History of Mathematics LET reviewer

 Who published a treatise on trigonometry which contains the earliest use of our abbreviations:

sin, tan, sec, for sine, tangent and secant?

-Albert Gerard

An 18th century Swiss Mathematician, he introduced the “Law of Large Numbers” in his (The Art

of Conjecture). In Statistics, this implies that the larger the sample, the more likely will the

sample become representative of the population. Who was he?

-Jacob Bernoulli

He has been described as the greatest “might have been” in the history of Mathematics.

-Blaise Pascal

He invented a method of determining the optimal values of a linear function subject to certain

constraints. This method is known as linear programming? Who was he?

-George Dantzig

He was a 16th-century mathematician, who was the first to define that the probability of an

event to happen is the quotient of the number of favorable outcomes and the number of all

outcomes. Who was he?

-Girolamo Cardano

The first to discover “zero”.

-Indian

He was mostly remembered for his formula for( cos 𝑥 + 𝑖𝑠𝑖𝑛𝑥)*, which was important in the

early development of the theory of complex numbers and for predicting the day of his own

death.

-Abraham de Moivre

He achieved real fame when he submitted a paper to the Institute solving one of Fermat’s claims

on polygonal numbers made to Mersenne. He also wrote the memoir on definite integrals that

later became the basis of his theory of complex functions.

-Augustin Cauchy

Italian Mathematician during the Renaissance period who was credited for solving one of the

outstanding ancient problems of mathematics, cubic equations.

-Scipione del Ferro

A Russian Mathematician in the 19th century who would instead develop geometry without

Euclid’s fifth postulate and whose achievement exhibits the development of non- Euclidean

Geometry.

-Nikolai Lobachevsky

A Greek mathematician who remembered for his prime number sieve

-Eratosthenes

He was the mathematician who proposed basic descriptions of a point, a line and shapes. He

also discovered that square root of two is an irrational number and that there were infinitely

many prime numbers.

-Euclid

An 18th century mathematician who enunciated the principles of the Calculus of variations and

became a lecturer in the Royal Artillery School at the age of 19

-Louis Lagrange

Known as the father of modern analysis during 19th century who also devised tests for the

convergence and contributed to the theory of periodic functions, Abelian functions, elliptic

functions, etc.

-Karl Wierstrass

He proved his famous “Basis Theorem” as he worked on invariant theory and challenged

mathematicians to solve fundamental questions that led to his famous speech “the Problems of

Mathematics”.

-David Hilbert

A “grand” Russian mathematician who gave the basis for applying the theory of probability to

statistical data, worked on number of prime numbers not exceeding a given number, and

proved Bertrand’s conjecture in 1850.

-Patnuti Chebyshev

A mathematician of medieval ages who invented a type of coordinate geometry by finding the

logical equivalence between tabulating values and graphing them.

-Nicole Oresme

rich mathematician in France who invented a new, non-Greek way of doing geometry, now

called “projective” or “modern geometry”.

-Girard Desarques

He was considered a universal genius by his contemporaries whose work encompasses not only

Mathematics and Philosophy but also Theology, Law, Diplomacy, Politics, and Physics. He also

developed the basic notations of his version of the Calculus and perfected the binary system of

arithmetic.

-Gottfried Leibnitz

Archimedes proved, among many other geometrical results, that the volume of a sphere is two-thirds the volume of a circumscribed cylinder. This he considered his most significant accomplishments, requesting that a representation of a cylinder circumscribing a sphere be inscribed on his tomb.

-ARCHIMEDES OF SYRACUSE

A 19th century mathematician who added the integers from 1 to 100 within seconds by a flash of

mathematical insights.

-Johann Carl Friedrich Gauss

He measured the length of the year as 365.2421986 days. He was well known for inventing the

method of solving cubic equations by intersecting a parabola with a circle and for Fitzgerald’s

popular translation of Rubaiyat.

-Omar Khayyam

One of the earliest cities of the world built in India and was built to carefully planned and

tessellations.

-Indus

He did notable work in Geometry, particularly studying higher plane curves. He also considered

the geometric problem of finding the difference between the volume of the frustum of a solid of

revolution and the volume of the cylinder of the same height as frustum.

-Colin Maclaurin

An extinct Mesoamerican culture with surviving treatise on astronomy called Dresden Codex

and used vigesimal number system.

-Mayans

It is the famous Chinese Mathematics book of all time which is also called Nine Chapters on

Mathematical Art.

-Jiuzhang Suanshu or Suàn shù shū

A Bernoulli who considered the function 𝑦 = 𝑥^x. and investigated series using the method of

integration by parts.

-Johann Bernoulli

The FIRST mathematician to attempt to classify according to the types of equations that produce

them and also made contributions to the theory of equations.

-Rene Descartes

He was the writer of set theory and was first to appreciate the value of one-to-one correspondence for set theory.

-Georg Philip Cantor

He wrote De Triangulus Omnimodis, a systematic account of methods for solving triangles, and

made important contributions to Trigonometry and Astronomy.

-Regiomontanus

His greatest contributions include such groundbreaking texts in invention of divining rods used

as multiplication tables.

-John Napier

This century came to be known as the Age of Scientific Revolution which saw an unprecedented

explosion of mathematical and scientific ideas across Europe.

-17th century

It is a period prior to people kept written records.

-prehistory

An 18th century mathematician who invented an analytical machine that can tabulate the values

of any function and print the results.

-Charles Babbage

To whom the Greeks inherited their mathematical basis?

-babylonians

People in Early Civilization who used Quipo to encode the numerical details and a counting

board, called YUPANA, to solve mathematical problems.

-Incans

A 17th century French mathematician, philosopher, and scientist who was honored by having

Cartesian coordinate system. His rule of signs is also a commonly used method in modern

Mathematics.

-Rene Descartes

He was considered as the father of differential geometry who introduced geometrie descriptive

now known as orthographic projection

-Gaspard Monge, Comte de Péluse

Who laid the foundations for differential and integral Calculus?

-Sir Isaac Newton

Who introduced topographical methods into complex function theory and examined the zeta

function (s) = (1/ns) = (1 – p-s)-1 which resulted to one of the most important of the unsolved

problems f Mathematics?

-Bernhard Riemann

16th century who proposed the “Apollonian Problem” (drawing a circle to touch 3 given circles)

and introduced the first systematic algebraic notation in his book “In Artem Analyticam Isagoge”

(Introduction to the Analytic Art)

-Francois Viete

A Bernoulli who won in Paris Academy on 1725 because of his designed of an hour glass to be

used at sea and published Mathematical exercises in 1724 which consisted of four topics.

-Daniel Bernoulli

An Italian mathematician best known today by his principle “the volume of two objects are

equal if the areas of their corresponding cross-sections are in all cases equal” and was

responsible for introducing logarithms as a computational tool in Italy.

-Bonaventura Cavalieri

Cavalieri Principle: the volume of two objects are

equal if the areas of their corresponding cross-sections are in all cases equal