Babylonians establish the metric of
flat 2-dimensional space by observation, in their efforts to keep track
of land for legal and economic purposes.
Pythagoras, a Greek educated by mystics
in Egypt and Babylon, founds community of men and women calling themselves
mathematikoi, in southern Italy. They believe
that reality is in essence mathematical. Pythagoras noted that vibrating
lyre strings with harmonious notes have lengths that are proportional
by a whole number. The Pythagorean theorem proves by reasoning what the
Babylonians figured out by measurement 1000 years earlier.
Plato, after traveling to Italy and
learning about the Pythagoreans, founds his Academy in Athens, and continues
to develop the idea that reality must be expressible in mathematical terms.
But Athens at that time has developed a notoriously misogynist culture.
Unlike his role model Pythagoras, whose school developed many women mathematikoi,
Plato does not allow women to participate.
Euclid of Alexandria, a gifted teacher,
one of the top mathematics textbooks of recorded history, which organizes
the existing Mediterranean understanding of geometry into a coherent logical
Ionian mathematician Apollonius writes
Conics, and introduces the terms ellipse,
parabola and hyperbola to describe conic sections.
Nicaean mathematician and astronomer
Hipparchus develops what will be known as trigonometry.
by Alexandrian astronomer and mathematician Claudius Ptolemy asserts that
the Sun and planets orbit around the Earth in perfect circles. Ptolemy's
work is so influential that will become official church doctrine when
the Christians later come to rule Europe.
As a glorious 2000 years of ancient
Mediterranean mathematics and science comes to a close, Hypatia of Alexandria,
a renowned teacher, mathematician, astronomer, and priestess of Isis,
is kidnapped from a public religious procession and brutally murdered
by a mob of angry Christian monks.
Hindu mathematician-astronomer Brahmagupta
writes Brahma- sphuta- siddhanta (The Opening
of the Universe). Hindu mathematicians develop numerals and start investigating
The spread of Islam leads to the spread
of written Arabic language. As ancient Greek and Hindu works are translated
into Arabic, a culture of mathematics and astronomy develops. The peak
of this cultural flowering is represented by Arabic mathematician Al-Khworizmi,
working at the House of Wisdom in Baghdad, who develops what will be known
as algebra in his work Hisab al-jabr w'al-muqabala.
Iranian poet, mathematician and astronomer
Omar Khayyam begins his Treatise on Demonstration
of Problems of Algebra, classifying cubic equations that could
be solved by conic sections. Khayyam was such a brilliant poet that history
has nearly forgotten that he was also a brilliant scientist and mathematician.
The moving finger writes...
of Bath translates works of Euclid and Al-Khworizmi into Latin and introduces
them to European scholars.
is published using the revolutionary new technology of the printing press,
leading to a revolution in education and scholarship as information becomes
more difficult for authorities to control.
Copernicus publishes De
revolutionibus orbium coelestium (On the revolutions of the heavenly
spheres) asserting that the Earth and planets revolve about the Sun. The
Catholic Church has accorded an official holy status to Ptolemy's geocentric
Universe. Copernicus avoids prosecution as a heretic by waiting until
the end of his own life to publish his controversial claims.
Pisa University mathematics instructor
Galileo Galilei studies the motion of objects and begins a book De
Motu (On Motion) which he never finishes.
Galileo observes that the period of
a swinging pendulum is independent of the amplitude of the swing.
Johannes Kepler claims in the journal
Astronomia Nova that the orbit of Mars is
an ellipse with the Sun at one focus, and sweeps out equal areas in equal
time. He will later generalize these into his famous Three Laws of Planetary
Galileo makes his first telescope.
His observations of the moon show that it looks like a very large lumpy
rock, not a divinely smooth and perfect shining Platonic heavenly orb.
This discovery has enormously distressing cultural reverberations for
Western culture and religion.
Scottish theologian John Napier, who
does mathematics as a hobby, publishes his discovery of the logarithm
in his work Mirifici logarithmorum canonis descriptio.
Kepler's mother, Frau Katharina Kepler,
is accused of witchcraft by a local prostitute. European witch hunting
was at its peak during Kepler's career, and witch hunting was supported
by all levels of society, including secular officials and intellectuals
in universities. Kepler spends the next several years making legal appeals
and hiding his mother from legal authorities seeking to torture her into
confessing to witchcraft. Examining an accused witch ad
torturam was a standard court procedure during this era.
Under court order, Kepler's mother
is kidnapped in the middle of the night from her daughter's home and taken
to prison. Kepler spends the next year appealing to the duke of Württemberg
to prevent his imprisoned mother from being examined ad
On September 28, Katharina Kepler
is taken from her prison cell into the torture room, shown the instruments
of torture and ordered to confess. She replies "Do
with me what you want. Even if you were to pull one vein after another
out of my body, I would have nothing to admit," and says the
Lord's Prayer. She is taken back to prison. She is freed on October 4
upon order of the duke, who rules that her refusal to confess under threat
of torture proves her innocence. He also orders her accusers to pay the
cost of her trial and imprisonment.
After having spent most of the last
seven years under the legal threat of imminent torture, Katharina Kepler
dies on April 13, still being threatened with violence from those who
insist she is a witch.
Pope Urban VIII promises Galileo that
he is allowed write about Copernican heliocentrism if he treats it as
an abstract proposition.
Kepler uses Napier's logarithms to
compute a set of astronomical tables, the Rudolphine
Tables, whose accuracy is so impressive that it leads to the quiet
acceptance of the heliocentric solar system by everyone in the shipping
Basque mathematician Pierre de Fermat,
the founder of modern number theory, begins his brilliant career by reconstructing
the work of Apollonius on conic sections . Fermat and Descartes pioneer
the application of algebraic methods to solving problems in geometry.
Galileo publishes Dialogue
concerning the two greatest world systems, which argues convincingly
for the Copernican view that the Earth and planets revolve around the
The Inquisition calls Galieo to Rome
to answer charges of heresy against the Catholic Church.
Descartes publishes his revolutionary
Discours de la méthode (Discourse on Method)
containing three essays on the use of reason to search for the truth.
In the third essay Descartes describes analytic geometry, and uses the
letters (x,y,z) for the coordinate system that will later bear his name.
Galileo dies at his villa in Florence,
still under house arrest from charges of heresy.
Cambridge mathematician Isaac Barrow
delivers lectures on modern methods of computing tangents that inspire
his student Isaac Newton towards developing calculus
Newton's "miraculous years"
in math and physics, when he discovers the derivative, which he sees as
a ratio of velocities called fluxions, and
the integral, which he sees as a fluent
of the fluxions. Newton shows that the fluent
and fluxion are inversely related, a result now called the Fundamental
Theorem of Calculus. Newton also develops his ideas on optics and
gravitation. He tries to publish his work in 1671, but the publisher goes
Jacob Bernoulli, who studied mathematics
and astronomy against the wishes of his career-minded parents, teaches
Newtonian mechanics at the University of Basel, and turns mathematical
physics into a family business.
Leibniz publishes the beginning of
his work on differential and integral calculus. He discovers the Fundamental
Theorem of Calculus in his own way. Leibniz originates most of the current
calculus notation including the integral sign. He portrays an integral
as a sum of infinitesimals, a concept rejected by Newton.
Newton publishes Principia
Mechanica after Edmund Halley convinces Newton to write up his
alleged proof that an inverse square force law leads to elliptical orbits.
Newton's Laws of Motion and Law of Gravitation lead to the development
of theoretical physics itself. This event marks a permanent change in
the relationship between human beings and the Universe.
Newton has a nervous breakdown after
his close companion Fatio De Duillier becomes ill and has to return to
Brachistochrone problem solved by Jacob and Johann Bernoulli, an early
result in the calculus of variations.
Thanks to a campaign waged by Newton,
a commission appointed by Royal Society of London President Isaac Newton
rules that Leibniz is guilty of plagiarism against Newton in the discovery
of calculus. English mathematics and theoretical physics go into decline
because those loyal to Newton are hesitant to adopt Leibniz' infinitesimal
and his clean, intuitively appealing notation.
Leonhard Euler begins the field of
topology when he publishes his solution of the Konigsberg Bridge problem.
by Daniel Bernoulli
The multitalented Euler begins the
fields of mathematical analysis and analytical mechanics with Introductio
in analysin infinitorum. Euler introduces the formula eix
= cos x + i sin x
Joseph-Louis Lagrange finds the complete
general solution to the Newtonian equations of motion for a vibrating
string, which explains the harmonic relations observed by Pythagoras 22
Hyperbolic trigonometry -- cosh, sinh
-- is developed.
Henry Cavendish, a wealthy
but paranoid recluse, discovers that the electrostatic force is described
by an inverse square law similar to gravity, but doesn't tell anyone in
the science community.
Lagrange further develops
the analytical mechanics of Euler when he publishes Mécanique
Analytique, revealing Newtonian mechanics to be a rich field of
exploration for mathematicians.
Aristocrat Charles-Augustin de Coulomb,
hiding from the French Revolution after the storming of the Bastille,
shows that the electrostatic force between electric charges was very well
described by an inverse square law, in full analogy with Newtonian gravity.
This becomes known as Coulomb's Law, even though Henry Cavendish was the
first one to demonstrate it.
Lagrange is arrested during the Reign
of Terror, but is rescued by Antoine-Laurent Lavoisier, the founder of
modern chemistry. Unfortunately, Lavoisier's career in chemistry is ended
when he is taken to meet Madame Guillotine on May 8, 1794.
Pierre-Simon Laplace publishes his
work Traité du Mécanique Céleste (Treatise
on Celestial Mechanics) using differential equations to solve problems
in planetary motion and fluid flow.