Ancient Greek mathematics

In the Greek world mathematics was more closely related to philosophy than to practical affairs, and this kinship has persisted to the present day.

— Ancient Greek mathematics

Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him.

— Ancient Greek mathematics

It is important to remember that the ancient Greeks did not have an abstract system of number symbols, and used the letters of the alphabet as number symbols. They also commonly manipulated pebbles to learn arithmetic and used small stones on calculating boards. In this case, number patterns were their common experience of arithmetic. From this use of pebbles, we have inherited the word 'calculation,' from the Latin calculus, which means 'pebble.'

— Ancient Greek mathematics

The Greeks... were well aware of geometric magnitudes that we call "irrational," but simply did not think of them as numbers.

— Ancient Greek mathematics

It is well known that the commentary of Proclus on Eucl. Book I is one of the two main sources of information as to the history of Greek geometry which we possess, the other being the Collection of Pappus.

— Ancient Greek mathematics

The ancient Geometry had no symbols, nor any notation beyond ordinary language and the specific terms of the science.

— Ancient Greek mathematics

It is the purpose of this paper to show what is historically wrong with the traditional way the history of ancient Greek mathematics has been written and to call to the new generation of historians of Greek mathematics to rewrite the history on a new and historically sane basis.

— Ancient Greek mathematics

The history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several preceding centuries.

— Ancient Greek mathematics

The extraordinary ability of Diophantus appears rather in... the ingenuity with which he reduces every problem to an equation which he is competent to solve.

— Ancient Greek mathematics

The most common and characteristic of Diophantus' methods is his use of tentative assumptions which is applied in nearly every problem of the later books. It consists in assigning to the unknown a preliminary value which satisfies one or two only of the necessary conditions, in order that, from its failure to satisfy the remaining conditions, the operator may perceive what exactly is required...

— Ancient Greek mathematics

With Diophantus the history of Greek arithmetic comes to an end. No original work, that we know of, was done afterwards.

— Ancient Greek mathematics

Before giving the proof by which Thales probably established the truth... it will be well to consider the geometrical capital which this Grecian mathematician had at his command. ...i. The angles at the base of an are equal. ...ii. If two straight lines cut one another the vertically opposite angles are equal.

— Ancient Greek mathematics

For the mathematician the important consideration is that the foundations of mathematics and a great portion of its content are Greek. The Greeks laid down the first principles, invented the methods ab initio, and fixed the terminology. Mathematics in short is a Greek science, whatever new developments modern analysis has brought or may bring.

— Ancient Greek mathematics

Greek mathematics reveals an important aspect of the Greek genius of which the student of Greek culture is apt to lose sight.

— Ancient Greek mathematics

was the author of a book purporting to be a manual of mathematical subjects such as a student would require to enable him to understand Plato.

— Ancient Greek mathematics

Any one can use our algebraic notation, but only a gifted mathematician can deal with the Greek theory of proportions and with geometric algebra.

— Ancient Greek mathematics

An oral tradition makes it possible to indicate the line segments with the fingers; one can emphasize essentials and point out how the proof was found. All of this disappears in the written formulation... as soon as some external cause brought about an interruption in the oral tradition, and only books remained, it became very difficult to assimilate the work of the great predursors, and next to impossible to pass beyond it.

— Ancient Greek mathematics