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Greek mathematics refers to mathematics texts written during and ideas stemming from the Archaic through the Hellenistic periods, extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the Ancient Greek: μάθημα, romanized: máthēma Attic Greek: [má.tʰɛː.ma] Koine Greek: [ˈma.θi.ma], meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations.

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The abacus, also called a counting frame, is a calculating tool that was in use in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the written Arabic numeral system. The exact origin of the abacus is still unknown. The abacus essentially consists of a number of rows of movable beads or other objects, which represent digits. One of two numbers is set up, and the beads are manipulated to implement an operation involving a second number, or rarely a square or cubic root.

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In mathematics, informally speaking, Euclid's orchard is an array of one-dimensional "trees" of unit height planted at the lattice points in one quadrant of a square lattice. More formally, Euclid's orchard is the set of line segments from (i, j, 0) to (i, j, 1), where i and j are positive integers.

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The Attic numerals are a symbolic number notation used by the ancient Greeks. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by Herodian; or as acrophonic numerals because the basic symbols derive from the first letters of the (ancient) Greek words that the symbols represented.

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Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used elsewhere in the West. For ordinary cardinal numbers, however, Greece uses Arabic numerals.

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The Salamis Tablet is a marble counting board dating from around 300 B.C. that was discovered on the island of Salamis in 1846. A precursor to the abacus, it is thought that it represents an ancient Greek means of performing mathematical calculations common in the ancient world. Pebbles were placed at various locations and could be moved as calculations were performed. The marble tablet itself has dimensions of approximately 150 × 75 × 4.5 cm.

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The tetractys, or tetrad, or the tetractys of the decad is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. As a mystical symbol, it was very important to the secret worship of Pythagoreanism. There were four seasons, and the number was also associated with planetary motions and music.