanded as Puiseux series that are convergent in a neighborhood of the origin?

The Newton-Puiseux Theorem

14. What does the ø symbol denote in set theory?

An Empty Set

15. What kind of function is represented by ” ⌊?⌉ ” ?

A Nearest Integer Function

16. In arithmetic, what is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces a quotient and a remainder smaller than the divisor?

Euclidean Division or Division with Remainder

17. What is the smallest perfect number?

6

18. What is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion, which may use previously established statements, but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference?

A Mathematical Proof

19. Which theorem of probability establishes that in many situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed?

The Central Limit Theorem

20. In ring theory, what is the name of a ring that is a special subset of its elements, generalizes certain subsets of the integers, such as the even numbers or the multiples of 3, addition and subtraction of even numbers preserves evenness, and multiplying an even number by any other integer results in another even number?

An Ideal

21. What are the next three numbers in the golden ration? 1.61_ _ _

803

22. What does the blackboard bold ” ℕ ” symbol denote a set of?

Natural Numbers

23. Which theorem states that, given any separation of a plane into contiguous regions when producing a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color?

The Four Color Theorem

24. Which ancient language is the term “math” derived from?

Greek

In algebraic geometry, what is the ” ” symbol called?

A Lemniscate

25. What is the study of mathematical concepts independently of any application outside of mathematics, where the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles called?

Pure Mathematics

26. What does the ” Φ ” symbol represent?

The Golden Ratio

27. Which theorem describes the asymptotic distribution of the prime numbers among the positive integers, that formalizes the idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs?

The Prime Number Theorem

28. What branch of mathematical logic studies sets, which informally, are collections of objects?

Set Theory

29. What does the ” ≠ ” symbol mean?

Not Equal

30. What is the fundamental relation in Euclidean geometry among the three sides of a right triangle which states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides called?

The Pythagorean Theorem

31. What does logical predicate ” ⊤ ” symbol denote?

Always True

32. Who posed the 18th century question about knowing the probability that a dropped needle on a parallel strip wood floor will lie across a line between two strips?

Georges-Louis Leclerc

33. Who was the German-Austrian logician and mathematician, who published two incompleteness theorems in 1931, that demonstrated the inherent limitations of every formal axiomatic system capable of modeling basic arithmetic?

Kurt Gödel

34. Which theorem states that there are infinitely many prime numbers contained in the collection of all numbers of the form ?? + ?, in which the constants ? and ? are integers that have no common divisors except the number 1 and the variable ? is any natural number?

Dirichlet’s Theorem

35. What is this ” ∫ ” symbol called?

The Integral Symbol

36. What is the numeral system with sixty as its base, that originated with the ancient Sumerians in the 3rd millennium BC and was passed down to the ancient Babylonians, still used in a modified form for measuring time, angles, and geographic coordinates today?

Sexagesimal

37. In set theory, the what is the ” ℶ ” symbol called?

A Beth

38. If changing the order of operands in a binary operation, does not change the result, what is the property of this binary operation?

Commutative

39. Which theorem states that if a continuous function takes on two values ?1 and ?2 at points ? and ?, it also takes on every value between ?1 and ?2 at some point between ? and ??

The Intermediate Value Theorem

40. What is the branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions?

Number Theory

41. What does the ” > ” symbol in mathematics mean?

Greater Than

42. What is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane called?

The Area

43. Who was the Persian polymath and mathematician whose most notable work was on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics and contributed to the understanding of the parallel axiom?

Omar Khayyam

44. What is the ” ∘ ” symbol called in algebraic operations?

The Composition Operator

45. What does the acronym MSC, which is an alphanumeric classification scheme collaboratively produced from two major mathematical reviewing databases, stand for?

Mathematics Subject Classification

46. In mathematics, what is the name of the periodic function composed of harmonically related sinusoids, combined by a weighted summation, and with appropriate weights, one cycle of the summation can be made to approximate an arbitrary function in that interval?

A Fourier Series

47. Which theorem is the statement that every convex set in ℝⁿ which is symmetric with respect to the origin and which has volume greater than 2ⁿ contains a non-zero integer point?

Minkowski’s Theorem

48. In combinatorial mathematics, what is a permutation of the elements of a set, such that no element appears in its original position and is a permutation that has no fixed points called?

A Derangement

49. What does the ” ≥ ” symbol mean?

Greater Than or Equal To

50. What is the subfield of mathematics that explores the formal applications of logic to mathematics?

Mathematical Logic

51. Which theorem of linear algebra states that every square matrix over a commutative ring satisfies its own characteristic equation?

The Cayley–Hamilton Theorem

52. What does the abbreviation ” ∋ ” mean?

“Such that” or “Under the Condition that

53. Which branch of mathematics is concerned with properties of space that are related with distance, shape, size, and relative position of figures?

Geometry

54. What is the name of the widely read expository mathematical journal founded by Benjamin Finkel in 1894, published ten times each year by Taylor & Francis ,for the Mathematical Association of America?

The American Mathematical Monthly

55. What does the ” ¬ ” symbol read as in basic logic?

Not

56. In combinatorics, what problem is this the answer to? (? − ?) ⁄ (? + ?)

Bertrand’s Ballot Problem

57. What is the study of mathematical models of strategic interaction among rational decision-makers, and has applications in all fields of social science, as well as in logic, systems science and computer science called?

Game Theory

58. In ?^?, what would the ” ^ ” symbol denote?

Exponentiation

59. What does the ” ∥ ” symbol denote in elementary geometry?

Parallelism

60. Which two mathematicians independently developed calculus in the late 17th century?

Isaac Newton and Gottfried Wilhelm Leibniz

61. Which theorem states that every integer >1 has a prime factorization and that prime factorization is unique?

The Fundamental Theorem of Arithmetic

62. What kind of number is the square root of 2?

An Irrational Number

63. What does ” Ω ” symbol mean in math?

The Unit for Resistance or Ohms

64. What kind of numbers do number theorists study?

Prime Numbers

65. Who solved the Basel problem, first posed by Pietro Mengoli in 1650?

Leonhard Euler

66. What does the set ? ⊃ ? mean?

? is a Strict Superset of ?

67. Which theorem states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients?

The Abel–Ruffini Theorem

68. What does the logical predicate “⊥” symbol denote?

Always False

69. What is the name of the mathematical curve that describes a smooth periodic oscillation in a continuous wave and occurs often in both pure and applied mathematics?

Sine Wave or Sinusoid

70. In mathematics, what indicates how many times one number contains another?

A Ratio

71. What is the value of a function that must be provided to obtain the function’s result called?

An Argument or an Indépendant Variable

72. In number theory, what does the ” # ” symbol denote?

A Primorial

73. Which ancient Greek philosopher are Platonic solids named after?

Plato

74. In mathematics, what is the amount “left over” after performing some computation called?

The Remainder

75. Who proved that the sum of the reciprocals of all prime numbers diverges?

Leonhard Euler

76. What is the study of algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers called?

Ring Theory

77. In mathematics, what is the name of the technique for getting information on the number of positive real roots of a polynomial, which asserts that the number of positive roots is at most the number of sign changes in the sequence of polynomial’s coefficients, and that the difference between these two numbers is always even?

Descartes’ Rule of Signs

78. What does the ” ∖ ” symbol denote in set theory?

The Set Difference

79. In number theory, what is the name of a positive integer that is equal to the sum of its positive divisors, excluding the number itself?

The Perfect Number

80. In mathematics, what is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found called?

A Conjecture

81. Who was the Persian mathematician who has been credited with proposing the idea of a function and also developed a novel method for determining the conditions under which certain types of cubic equations would have two, one, or no solutions?

Sharaf al-Din al-Tusi

82. What is the application of probability theory, specifically to mathematical techniques, which is used for mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory called?

Mathematical Statistics

83. What is the name of the equation, which is any Diophantine equation of the form ?² − ??² = 1 where ? is a given positive non-square integer and integer solutions are sought for ? and ??

Pell’s Equation

84. What does the blackboard bold ” ℚ ” symbol denote a set of?

Rational Numbers

85. Who was the Dutch mathematician and philosopher that established himself as the founder of modern topology, with his fixed-point theorem and the topological invariance of dimension?

L. E. J. Brouwer

86. In Euclidean geometry, which theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral, which is a quadrilateral whose vertices lie on a common circle?

Ptolemy’s Theorem

87. What kind number is a number that can be expressed as the ratio of two integers?

A Rational Number

88. Who first presented the form of the theorem, which later became Green’s theorem?

Augustin-Louis Cauchy

89. What is the method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape called?

The Method of Exhaustion

90. Which theorem states that a natural number ? > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of ??

Wilson’s Theorem

91 .Who is de Moivre’s formula named after?

Abraham de Moivre

92. What does the ” ∨ ” symbol read as in basic logic?

“Or”

93. What is the algebraic structure that is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers?

A Ring

94. Which theorem was the first major theorem to be proved using a computer?

The Four Color Theorem

95. Who proved the polyhedron formula?

Leonard Euler

96. What are the next three numbers of pi? 3.14_ _ _

159

97. In logic, what is the procedure by which an entire system is generated in accordance with specified rules by logical deduction from certain basic propositions, which in turn are constructed from a few terms taken as primitive called?

Axiomatic Method

98. Who was the Italian mathematician and glottologist that authored over 200 books and papers, and was a founder of mathematical logic and set theory?

Giuseppe Peano

99. In number theory, what is the theorem that states that for any integer ? > 3, there always exists at least one prime number ? with ? < ? < 2? – 2 ?

Bertrand’s Postulate

100. What are two quantities in, if their ratio is the same as the ratio of their sum to the larger of the two quantities?

The Golden Ratio

101. What is the perimeter of a circle called?

The Circumference

102. What is the type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set, with two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows?

Hyperbola

103. In combinatorics, what is the counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets called?

The Inclusion–Exclusion Principle

104. Who was the Persian polymath who produced vastly influential works in mathematics, astronomy, and geography and wrote the treatise on algebra, The Compendious Book on Calculation by Completion and Balancing?

105. Which theorem states that a polynomial ƒ(?) has a factor (? − ?) if and only if ƒ(?) = 0 ?

The Factor Theorem

106. Which theorem states that if polynomial ƒ(?) is divided by a linear binomial of (? – ?) then the remainder will be ƒ(?). Factor Theorem states that if ƒ(?) = 0 in this case, then the binomial (? – ?) is a factor of polynomial ƒ(?) ?

The Remainder Theorem

107. What does the ” ∩ ” symbol denote in set theory?

A Set Theoretic Intersection

108. In the foundations of mathematics, what is the term that came from a famous British polymath and mathematician showing that some attempted formalizations of the naive set theory created by Georg Cantor led to a contradiction?

109. What does the ” < ” symbol mean in mathematics?

Less Than

110. In number theory, what kind of numbers are “almost rational”, and can thus be approximated “quite closely” by sequences of rational numbers?

Liouville Numbers

111. What is the mathematic study of points of algebraic varieties with coordinates in the integers, rational numbers, and their generalizations, which are typically fields that are not algebraically closed, such as number fields, finite fields, function fields, and p-adic fields?

Diophantine Geometry

112. Which theorem states that, in a party of ? persons, if every pair of persons has exactly one common friend, then there is someone in the party who is everyone else’s friend?

The Friendship Theorem

113. In the mathematical field of topology, what is a continuous function between topological spaces that has a continuous inverse function called?

A Homeomorphism

114. What is this equation called? ?² + ?² = ?²

The Pythagorean Equation

115. In the field of algebra, what is a ring formed from the set of polynomials in one or more variables with coefficients in another ring, often a field called?

A Polynomial Ring

116. Which theorem in combinatorics both follows from and ultimately generalizes Burnside’s lemma on the number of orbits of a group action on a set?

The Pólya Enumeration Theorem

117. What does the ” √ ” symbol denote?

The Square Root

118. What is the branch of number theory that uses methods from mathematical analysis to solve problems about the integers?

Analytic Number Theory

119. In mathematics, what is a set S which is the set of all subsets of S, including the empty set and S itself called?

The Power Set

120. Which theorem links the concept of differentiating a function with the concept of integrating a function?

Fundamental Theorem of Calculus

121. What is the ratio of a circle’s circumference to its diameter called?

Pi

122. What kind of function is represented by ⌈x⌉ ?

A Ceiling Function or Ceil

123. What is the name of the professional society, founded in 1915, that focuses on mathematics accessible at the undergraduate level, with 25,000+ members, spanning university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry professionals?

The Mathematical Association of America or MAA

124. What kind of real number cannot be written as a simple fraction?

An Irrational Number

125. What is the name of the theorem that is an efficient method for computing the greatest common divisor of two integers, the largest number that divides them both without a remainder, and is named after an ancient Greek mathematician, who first described it in his book Elements?

The Euclidean Algorithm

126. What is does this formula represent? 1 – ⅓ + ⅕ – ¹⁄₇ + ¹⁄₉ – ⋯ = π⁄₄

The Leibniz Formula for Pi

127. The sum of the three angles of any triangle is equal to how many degrees?

180 Degrees

128. Which theorem states that if a function ? is continuous on the closed interval [?,?] and differentiable on the open interval (?,?), then there exists a point ? in the interval (?,?) such that ?'(?) is equal to the function’s average rate of change over [?,?] ?

Mean Value Theorem

129. What was the Swiss mathematician who made important and influential discoveries in many branches of mathematics, such as calculus, graph theory, and analytic number theory, while also introducing much of the modern mathematical terminology and notation?

Leonhard Euler

130. What does this equation represent? ? = ?θ

The Spiral of Archimedes

131. Which theorem states that every natural number can be represented as the sum of four integer squares?

Lagrange’s Four-square Theorem

132. What is the mathematical term for the number that sits below the line in a fraction?

The Denominator

133. In two-dimensional geometry, which postulate states that if a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles?

The Parallel Postulate

134. Which theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side?

The Triangle Inequality Theorem

135. What does the ” ∈ ” symbol mean in set theory?

Is an Element of

136. Which theorem is a hypothesis about the possible sizes of infinite sets and states, there is no set whose cardinality is strictly between that of the integers and the real numbers?

The Continuum Hypothesis

137. What is the name of the explicit formula in linear algebra, which is the explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution, and expresses the solution in terms of the determinants of the coefficient matrix and of matrices obtained from it by replacing one column by the column vector of right-hand-sides of the equations?

Cramer’s Rule

138. What is the branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them such as addition, subtraction, multiplication, division, exponentiation and extraction of roots called?

Arithmetic

139. Which theorem states that if two sides of a triangle are congruent, then angles opposite to those sides are congruent?

The Isosceles Triangle Theorem

140. What is a binary relation between two sets that associates to each element of the first set exactly one element of the second set called?

A Function

141. In Mathematics, what is the study of the relationship between formal theories and their models, taken as interpretations that satisfy the sentences of that theory called?

Model Theory

142. Which theorem states that if  ?  is a prime number, then for any integer  ?, the number  ?p − ?  is an integer multiple of  ??

Fermat’s Little Theorem

143. What does the symbol ” ? ” represent in math?

Euler’s Number

144. What is a set endowed with some additional features on the set, such as an operation, relation, metric, or topology, where often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance called?

A Mathematical Structure

145. What is the name of the mathematics formula that is an approximation for factorials, which is a good approximation, leading to accurate results even for small values of ??

Stirling’s Formula or Stirling’s Approximation

146. What is the name of the historically notable problem in mathematics, where the problem was to devise a walk through of a Russian city, where the walker would only cross each of two bridges between two islands once?

The Seven Bridges of Königsberg

147. In mathematics, what is a method for calculating a function that cannot be expressed by just elementary operators such as addition, subtraction, multiplication and division, with examples that include a Taylor series, a Maclaurin series, a Laurent series, a Dirichlet series, a Fourier series, and more?

A Series Expansion

148. In which ancient cultures did elementary arithmetic such as addition, subtraction, multiplication and division first appear, according to archaeological record?

Babylon and Egypt

149. Which theorem of plane geometry states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle?

Morley’s Trisector Theorem

150. In group theory, what is the order of a group and the number of elements in its set called?

Its Cardinality

151. What is the name of the association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs, which goes by the acronym AMS?

American Mathematical Society

152. What does the ” ∪ ” symbol denote in set theory?

A Set Theoretic Union

153. Which theorem of set theory states that, if there exist injective functions ? : ? → ? and ? : ? → ? between the sets ? and ?, then there exists a bijective function ℎ : ? → ??

Schröder–Bernstein Theorem

154. What is the branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations?

Algebraic Number Theory

155. Who was the English mathematician, known for his achievements in number theory, mathematical analysis, the Hardy–Weinberg principle in biology, and his 1940 essay, A Mathematician’s Apology?

G. H. Hardy

156. Which theorem represented by this formula? ? = ? + ᵇ⁄₂ − 1

Pick’s Theorem

157. What does the ” ≡ ” symbol mean in math?

Identical To

158. Which ancient language is the term “algebra” derived from?

Arabic

159. In the hexagrammum mysticum theorem, if six arbitrary points are chosen on a conic and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon meet at three points which lie on a straight line; what is the name of the line where the hexagon points meet?

The Pascal Line

160. In mathematics, what is a value of a continuous quantity that can represent a distance along a line or alternatively, a quantity that can be represented as an infinite decimal expansion called?

A Real Number

161. In set theory, what is the ” ” symbol called?

An Aleph

162. In algebra, what is a structure-preserving map between two algebraic structures of the same type such as two groups, two rings, or two vector spaces called?

A Homomorphism

163. Which is the mathematical study of continuous change called?

Calculus

164. What operation does the ” ! ” symbol denote?

A Factorial Operation

165. In arithmetic, what is the term for a quantity produced by the division of two numbers?

A Quotient

166. What is the theorem of real analysis, which states that for almost every point, the value of an integrable function is the limit of infinitesimal averages taken about the point?

The Lebesgue Differentiation Theorem

167. What does this formula represent? ?=π

The Area of a Circle

168. What does the blackboard bold ” ℝ ” symbol denote a set of?

Real Numbers

169. What is the branch of mathematics, that classically studies zeros of multivariate polynomials?

Algebraic Geometry

170. What is this equation a general mathematical representation of? ??³ + ??² + ?? + ? = 0

A Cubic Equation

171. What is the name of the operator used often in vector calculus as a vector differential operator, that when applied to a function defined on a one-dimensional domain, denotes the standard derivative of the function as defined in calculus?

Del or Nabla

172. Who introduced the axiomatic method, still used today?

Giuseppe Peano

173. Which Swiss mathematician initially introduced a theorem to Guillaume de l’Hôpital in 1694, that would later go on to become the L’Hôpital’s rule?

Johann Bernoulli

174. In additive number theory, who first made the observation on the theorem on sums of two squares, published in 1625?

Albert Girard

175. What does the ” ∤ symbol denote?

Non-divisibility

176. Which theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle and states that the products of the lengths of the line segments on each chord are equal?

Intersecting Chords Theorem

177. What is the name of the major international reviewing service that provides reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe?

zbMATH or Zentralblatt MATH

178. What does the ∧ symbol read as in basic logic?

“And”

179. Which ancient language is the term “equal” derived from?

Latin

180. Who was the influential German mathematician that discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics, particularly in proof theory?

David Hilbert

181. Which theorem of projective geometry states that two triangles are in perspective axially if and only if they are in perspective centrally?

Desargues’s Theorem

182. What is the plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant, and generalizes a circle?

An Ellipse

183. What does the ” ∏ ” symbol denote of a finite number of terms, in linear and multilinear algebra?

The Product

184. Which theorem states that any sequence of (?-1)^2+1 distinct real numbers contains a monotone subsequence of length ? ?

Erdős-Szekeres Theorem

185. In Mathematics, what assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data?

An Integral

186. What does the blackboard bold ” ℂ ” symbol represent a set of?

Complex Numbers

187. In probability theory, what is the name of the paradox which shows that in a set of ? randomly chosen people, some pair of them will have the same birthday?

The Birthday Problem or the Birthday Paradox

188. Who are the finite group theory Sylow theorems named after?

Peter Ludwig Sylow

189. What is the name of this broad area of mathematics, which is the study of mathematical symbols and the rules for manipulating these symbols and functions is a unifying thread of almost all of mathematics, including everything from elementary equation solving to the study of abstractions such as groups, rings, and fields?

Algebra

190. Which theorem states that no three positive integers ?, ?, and ? satisfy the equation ?ⁿ + ?ⁿ = ?ⁿ for any integer value of ? greater than 2?

Fermat’s Last Theorem

191. What are the next three numbers of Euler’s number? 2.718_ _ _

281

192. What does this formula find the sum of, where ? is the number of terms, ?1 is the first term and ? is the common ratio?  ??=?1(1−??)1−?,?≠1

A Finite Geometric Series

193. What does the ” ⊻ ” symbol denote in basic logic?

The Exclusive Or

194. What is the Delian problem more commonly known as?

Doubling the Cube

195. What is the study of algebraic structures, which includes groups, rings, fields, modules, vector spaces, lattices, and algebras called?

Abstract Algebra or Modern Algebra

196. Which proposition states that the nine-point circle of any triangle is tangent internally to the incircle and tangent externally to the three excircles?

Feuerbach’s Theorem

197. Which theorem proves there are infinitely many primes?

Euclid’s Theorem

198. What is the name of the identities, that are a set of three identities in vector calculus relating the bulk with the boundary of a region on which differential operators act?

Green’s Identities

199. What was complex analysis traditionally known as?

The Theory of Functions of a Complex Variable

200. In mathematics, what is a multiplicative factor in some term of a polynomial, a series, or any expression, which is usually a number, but may be any expression, including variables such as ?, ? and ? ?

A Coefficient

201. What does the ” ∉ ” symbol mean in set theory?

Not In

202. Which theorem states that the intersection of a variety of degree ? with a variety of degree ? in complex projective space is either a common component or it has ?? points when the intersection points are counted with the appropriate multiplicity?

Bezout’s Theorem

203. Which ancient Greek mathematician is considered to be one of the greatest of all time, with achievements that include deriving an accurate approximation of pi; defining and investigating the spiral that now bears his name; and creating a system using exponentiation for expressing very large numbers?

Archimedes

204. What is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns called in mathematics?

A Matrix

205. What are the two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modeling basic arithmetic?

Gödel’s Incompleteness Theorems

206. What is the π symbol called?

Pi

207. Which branch of mathematics deals with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions, and these theories are usually studied in the context of real and complex numbers and functions?

Analysis

208. What is the name of the type of triangle where the three points of intersection of the adjacent angle trisectors form an equilateral triangle?

A Morley Triangle

209. When a triangle’s sides are a Pythagorean Triple, what kind of triangle is it?

A Right Angled Triangle

210. In mathematics, what is the term for the fundamental algebraic structure where addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do?

A Field

211. Which area of mathematics is primarily concerned with counting, both as a means and an end in obtaining results, certain properties of finite structures, and finding the best structure or solution among several possibilities?

Combinatorics

212. Which mathematical proof is a technique that is used to prove that a statement ?(?) holds for every natural number ? = 0, 1, 2, 3, … meaning that the overall statement is a sequence of infinitely many cases?

Mathematical Induction

213. What does the set ? ⊂ ? mean?

? is a Strict Subset of ?

214. What is the major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques?

Proof Theory

215. Which theorem of set theory states that the cardinality of a set is strictly less than the cardinality of its power set, or collection of subsets?

Cantor’s Theorem

216. What term denotes the mathematics developed or practiced by the people of Mesopotamia?

Babylonian Mathematics

217. In probability theory, what is a sequence of random variables for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values called?

A Martingale

218. Who developed internal set theory, the mathematical theory of sets that provides an axiomatic basis for a portion of the nonstandard analysis introduced by Abraham Robinson?

Edward Nelson

219. Which theorem states that if ?₁, …, ?n are algebraic numbers that are linearly independent over the rational numbers ℚ, then ?ª₁, …, ?ªn are algebraically independent over ℚ?

Lindemann–Weierstrass Theorem

220. What kind of number in mathematics, is a number that is not algebraic, i.e. not the root of a non-zero polynomial with rational coefficients?

A Transcendental Number

221. What is the ” ∆ ” symbol called in calculus?

The Laplace Operator or a Laplacian

222. What is the colloquial term for a number that can be written without a fractional component?

An Integer

223. Which theory of probability theorem describes the result of performing the same experiment a large number of times and according to the law, the average of the results obtained from a large number of trials should be close to the expected value and will tend to become closer to the expected value as more trials are performed?

The Law of Large Numbers

224. What does the ” : ” symbol denote of two quantities?

The Ratio

225. In number theory, what is the theorem that is about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers?

226. Which ancient language is the term “geometry” derived from?

Greek

227. Taylor’s theorem is named after which 18th century mathematician?

Brook Taylor

228. What is the only even prime number?

2

229. What does the ” ∥ ” symbol denote in elementary geometry?

Parallelism

230. What is the process in mathematics of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena called?

Abstraction

231. What does the ” ∀ ” symbol read as in basic logic?

For All

232. What is the title of the book of mathematical proofs by Martin Aigner and Günter M. Ziegler, which contains 45 sections in the sixth edition, each devoted to one theorem but often containing multiple proofs and related results?

Proofs from THE BOOK

233. What is the mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity?

Big O Notation

234. What does the ” ∑ ” symbol denote of a finite number of terms, in linear and multilinear algebra?

The Sum

235. What is the mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry, using the theory of plane and space curves and surfaces in the three-dimensional Euclidean space?

Differential Geometry

236. In group theory, GH denotes what, of the groups G and H?

The Wreath Product

237. What kind of function is represented by ” ⌊x⌋ ” ?

A Floor Function

238. What is the name of the geometric formula that gives the area of a triangle when the length of all three sides are known, and there is no need to calculate angles or other distances in the triangle first?

Heron’s Formula

239. What is the philosophy of mathematics term that asserts that it is necessary to find a mathematical object to prove that something exists?

Constructivism

240. What is the name of the journal published by the American Mathematical Society that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science?

Mathematical Reviews

241. What does the ” ≈ ” symbol mean?

Approximately Equal To

242. Which fundamental tool of calculus is a function of a real variable that measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value)?

The Derivative

243. Which numeral system and the rules for the use of its operations, are still in use almost exclusively throughout the world today?

Hindu–Arabic Numeral System

244. What is the name of a sequence of numbers such that the difference between the consecutive terms is constant, for example, the sequence 5, 7, 9, 11, 13, 15?

An Arithmetic Progression

245. Who wrote the mathematical treatise Elements, which consists of 13 books and is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions?

Euclid

246. What is the branch of mathematics that investigates the intuitive notion of order using binary relations and provides a formal framework for describing statements such as “this is less than that” or “this precedes that”?

Order Theory

247. What is the name of the mathematical model of computation that defines an abstract machine that manipulates symbols on a strip of tape according to a table of rules, and given any computer algorithm, is capable of simulating that algorithm’s logic?

A Turing Machine

248. What does the ” ∃ ” symbol read as in basic logic?

“There Exists”

249. What is the name of this formula, typically used in applications? ln ?! = ? ln ? – ? + 0(ln ?)

Stirling’s Formula

250. In probability theory, which theorem says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value?

The Optional Stopping Theorem

251. Which theorem states that for any continuous function ƒ mapping a compact convex set to itself there is a point ?₀ such that ƒ( ?₀ ) = ?₀ ?

The Brouwer Fixed-point Theorem

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