The art of Navigation--->RigVeda

Concept of indivisible Atoms--->Adi ShankaraCharya

Concept of Pulsating Universe--->RigVeda

Defying Gravity 'n making invisible Objects--->Vimana Shastra

Theory of Energy Conservation--->Karma Theory

Law of Gravitation--->BrahmaGupta

Light rays bend near a massive object--->RigVeda

Distance between the Earth and the Sun--->RigVeda

Distance between the Earth and the Moon--->RigVeda

Evolution of Life--->Manusmriti

Usage of Smallest(1 millionth of second) and largest(~400 Trillion years)
fraction of time--->RigVeda

Taylor Series of Sine 'n Cosine functions--->Madhavacharya

Newton Power Series--->Madhavacharya

Gregory Leibnitz series for the Inverse Tangent--->Madhavacharya

Leibtnitz power series for PI--->Madhavacharya

Time taken by the Earth to orbit the Sun--->Bhaskaracharya

Examples 'n usage of Infinity and Zero--->Bhaskaracharya II

Arithmetic 'n Geometric Progression--->Yajurveda

Gauss Interpolation formula--->GovendaSwamin

Newton Gauss Backward Interpolation formula--->Vateswaracharya

Lhuiler’s formula--->Parameswaracharya

Infinite Geometric Progression convergent series--->Nilakanta

Positive and negative numbers--->Brahmagupta

HelioCentric theory of Gravitation--->Aryabhatta

Value of PI and Pythagorean theorem--->Boudhayana

Algebra, Trigonometry, Calculus, Quadratic equations---> Sridharacharya

Surgery and usage of anaesthesia, surgical instruments--->Maharshi Sushruta

Detailed knowledge of anatomy, physiology, aetiology, embryology, digestion, metabolism, genetics 'n immunity.

Zinc distillation

Drilling of human teeth-->Mehrgarh Culutre

The Art of Sex--->KamaSutra

The oldest names of "astronomical" numbers such as quadrillions and
quintillions ---> RigVeda

The aquatic life precedes the monkey life" and that "the monkey life is the precursor of the human life --> Brihat Vishnu Purana

Chemical processes associated with the dying of textiles and extraction of metals --> Ancient India

The use of mordants (in dyeing) and catalysts (in metal-extraction/purification) --> Ancient India

Arithmetic operations ---> Narad Vishnu Purana

Description about Ellipses ---> Surya Prayapti

Square root of 2, squaring a circle, dividing a segment into seven equal parts ---> Apasthamba's sutra

Irrational numbers ---> Ancient India

Permutations ---> Bhagvati Sutras

combinations ---> Sathananga Sutra

Infinite numbers ---> Anuyoga Dwara Sutra

The law of indices and Base System ---> Anuyoga Dwara Sutra

Knowledge of the tides and the stars ---> Ancient India

Circumference of the Earth and the lenght of the SOlar year and
instantaneous motion of the moon ---> Aryabhatta

Calculation of Sine Function, Lunar Crescent ---> Bhaskar I

Calculation of nCr and solutions to quadratic indeterminate equations ---> Varahamira

Least Common Multiple, Area of an ellipse ---> Mahaviracharya

Ratios, barter, simple interest, mixtures, purchase and sale, rates of travel, wages, and filling of cisterns, arithmetic and geometric progressions, including progressions with fractional numbers or terms, and formulas for the sum of certain finite series ----> Sridhara

Study of the sphere and it's properties and applications to geography, planetary mean motion, eccentric epicyclical model of the planets, first visibilities of the planets, the seasons, the lunar crescent, sin(a + b) = sin a cos b + cos a sin b; sin(a - b) = sin a cos b - cos a sin b;etc ---> Bhaskaracharya

Expansion of the cos and sine functions ---> Madhava

Integer solutions to 21 types of systems of 2 algebraic equations ---> Chitrabhanu

physical properties of different types of plants and natural substances -->Vaisheshikas

Molecular groupings and Molecular/atomic motion and Sound properties like (echos, pitch, tonem harmonics, musical theory) ---> Prasastapada

Concept of Light Illumination ---> Susruta

Wave nature of Light and Sound ---> Chakrapani

Particle nature of Light ---> Mimamsakas

Reflection of Light ---> Varahamihira

Phenomenon of Shadows and opacity of materials ---> Vatsyayana

Refraciton of Light ---> Uddyotakara

Linear, Rotary, Curvilinear motion, quantifications of the laws of motion. --->Prasastapada

Velocity = distance/time --->Bhaskaracharya

Phenomenon of Magnetism --->bhoja

Phenomenon of Electrostatic Attraction, concept of kinetic energy, the process of boiling to evaporation, capillary motion, surface tension, viscosity ---> Shankara Misra

Concept of Solar heat ---> Udayana

Irrigation canals, wells of different types, storage tanks and a variety of water-harvesting techniques ---> Ancient India

Revolving water spray for cooling the air ---> ArthaShastra

A model to predict earthquakes ---> Varahamihira's Brihat Samhita

Architecture of houses and palaces ---> RigVeda

First Calendar ---> Vedas

Elliptical motion of planets around the Sun ---> Aryabhatta

[ Mrujjalashikhivaayumayo Bhoogola: sarvatho vruttha ]
Meaning: Earth which is made of soil, water, fire and air is circular when viewed from all sides. i.e., The Earth is spherical ---> Aryabhatta

[ Bhakthe vilomavivare gathiyogenaanulomavivare dvow, Gathyantharena labdow dviyogakaalaavatheethaishyow ]
Meaning: If two objects are traveling in opposite directions, the time required for them to meet is equal to the distance between them divided by the sum of their speeds. If they travel in the same direction the time that has elapsed equals the distance between them divided by the difference in their speeds --->Aryabhatta