Mathematics

AP: common difference; GP: common ratio; formulas for nth term and sum — essential for finance and science

Equations of the form ax+b=c; graphed as straight lines; fundamental to all applied mathematics

ax²+bx+c=0; solved by quadratic formula, factoring or completing the square; parabola graphs

5th century Indian mathematician; approximated π; zero; sine; Earth rotates on its axis

Father of Geometry; Elements (300 BC) — 13 books of 465 theorems that shaped mathematics for 2,000 years

Self-taught Indian genius; 3,900 mathematical results; worked with Hardy at Cambridge; died aged 32

Descartes' 1637 synthesis of algebra and geometry using Cartesian coordinates (x, y)

Euclid's Elements (300 BC) — 13 books, 465 propositions; the most influential maths textbook ever

In a right triangle: a²+b²=c²; most famous theorem in mathematics; known to Babylonians 1,000 years before Pythagoras

Natural, Integer, Rational, Irrational, Real and Complex — the hierarchy of number systems

Numbers divisible only by 1 and themselves; infinite in number; key to cryptography and security

Foundation of modern mathematics; Venn diagrams, union, intersection — universally taught worldwide

India's greatest gift to mathematics — zero as a number was invented by Brahmagupta in 628 AD

Bar charts, pie charts, line graphs, histograms — tools for visualising and interpreting data

Statistics analyses data; probability quantifies chance; both essential for AI, medicine and policy

Study of triangles and angles; sin, cos, tan ratios; essential for physics, engineering and navigation