THE CONCEPT OF INFINITY TIMELINE

BLAISE PASCAL, FRANCE, 1623-1662

1662 BCE

Blaise Pascal was a French mathematician, physicist, inventor, writer and Catholic theologian. So he thinks that infinity should not be looked at as something we can explain.
He also states that mankind is condemned to live in a state of instability and uncertainty because it is between infinite and nothingness: in fact he believes that man is nothing compared to infinity but, at the same time, everything compared to nothingness.

RENÉ DESCARTES, FRANCE 1596-1650

1650 BCE

Descartes was a French philosopher, mathematician, and scientist who is regarded as one of the greatest philosophers in history.
In The Meditations on First Philosophy he presents with an alleged proof for the existence of God that proceeds from the existence of an idea of an infinite being in the human mind—an idea of God—to the existence of God himself.

ZENO OF ELEA, MAGNA GRECIA 490-430 B.C.

430 BCE

The Zenonian legacy is a number of arguments known as paradoxes because of their implausible conclusions. Many of them have the form of an antinomy, which is a special kind of reductio ad absurdum argument and implies the impossibility of an infinite division of space or time.

ARISTOTLE, GREECE 384-322 B.C.

322 BCE

Aristotle famously rejects infinity in mathematics and physics, with some notable exceptions.
Aristotle argues that in the case of magnitudes, an infinitely large magnitude and an infinitely small magnitude cannot exist. In fact, he thinks that universe is finite in size. Since it is always possible to divide a magnitude, the series of divisions is unending and so is infinite. This is a potential, but never actual infinite. For each division potentially exists.

ARCHIMEDES, SYRACUSE 287-212 BC

212 BCE

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor and astronomer. He is considered the greatest mathematician of antiquity and one of the greatest of all time. Archimedes used Eudoxus' method of exhaustion to determinate the area of a circle by incribing in it a sequence of regular polygons with an increasing number of angles. In fact the circle can be considered a polygon with infinite angles

EUCLID, GREECE III BC

111 BCE

Greek mathematician, often referred to as the "founder of geometry". He worked on infinite by using a mathematical point of view, in fact he developed a theorem which asserts that there are infinitely many prime numbers.

ST. AUGUSTINE, ALGERIA 354-430

430

Aurelio Augustine of Hippo was a Berber philosopher, bishop and theologian with the Roman citizenry. He stated that the concept of infinity had been put in mankind by an infinite identity, known as God, which humanity itself can't reach because of God's divine nature.

PYTHAGORAS OF SAMOS, GREECE 570-495 BC

495

He was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement. Pythagoreans were busy telling the initiated that all numbers could be expressed as the ratio of integers. It made for a nice, orderly, comprehensible universe. Along comes Hippasus and in trying to inscribe a regular dodecahedron inside a sphere, happened across the existence of irrational numbers.

ANAXIMANDER, GREECE 610 a.C. - 546 a.C

546

He was a pre-Socratic Greek philosopher Aristotle cites Anaximander as the first one to name the infinity, Apeiron, as the material cause of all things as well as their ultimate be-ing, since all the other elements which exist are finite, deriving their existence from infinity.

AVICENNA, IRAN 980-1037

1037

Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Sīnā was a Persian polymath who is regarded as one of the most significant physicians, astronomers, thinkers and writers of the Islamic Golden Age.
In the astronomical field he believed in the eternity of the cosmos and in the infinity of the past and the future time, he thought that existence had not an initial or final point. In physical terms, he supposed that the light speed wasn't infinite and misurable.

THOMAS AQUINAS, ITALY 1225-1274

1274

Saint Thomas Aquinas was an Italian Dominican friar, Catholic priest and Doctor of the Church. He was an immensely influential philosopher, theologian, and jurist in the tradition of scholasticism. He used the expression "infinite" and its derivatives in a variety of senses that range from the essential infinity of God himself to the quantitative infinity of the series of natural numbers or of the measure of an infinitely extended body which he, as an Aristotelian, believed to be impossible.

FILIPPO BRUNELLESCHI , ITALY 1377-1446

1446

He was an Italian designer and a key figure in architecture, recognised to be the first modern engineer, planner and sole construction supervisor. He invented the linear prospective, in which all parallel lines converge in a specific point,the vanishing point, which is set infinitely

NICOLAUS OF CUSA, GERMANY 1401-1464

1464

German philosopher, theologian, astronomer and jurist. He thought that human mind contained infinity without being infinite, so it couldn't know and understand infinity, that he identified with God. He also thought that cosmos was infinite and without a centre.

PIERO DELLA FRANCESCA, ITALY 1416-1492

1492

Piero della Francesca was an Italian painter and mathematician. He turned the Leon Battista Alberti's idea of infinity into a technique.
In Alberti's idea of infinite space all measure moves from the realm of sense knowing to that of intellectual conjecture: from the visible point of infinity at the center of the construction to the conjectured, invisible centre that is everywhere at once.

GIORDANO BRUNO, ITALY, 1548-1600

1600

One of the main points of his reflection is the theory of infinitive. The philosopher refers to Cusano's "coincidentia oppositorum" to state that "In the Universe, no center and no circumference exist, but the center is everywhere" and that is infinity. With his theory of infinity he polemicizes the Aristotelic vision, because he sees the universe as unlimited and infinitive with an inexhaustible multiplicity of worlds and creatures, because of these theories he was burned at the stake

GALILEO GALILEI, ITALY 1564-1642

1642

Galileo is the first person in history who introduced the actual infinity and tolerated the consequences for the rest of his life. He is the first to show the fact that whole can be equal to a part of it. He is the one who dares to face the world that has always tried to stop or tortured philosophers from touching infinity.

BONAVENTURA CAVALIERI, ITALY 1598-1647

1647

Bonaventura Francesco Cavalieri was an Italian mathematician. He is known for his work on the problems of optics and motion, on the indivisibles, the precursors of infinitesimal calculus, and the introduction of logarithms in Italy. Cavalieri accepted the idea of infinity: for example, in 1635, Cavalieri asserted that a line was made up of an infinite number of points, a surface of an infinite number of lines, and a volume of an infinite number of surfaces.

GIRARD DESARGUES, FRANCE, 1591-1666

1666

esargues was a French architect, matematician and engineer. He is considered one of the founders of the projective geometry thanks to his work "Exemple de l'une des manières universelles du S.G.D.L. touchant la pratique de la perspective " in which he presented a geometric method for constructing perspective images of objects.

JOHN WALLIS, UNITED KINGDOM 1616-1703

1703

John Wallis was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal court. He is credited with introducing the symbol ∞ for infinity. He similarly used 1/∞ for an infinitesimal.

GOTTFRIED LEIBNITZ, GERMANY, 1646-1716

1716

In 1673 he stated that indivisibles have to be defined as infinitely small quantities or the ratio of which to a perceivable quantity is infinite. What does it mean to be infinitely small? Infinitely small means smaller than any given quantity.

SIR ISAAC NEWTON, UNITED KINGDOM, 1642-1727

1727

Newton has been the father of the infinitesimal calculus. He used the infinitesimal processes in order to understand the concept of infinite and lay the foundation of the calculus, which is the base for the development of methods and models for the quantitative study of the objects of the Scientific Research.

CASPAR DAVID FRIEDRICH, GERMANY 1774-1840

1840

Caspar David Friedrich was a German painter. One of the most significant exponents of Romanticism.
His most famous painting is The wanderer on the sea of fog, which is the most representative painting of Romanticism and gives us the perception of the contact between human and infinity. This painting is also a proof of how he considered infinity as a means for man to evolve.

CARL FRIEDRICH GAUSS, GERMANY 1777-1855

1855

He was a child prodigy mathematician and physicist, considered one of the greatest geniuses of all time. He made significant contributions to many fields, including number theory, algebra, statistics, analysis, differential geometry, mechanics, magnetic fields, astronomy and optics. Discussing infinity, he believed that the limit itself was potentially an infinite process. Moreover, he did not consider infinite as a number subject to the same rules of arithmetic as the other numbers.

M.C. ESCHER, THE NETHERLANDS 1898-1972

1972

Escher was an artist who is known for his works based on maths, geometry and physics (for example "The sphere"). He tried to represent his concept of infinity in his four woodcuts called "Circle Limits".