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**Griechische Mathematik**

*The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.*Saint Augustine (354-430)

*Poetry is the only place where the power of numbers proves to be nothing *Odysseas Elytis, Nobel Prize Literature 1979

Greeks like Thales from the Ionian islands around 600 BC visited Egypt and Babylon. They acquired the practical knowledge accumulated over centuries and promoted it into Science. Greeks obtained Geometry as an art of measuring the land from the Egyptians as Herodotus describes. The influence of Greek mathematics continues through the ages. Arithmetic, music, geometry, and astronomy – pure number, applied number, stationary magnitude, and magnitude in motion respectively – began life in Plato’s *Republic* and constituted the quadrivium of sciences up to 1600 AD and later. Eudoxus and Archimedes exhaustion methods were only extended by Cauchy and Weierstrass. The discovery of a proof of Fermat’s last theorem in 1993-4 shows how even current mathematical activity originates in Greek mathematical activity. Also the last years we have some remarkable discoveries analyzing the work of Archimedes and Hipparchus. A characteristic Greek discovery that the square root of 2 is not a rational number is for me one of the best examples that Greeks were interested in true science. One has to think that how surprising it is to discover that you cannot express this number in the form a/b where a and b are integer numbers. You can approach it with an accuracy as good as you want if you choose very large numbers for a and b but whatever you choose it will be never exactly the square root of 2. So there is a special type of numbers, the irrational numbers. For engineering purposes even small numbers for a and b would be enough but the proof of the irrationality of the square root of 2, although so simple, shows what the difference is between engineering and pure science.

**Ancient Greece Mathematics Timeline** , **Mathematicians and other Scientists: Graphical Timeline from 800 BC - 700 AD**

** Thales of Miletus, the first Greek scientist** “the first man in history to whom specific mathematical discoveries have been attributed.” Boyer in A History of Mathematics

** a) Pythagoras of Samos, strange and mysterious **,

**b) The Life of Pythagoras by Diogenes Laertios**

Pythagoras most important achievement is his idea that everything in the Universe can be expressed by numbers. Plato was fascinated by this idea and he used the Platonic solids as the building blocks of the Universe, the first primitive mathematical cosmological model. Today mathematical physicists try to fulfill the dream of Pythagoras. The only mistake of Pythagoras is that mathematics can describe everything except that what is really personally important.

**Pythagoras: Everything is a number: The revival of his idea**

**The irrational behavior of Pythagoras discovering the irrational numbers**

__The irrationality in the Pentagon and the most irrational number__

**The Ten Means of Ancient Greece**

**Ancient Greece: The Golden Section and the Golden Rectangle**

** The Prime numbers, infinite, perfect and amicable their erotic effects and the number of the fish** ,

__Geometric Numbers____The quadrature of a convex polygon and Hippocrates Lune__

__Eudoxus of Cnidus, one of the the greatest mathematicians__

**Archimedes Mathematics** , **Archimedes and Combinatorial Problems (The loculus of Archimedes)**

**Archimedes the Arbelos and the Salinon** , **Archimedes semi-regular Convex Solids** , **Archimedes Cubic and Quadric Equations**

**Did Archimedes Know Gauss-Bonnet?**

** Archimedes and the Palimpsest** ,

__The death of Archimedes, a transition to a new era__** Aristotle's Potential and Actual Infinite and Cantor** ,

**Aristotle's Syllogism : Logic takes form**, A more advanced description of

**Aristotle on Mathematics, Logic (from Stanford University)**,

**Apollonius Conics and Circles and the Delian Problem** , Greek Geometry from Thales to Euclid (Conics)

**Ptolemy of Alexandria** , **Mathematics of Heron, his equation extended after 2000 years to polyhedra** ,

**Diophantus and Hilberts 10 ^{th} Problem** ,

**Pappus of Alexandria**

**The Menelaus Theorem** (**More information**) , **The Menelaus Theorem and Albert Einstein**

__Combinatorics: Did Hipparchus discover the Schröder numbers?__

*Isaac Newton's assistant at Cambridge claimed that during five years he saw Newton laugh only once. Newton had loaned a copy of Euclid to an acquaintance, and the gentleman asked what use it was to study Euclid, "upon which Sir Isaac was very merry".* Euclid's Plan and Proposition 6

**Euclid's Proof of existence of infinite prime numbers, The Erdös BOOK and the Library of Borges** , **Euclid's Fourteenth Book?**

**Euclid's algorithm and integer relations** , **From Euclid to Gregory**

**Euclid's Elements** (The Web version)

**Mathematical Curves (Parabolas, Ellipse, Conchoids, Spirals etc discovered by Greeks)**

**Duplication of the Cube ( A students project)**

*The human mind has first to construct forms, independently, before we can find them in things*. Albert Einstein

** Plato's Cave - The Enlightenment Process: Enter the Matrix** or

**Enter the Meatrix :-)**

__Socrates teaching Mathematics, from Plato's dialogue the “Meno”__

**Greek Numbers and how Archimedes extended the number of seats in the Paradise or Hell**

and Is the Number of the Beast 666 or 616 ?

*By the time Gauss left Göttingen, he had already developed a concept of the physical reality of the square roots of negative numbers, which he called, complex numbers. Adopting the method of Plato's cave metaphor, from The Republic, Gauss understood his complex numbers to be shadows reflecting a complex of physical actions (action acting on action)*. Plato and Carl Gauss's Fundamental Theorem of Algebra

From Plato's Theaetetus to Gauss's Pentagramma Mirificum: A Fight for Truth (PDF) by Bruce Director

The ancient soul of the new science

**University of St. Andrews (Includes an extensive list with biographies of Greek mathematicians and from all other countries )****The classic Greek mathematic Problems**- Squaring the circle
- Doubling the cube
- Trisecting an angle
- The teaching of mathematics in Ancient Greece
- How do we know about Greek mathematicians?
- How do we know about Greek mathematics?
- Enquiries about the genesis of formal thinking and about syntactic knowledge representation

## Individual Biographies from the University of St Andrews of the mathematical work of: |

Anaxagoras , Anthemius , Antiphon , Apollonius , Archimedes , Archytas , Aristaeus , Aristarchus , Aristotle , Autolycus of Pitane , Bryson , Callippus , Chrysippus , Cleomedes , Conon , Democritus , Dinostratus , Diocles , Dionysodorus , Diophantus , Domninus , Eratosthenes , Euclid , Eudemus of Rhodes , Eudoxus , Eutocius , Geminus , Heraclides of Pontus , Heron , Hipparchus , Hippias , Hippocrates , Hypatia , Hypsicles , Leucippus , Marinus of Neapolis , Menaechmus , Menelaus , Nicomachus , Nicomedes , Oenopides of Chios , Pappus , Perseus , Philon of Byzantium , Plato , Porphyry , Posidonius , Proclus , Ptolemy , Pythagoras , Serenus , Simplicius , Sporus , Thales , Theaetetus , Theodorus , Theodosius , Theon of Alexandria , Theon of Smyrna , Thymaridas , Xenocrates , Zeno of Elea , Zeno of Sidon , Zenodorus |

**Ancient Greek Mathematics** Greek and English Website

**Mathematics LINKS** (including links to Biographies from Anaxagoras to Zenodorus)

Ancient Greece |
Medieval Greece / Byzantine Empire |
Modern Greece |
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