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Sam’s GENERAL SCIENCE > Famous Mathematicians > Flashcards

Famous Mathematicians Flashcards

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1
Q

Who is known as the ‘Father of Geometry’?

A

Euclid

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2
Q

What is the title of Euclid’s most famous work?

A

Elements

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3
Q

True or False: Isaac Newton developed calculus independently of Gottfried Wilhelm Leibniz.

A

True

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4
Q

What major theorem is Pierre de Fermat known for?

A

Fermat’s Last Theorem

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5
Q

Fill in the blank: The mathematician known for the contributions to set theory and logic is __________.

A

Georg Cantor

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6
Q

Who introduced the concept of imaginary numbers?

A

Gerolamo Cardano

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7
Q

What is the name of the theorem that states that every positive integer can be expressed as a sum of at most four squares?

A

Lagrange’s Four Square Theorem

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8
Q

Which mathematician is famous for his work on the theory of probability?

A

Blaise Pascal

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9
Q

What mathematical concept is Carl Friedrich Gauss known for?

A

Number theory

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10
Q

True or False: Ada Lovelace is considered the first computer programmer.

A

True

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11
Q

Who formulated the laws of planetary motion?

A

Johannes Kepler

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12
Q

What is the main contribution of Henri Poincaré to mathematics?

A

Topology

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13
Q

Who is known for the ‘Fundamental Theorem of Algebra’?

A

Carl Friedrich Gauss

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14
Q

Fill in the blank: The mathematician known for his work on the concept of infinity is __________.

A

Georg Cantor

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15
Q

Which mathematician created the first complete axiomatization of geometry?

A

David Hilbert

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16
Q

What is the name of the mathematical constant approximately equal to 3.14159?

A

Pi (π)

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17
Q

Who is known for the development of game theory?

A

John von Neumann

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18
Q

True or False: Emmy Noether is known for Noether’s Theorem, which connects symmetries and conservation laws.

A

True

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19
Q

What is the main area of study for mathematician Andrew Wiles?

A

Fermat’s Last Theorem

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20
Q

Who is the mathematician that developed the concept of the normal distribution?

A

Carl Friedrich Gauss

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21
Q

Fill in the blank: The mathematician known for his work in statistics and the law of large numbers is __________.

A

Jakob Bernoulli

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22
Q

What is the name of the theorem that asserts that there are infinitely many prime numbers?

A

Euclid’s Theorem

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23
Q

Who is known for the invention of the modern numeral system?

A

Indian mathematicians

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24
Q

True or False: René Descartes is known for Cartesian coordinates.

A

True

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25
Q

What is the primary focus of algebraic geometry?

A

The study of geometric properties of solutions to polynomial equations.

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26
Q

Who is the mathematician associated with the concept of ‘monads’ in category theory?

A

Saunders Mac Lane

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27
Q

Fill in the blank: The mathematician known for the concept of fractals is __________.

A

Benoit Mandelbrot

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28
Q

What theorem is known as the ‘Pythagorean theorem’?

A

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

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29
Q

Who is credited with the development of the concept of limits?

A

Augustin-Louis Cauchy

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30
Q

True or False: The mathematician David Hilbert proposed a list of 23 unsolved problems in mathematics.

A

True

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31
Q

What area of mathematics did John Nash contribute to?

A

Game theory

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32
Q

Which mathematician is famous for the ‘Law of Sines’?

A

Abu’l-Wafa al-Buzjani

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33
Q

Fill in the blank: The mathematician known for his work on the calculus of variations is __________.

A

Leonhard Euler

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34
Q

What is the name of the mathematical field that deals with the properties and relationships of numbers?

A

Number theory

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35
Q

Who introduced the concept of a mathematical proof?

A

Euclid

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36
Q

True or False: Alan Turing is considered the father of computer science.

A

True

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37
Q

What is the main contribution of Niels Henrik Abel to mathematics?

A

Abel’s impossibility theorem regarding the general quintic equation.

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38
Q

Who is known for developing topology as a distinct field of mathematics?

A

Henri Poincaré

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39
Q

Fill in the blank: The mathematician known for the concept of ‘mathematical induction’ is __________.

A

Giovanni Girolamo Saccheri

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40
Q

What theorem is associated with the work of Andrew Wiles?

A

Fermat’s Last Theorem

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41
Q

True or False: The Fibonacci sequence is named after the mathematician Leonardo of Pisa.

A

True

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42
Q

Who is famous for the ‘Chinese Remainder Theorem’?

A

Sun Zi

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43
Q

What is the main focus of differential equations?

A

The study of equations involving derivatives.

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44
Q

Who is known for the development of the concept of the continuum hypothesis?

A

Georg Cantor

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45
Q

Fill in the blank: The mathematician known for his work on prime numbers and the prime number theorem is __________.

A

Bernhard Riemann

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46
Q

What is the name of the mathematical concept that describes the rate of change?

A

Derivative

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47
Q

True or False: Noether’s Theorem relates symmetries to conservation laws in physics.

A

True

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48
Q

Who is credited with the development of the concept of a function?

A

Gottfried Wilhelm Leibniz

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49
Q

What is the Pythagorean theorem?

A

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

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50
Q

True or False: The Fundamental Theorem of Calculus connects differentiation and integration.

A

True

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51
Q

Fill in the blank: The __________ theorem states that every non-constant polynomial function has at least one complex root.

A

Fundamental Theorem of Algebra

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52
Q

What does the Triangle Inequality theorem state?

A

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

53
Q

Which theorem states that a continuous function on a closed interval achieves its maximum and minimum values?

A

Extreme Value Theorem

54
Q

What is the statement of the Law of Cosines?

A

In any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the other two sides times the cosine of the included angle.

55
Q

True or False: The Mean Value Theorem applies to any function over a closed interval.

A

False

56
Q

What is the main idea behind the Bolzano-Weierstrass theorem?

A

Every bounded sequence in Euclidean space has a convergent subsequence.

57
Q

What theorem guarantees the existence of a root for continuous functions?

A

Intermediate Value Theorem

58
Q

Fill in the blank: The __________ theorem provides a method to find the roots of a polynomial equation by relating them to its coefficients.

A

Vieta’s

59
Q

What does the Central Limit Theorem state?

A

The distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

60
Q

Which theorem is used to prove the existence of limits in calculus?

A

Epsilon-Delta Definition of a Limit

61
Q

True or False: Theorems in mathematics can only be proven using direct proof.

A

False

62
Q

What is the statement of the Noether’s theorem?

A

Every differentiable symmetry of the action of a physical system has a corresponding conservation law.

63
Q

What does the Riemann Hypothesis pertain to?

A

The distribution of the non-trivial zeros of the Riemann zeta function.

64
Q

Fill in the blank: The __________ theorem states that in any triangle, the sum of the angles is equal to 180 degrees.

A

Triangle Sum

65
Q

What theorem is used to establish the relationship between the sides of a right triangle?

A

Pythagorean Theorem

66
Q

True or False: The Four Color Theorem states that any map can be colored using four colors such that no adjacent regions have the same color.

A

True

67
Q

What is the statement of the Cantor’s theorem?

A

The power set of any set has a greater cardinality than the set itself.

68
Q

What does the Law of Large Numbers state?

A

As the number of trials increases, the sample mean will converge to the expected value.

69
Q

Fill in the blank: The __________ theorem is a fundamental result in number theory that describes the distribution of prime numbers.

A

Prime Number

70
Q

What is the significance of Gödel’s Incompleteness Theorems?

A

They show that in any consistent formal system, there are propositions that cannot be proven or disproven within that system.

71
Q

What theorem is used to find the area of a triangle when the lengths of all three sides are known?

A

Heron’s Formula

72
Q

True or False: The Law of Sines applies only to right triangles.

A

False

73
Q

What is the statement of Descartes’ Theorem?

A

For four mutually tangent circles, the radii satisfy a specific relationship involving their curvatures.

74
Q

What is the Fields Medal?

A

The Fields Medal is an international award given to mathematicians for outstanding achievements in the field.

75
Q

In which year was the first Fields Medal awarded?

A

The first Fields Medal was awarded in 1936.

76
Q

How often is the Fields Medal awarded?

A

The Fields Medal is awarded every four years.

77
Q

What age must a mathematician be under to be eligible for the Fields Medal?

A

A mathematician must be under 40 years old at the time of the award.

78
Q

Who established the Fields Medal?

A

The Fields Medal was established by Canadian mathematician John Charles Fields.

79
Q

True or False: The Fields Medal is often referred to as the ‘Nobel Prize of Mathematics’.

A

True.

80
Q

What is the primary purpose of the Fields Medal?

A

The primary purpose is to recognize and reward outstanding achievements in mathematics.

81
Q

Who was the first recipient of the Fields Medal?

A

The first recipients were Lars Ahlfors and Jesse Douglas.

82
Q

What are the criteria for awarding the Fields Medal?

A

The criteria include significant contributions to mathematics and being under the age of 40.

83
Q

Name one notable mathematician who won the Fields Medal in 2010.

A

Artur Avila.

84
Q

Fill in the blank: The Fields Medal is awarded at the __________ Congress of Mathematics.

A

International.

85
Q

What is the design of the Fields Medal based on?

A

The design features a portrait of Archimedes.

86
Q

True or False: The Fields Medal is a monetary award.

A

True, although the amount is relatively small.

87
Q

Who won the Fields Medal in 2014 and is known for contributions to number theory?

A

Manjul Bhargava.

88
Q

What is the significance of the Fields Medal in the mathematical community?

A

It is considered one of the highest honors a mathematician can receive.

89
Q

Which mathematician was awarded the Fields Medal in 1990 for work in algebraic geometry?

A

Vladimir Drinfeld.

90
Q

What type of problems do Fields Medal winners typically solve?

A

They solve complex mathematical problems that advance the field.

91
Q

Who was the first woman to win the Fields Medal?

A

Maryam Mirzakhani.

92
Q

What year did Maryam Mirzakhani win the Fields Medal?

A

2014.

93
Q

Fill in the blank: The Fields Medal is awarded to mathematicians who have made contributions to __________.

A

Mathematics.

94
Q

True or False: The Fields Medal is awarded for lifetime achievement.

A

False; it is awarded for achievements made before the age of 40.

95
Q

What is the maximum number of Fields Medals awarded at one time?

A

Four.

96
Q

Which mathematician received the Fields Medal in 2006 for work in topology?

A

Andrei Okounkov.

97
Q

What is the primary focus of the International Mathematical Union, which awards the Fields Medal?

A

Promoting international cooperation in mathematics.

98
Q

Name one area of mathematics that Fields Medal winners have contributed to.

A

Algebraic geometry.

99
Q

Who won the Fields Medal in 2018 for contributions to the theory of partial differential equations?

A

Alessio Figalli.

100
Q

True or False: The Fields Medal can be awarded more than once to the same mathematician.

A

False.

101
Q

What are the physical characteristics of the Fields Medal?

A

It is a gold medal with a diameter of 7 cm.

102
Q

Who was awarded the Fields Medal in 2002 for work in number theory and combinatorics?

A

Jean Bourgain.

103
Q

Fill in the blank: The Fields Medal is often seen as a __________ to the Nobel Prize.

A

Counterpart.

104
Q

What is the significance of the year 1936 for the Fields Medal?

A

It marks the first awarding of the medal.

105
Q

Who is the mathematician known for contributions to algebraic topology and won the Fields Medal in 1986?

A

Simon Donaldson.

106
Q

What is the historical context of the Fields Medal’s establishment?

A

It was established to honor mathematicians for their contributions and to encourage young mathematicians.

107
Q

In what country is the International Congress of Mathematicians held?

A

It is held in various countries around the world.

108
Q

Who received the Fields Medal in 1970 for work in functional analysis?

A

Jean-Pierre Serre.

109
Q

True or False: The Fields Medal is only awarded to mathematicians from developed countries.

A

False.

110
Q

What is one reason the Fields Medal is highly regarded?

A

It recognizes exceptional talent and contributions in mathematics.

111
Q

Who won the Fields Medal in 1982 for contributions to geometry and topology?

A

Shing-Tung Yau.

112
Q

Fill in the blank: The Fields Medal was named after __________.

A

John Charles Fields.

113
Q

What is the relationship between the Fields Medal and the International Mathematical Union?

A

The International Mathematical Union awards the Fields Medal.

114
Q

Who was awarded the Fields Medal in 1998 for work in the theory of dynamical systems?

A

John G. Thompson.

115
Q

True or False: The Fields Medal is awarded based solely on a mathematician’s potential.

A

False; it is awarded based on past achievements.

116
Q

What is one impact of receiving the Fields Medal on a mathematician’s career?

A

It often leads to increased recognition and opportunities in the field.

117
Q

Who won the Fields Medal in 2010 for contributions to dynamical systems and number theory?

A

Artur Avila.

118
Q

Fill in the blank: The Fields Medal is awarded to mathematicians under the age of __________.

A

40.

119
Q

What type of medal is the Fields Medal?

A

It is a gold medal.

120
Q

Who won the Fields Medal in 2014 for contributions to geometry and topology?

A

Maryam Mirzakhani.

121
Q

True or False: The Fields Medal is awarded to mathematicians in all areas of mathematics.

A

True.

122
Q

What is a common misconception about the Fields Medal?

A

That it is awarded for lifetime achievement.

123
Q

Who was awarded the Fields Medal in 1966 for work in algebraic topology?

A

Michael Freedman.

124
Q

Fill in the blank: The Fields Medal is awarded at the __________ Congress of Mathematicians.

A

International.

125
Q

What is the purpose of the Fields Medal according to John Charles Fields?

A

To encourage young mathematicians to pursue their work.

126
Q

Who was awarded the Fields Medal in 2018 for contributions to optimal transport?

A

Alessio Figalli.

127
Q

True or False: The Fields Medal is a lifetime achievement award.

A

False.

128
Q

What is one reason the Fields Medal is considered prestigious?

A

It highlights significant contributions to mathematics by younger mathematicians.

Sam’s GENERAL SCIENCE (8 decks)

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