What the world would be without inventions?

GREEK INVENTORS THROUGH TIME “The introduction of noble inventions seems to hold by far the most excellent place among human actions” ~ Francis Bacon 7 Greek inventors through time • Archimides • Euclid • Pythagoras • Thucydides • Ctesibius of Alexandria • Constantin Carathéodory • George Papanikolaou Archimides, the great mathematician and inventor of the “Archimides principle”

GREEK INVENTORS I Archimedes of Syracuse (Ancient Greek: Ἀρχιμήδης [ar.kʰi.mɛː.dɛ̂ːs]; c . 287 – c. 212 BC) was a Greek mathematician, physicist, en gineer, inventor, and astronomer. He is regarded as one of the leading scientists in classical antiquity. Considered to be the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including: the area of a circle; the surface area and volume of a sphere; area of an ellipse; the area under a parabola; the volume of a segment of a paraboloid of revolution; the volume of a segment of a hyperboloid of revolution; and the area of a spiral. His other mathematical achievements 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. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever. He is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion. Archimedes' principle A metal bar, placed into a container of water on a scale, displaces as much water as its own volume, increasing the mass of the container's contents and weighing down the scale. The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a votive crown for a temple had been made for King Hiero II of Syracuse, who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. "Eureka!“ While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (Greek: "εὕρηκα, heúrēka!, lit. 'I have found [it]!'). The test was conducted successfully, proving that silver had indeed been mixed in. The death of Archimides

Archimedes died c. 212 BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year- long siege. According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. He was said to have implored the soldier not to destroy his work by the famous phrase “Do not disturb my circles!”. The soldier was enraged by this, and killed Archimedes with his sword. Nowadays, Archimides is considered to be the greatest mathematician of ancient history, and one of the greatest of all time. Euclid, the father of Geometry

GREEK INVENTORS II Euclid (Ancient Greek: Εὐκλείδης – Eukleídēs, pronounced [eu̯ .kleː.dɛːs]; fl. 300 BC), was a Greek mathematician, often referred to as the "founder of geometry or the "father of geometry". The English name Euclid i s the anglicized version of the Greek name Εὐκλείδης, which means "renowned, glorious”. If he came from Alexandria, he would have known the Serapeum of Alexandria, and the Library of Alexandria, and may have worked there during his time. Euclid's arrival in Alexandria came about ten years after its founding by Alexander the Great, which means he arrived c. 322 BC. He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especiall y geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigor. Euclid's Elements Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later. Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclid's Elements, "Euclid replied there is no royal road to geometry." One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to circa AD 100 (P. Oxy. 29). The diagram accompanies Book II, Proposition 5. Euclid's construction of a regular dodecahedron. Construction of a dodecahedron by placing faces on the edges of a cube. Euclid in Rafaello’s “The School of Athens” Fresco, Vatican. Euclid’s statue in Oxford University Euclidean Geometry, the main Geometry corpus for Greek High School students. Pythagoras, the great mathematician and musician

GREEK INVENTORS III Pythagoras of Samos (c. 570 BC – 495 BC) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Pythagoreanism Around 530 BC, Pythagoras travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. The members of the sect shared all their possessions in common and were devoted to each other to the exclusion of outsiders. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism.

Pythagoreans Celebrate the Sunrise (1869) by Fyodor Bronnikov Illustration from 1913 showing Pythagoras teaching a class of women. Many prominent members of his school were women and some modern scholars think that he may have believed that women should be taught philosophy as well as men. In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus. It was said that he was the first man to call himself a philosopher ("lover of wisdom") and that he was the first to divide the globe into five climatic zones. Pythagoras is credited with having devised the tetractys, an important sacred symbol in later Pythagoreanism. The teaching most securely identified with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon death, enters into a new body. He may have also devised the doctrine of musica universalis, which holds that the planets move according to mathematical equations a nd thus resonate to produce an inaudible symphony of music. The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c). Pythagoras’ influence Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was used throughout early modern European esotericism, and his teachings as portrayed in Ovid's Metamorphoses influenced the modern vegetarian movement. In Raphael's fresco The School of Athens, Pythagoras is shown writing in a book as a young man presents him with a tablet showing a diagrammatic representation of a lyre above a drawing of the sacred tetractys. Thucidides, the father of scientific History

GREEK INVENTORS IV Thucydides (Ancient Greek: Θουκυδίδης Thoukūdídēs [tʰuːkyːdídɛːs]; c. 460 – c. 400 BC) was an Athenian historian and general . His History of the Peloponnesian War recounts the fifth-century BC war between Sparta and Athens u ntil the year 411 BC. Thucydides has been dubbed the father of "scientific history" by those who accept his claims to have applied strict standards of impartiality and evidence-gathering and analysis of cause and effect, without reference to intervention by the deities, as outlined in his introduction to his work. The Peloponnesian War Thucydides identifies himself as an Athenian, telling us that his father's name was Olorus and that he was from the Athenian deme of Halimous. A somewhat doubtful anecdote of his early life still exists. While still a youth of 10-12 years, he and his father were supposed to have gone to the agora of Athens where the young Thucydides heard a lecture by the historian Herodotus. According to some accounts the young Thucydides wept with joy after hearing the lecture, deciding that writing history would be his life's calling. The same account also claims that after the lecture, Herodotus spoke with the youth and his father, stating: Oloros your son yearns for knowledge.

Thucydides and Herodotus, Museo Archeologico Nazionale in Naples The Acropolis of Athens Thucydides also has been called the father of the school of political realism, which views the political behavior of individuals and the subsequent outcomes of relations between states as ultimately mediated by, and constructed upon, the emotions of fear and self- interest. His text is still studied at universities and military colleges worldwide. The Melian dialogue is regarded as a seminal work of international relations theory, while his version of Pericles' Funeral Oration (“Epitaph”)is widely studied by political theorists, historians, and students of the classics. Pericles delivering the “Epitaph” speech. More generally, Thucydides developed an understanding of human nature to explain behaviour in such crises as plagues, massacres, and civil war.

Michiel Sweerts “The plague of Athens” (1652) Thucydides still remains one of the most consistent to historical accuracy historians and the precursor of modern scientific history. Ctesibius of Alexandria, inventor of the hydraulis, predecessor of the church organ

GREEK INVENTORS V The hydraulic (or hydraulis), the so-called water instrument, was an invention of the engineer Ktisivios of Alexandria. It was built in Alexandria in the 3rd century BC and we have the descriptions of the Hero of Alexander and Vitruvius about the way of its operation and use. The hydraulis A feature of this instrument was the hydraulic system on which it relied to operate, as it was responsible for producing, moving and regulating the air pressure, which was fed into the lumens through a series of levers. The way hydraulis functions The development of the hydraulis to church organ

After the Greeks, this pioneering acoustic and technological structure traveled and was willingly adopted by many, reaching as far as the Romans and then the Byzantines. In the 7th and 8th centuries the hydraulis was now called Organ and flourished in Byzantium, but also in all its major centers of construction and production such as Constantinople. It is remarkable that a church organ was sent as a gift in 757 AD from the Byzantine emperor Constantine 5th to the Frankish emperor Pepin the Short, father of Charlemagne. The Byzantines did not use it in church music, as their ecclesiastical music was vocal. A little later, in 812 AD, the Byzantines gave a second same organ to Charlemagne himself. In the 10th century, the English church organ of Winchester was made at the expense of the church, with an unusually large size and with 26 bellows, which required 70 people, also having 40 notes, with 10 flutes for each note.An evolution of this instrument is the later ecclesiastical instrument, which is based on the same construction bases and was used mostly in the ecclesiastical music of the West, but also in symphonic music and the early cinema. The modern church organ The Greeks do not use a church organ in their services, however they were the inventors of the first type of such an organ! Is it not strange? Constantin Karatheodory, the great mathematician and Einstein's counselor

GREEK INVENTORS VI Constantin Carathéodory (Greek: Κωνσταντίνος Καραθεοδωρή, romanized: Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany. He made significant contributions to real and complex analysis, the calculus of variations, and measure theory. He also created an axiomatic formulation of thermodynamics. Constantin Carathéodory was born in 1873 in Berlin to Greek parents and grew up in Brussels. His father Stephanos, a lawyer, served as the Ottoman ambassador to Belgium, St. Petersburg and Berlin. The Carathéodory family, originally from Bosnochori or Vyssa, was well established and respected in Constantinople, and its members held many important governmental positions. Carathéodory studied engineering in Belgium at the Royal Military Academy, where he was considered a charismatic and brilliant student. Since he was a trained engineer he was offered a job in the British colonial service. This job took him to Egypt where he worked on the construction of the Assiut dam until April 1900. University career Carathéodory soon became professor to various German universities and created a great scientific work. Carathéodory's contacts in Germany were many and included such famous names as: Hermann Minkowski, David Hilbert, Felix Klein, Albert Einstein, Edmund Landau, Hermann Amandus Schwarz, Lipót Fejér. During the difficult period of World War II his close associates at the Bavarian Academy of Sciences were Perron and Tietze.

Carathéodory (left) with Hungarian mathematician Lipót Fejér Works Calculus of variations: In his doctoral dissertation, Carathéodory showed how to extend solutions to discontinuous cases and studied isoperimetric problems. Convex geometry: “Carathéodory's theorem” in convex geometry (see: https://en.wikipedia.org/wiki/ Carath%C3%A9odory%27s_t heorem_(convex_hull))

An illustration of Carathéodory's theorem (convex hull) for a square in R2. Real analysis He proved an existence theorem for the solution to ordinary differential equations under mild regularity conditions. Complex analysis He greatly extended the theory of conformal transformation proving his theorem about the extension of conformal mapping to the boundary of Jordan domains. In studying boundary correspondence he originated the theory of prime ends. He exhibited an elementary proof of the Schwarz lemma. Theory of measure He is credited with the “Carathéodory extension theorem” which is fundamental to modern measure theory. Later Carathéodory extended the theory from sets to Boolean algebras. Thermodynamics Thermodynamics had been a subject dear to Carathéodory since his time in Belgium. In 1909, he published a pioneering work "Investigations on the Foundations of Thermodynamics“ in which he formulated the second law of thermodynamics axiomatically, that is, without the use of Carnot engines and refrigerators and only by mathematical reasoning.

Optics Carathéodory's work in optics is closely related to his method in the calculus of variations. In 1926 he gave a strict and general proof that no system of lenses and mirrors can avoid aberration, except for the trivial case of plane mirrors. In his later work he gave the theory of the Schmidt telescope. In his Geometrische Optik (1937), Carathéodory demonstrated the equivalence of Huygens' principle and Fermat's principle starting from the former using Cauchy's theory of characteristics. Carathéodory and Einstein Einstein, then in a member of the Prussian Academy of Sciences in Berlin, was working on his general theory of relativity when he contacted Carathéodory asking for clarifications on the Hamilton-Jacobi equation and canonical transformations. Carathéodory’s contribution to the completion of both the specific and the General Theory of Relativity was very important. When Einstein completed the General Theory of Relativity in 1916 and published it in the Annalen der Physik under the title "Die grundlagen der allgemeinen Relativitatstheorie", many said that Karatheodoris's contribution and help in the elaboration of the mathematical part of this theory, was very large. They had a scientific correspondence for years and Einstein often asked for his counsel in his equations. Legacy In 2002, in recognition of his achievements, the University of Munich named one of the largest lecture rooms in the mathematical institute the Constantin-Carathéodory Lecture Hall. In Greece, there is a Carathéodory museum in Komotini, with archives, works and personal items of the great Greek scientist. George Papanikolaou, the inventor of Pap test

GREEK INVENTOPS VII Georgios Nikolaou Papanikolaou (or George Papanicolaou / Greek: Γε ώργιος Ν. Παπανικολάου [papanikoˈl au]; 13 May 1883 – 19 February 1962) was a Greek physician who was a pioneer in cytopathology and early cancer detection, and inventor of the "Pap smear". Career Born in Kymi, Greece, Papanikolaou attended the University of Athens, where he studied literature, philosophy, languages and music. Urged by his father, he pursued a medical degree, which he received in 1904. After studying medicine in Greece and Germany, he emigrated in 1913 to the United States. The Pap test

In 1928, Papanikolaou told an incredulous audience of physicians about the noninvasive technique of gathering cellular debris from the lining of the vaginal tract and smearing it on a glass slide for microscopic examination as a way to identify cervical cancer. At a 1928 medical conference in Battle Creek, Michigan, Papanicolaou introduced his low- cost, easily performed screening test for early detection of cancerous and precancerous cells. However, this potential medical breakthrough was initially met with skepticism and resistance from the medical community. Ultimately, Dr. Papanicolaou’s contributions were recognized worldwide. He was nominated several times for a Nobel Prize and in 1953 received the Cross of Grand Commander, the highest decoration bestowed by the King of Greece. He would go on to establish his own cancer research center in Miami shortly before his death in 1962. The Pap test, when combined with a regular program of screening and appropriate follow-up, can reduce cervical cancer deaths by up to 80%. Due to Pap test thousands of women avoid the effects and death by cervical cancer, which is the most usual cause of death by cancer in women.

Pap test abnormal Legacy We have had a significant drop in deaths from cervical cancer, It is estimated that the Pap test has reduced the mortality rate of cervical cancer by 70 percent. Dr. Papanicolaou’s contributions as both a doctor and an inventor were game- changing. The Pap test is one of the most important inventions in humankind because it was extremely challenging to prevent cervical cancer and the severity of it. George Papanikolaou on a Greek note Let’s try together to invent a new world!!

The legacy does exist…