---
title: "Timeline of scientific discoveries"
chunk: 2/7
source: "https://en.wikipedia.org/wiki/Timeline_of_scientific_discoveries"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:28:31.534973+00:00"
instance: "kb-cron"
---

500 BC: Hippasus, a Pythagorean, discovers irrational numbers.
500 BC: Anaxagoras identifies moonlight as reflected sunlight.
5th century BC: The Greeks start experimenting with straightedge-and-compass constructions.
5th century BC: The earliest documented mention of a spherical Earth comes from the Greeks in the 5th century BC.  It is known that the Indians modeled the Earth as spherical by 300 BC
460 BC: Empedocles describes thermal expansion.
Late 5th century BC: Antiphon discovers the method of exhaustion, foreshadowing the concept of a limit.
4th century BC: Greek philosophers study the properties of logical negation.
4th century BC: The first true formal system is constructed by Pāṇini in his Sanskrit grammar.
4th century BC: Eudoxus of Cnidus states the Archimedean property.
4th century BC: Thaetetus shows that square roots are either integer or irrational.
4th century BC: Thaetetus enumerates the Platonic solids, an early work in graph theory.
4th century BC: Menaechmus discovers conic sections.
4th century BC: Menaechmus develops co-ordinate geometry.
4th century BC: Mozi in China gives a description of the camera obscura phenomenon.
4th century BC: Around the time of Aristotle, a more empirically founded system of anatomy is established, based on animal dissection. In particular, Praxagoras makes the distinction between arteries and veins.
4th century BC: Aristotle differentiates between near-sighted and far-sightedness. Graeco-Roman physician Galen would later use the term "myopia" for near-sightedness.
4th century BC: Pāṇini develops a full-fledged formal grammar (for Sanskrit).
Late 4th century BC: Chanakya (also known as Kautilya) establishes the field of economics with the Arthashastra (literally "Science of wealth"), a prescriptive treatise on economics and statecraft for Mauryan India.
4th – 3rd century BC: In Mauryan India, The Jain mathematical text Surya Prajnapati draws a distinction between countable and uncountable infinities.
350 BC – 50 BC: Clay tablets from (possibly Hellenistic-era) Babylon describe the mean speed theorem.
300 BC: Finite geometric progressions are studied by Euclid in Ptolemaic Egypt.
300 BC: Euclid proves the infinitude of primes.
300 BC: Euclid proves the Fundamental Theorem of Arithmetic.
300 BC: Euclid discovers the Euclidean algorithm.
300 BC: Euclid publishes the Elements, a compendium on classical Euclidean geometry, including: elementary theorems on circles, definitions of the centers of a triangle, the tangent-secant theorem, the law of sines and the law of cosines.
300 BC: Euclid's Optics introduces the field of geometric optics, making basic considerations on the sizes of images.
3rd century BC: Archimedes relates problems in geometric series to those in arithmetic series, foreshadowing the logarithm.
3rd century BC: Pingala in Mauryan India studies binary numbers, making him the first to study the radix (numerical base) in history.
3rd century BC: Pingala in Mauryan India describes the Fibonacci sequence.
3rd century BC: Pingala in Mauryan India discovers the binomial coefficients in a combinatorial context and the additive formula for generating them 
  
    
      
        
          
            
              
                (
              
              
                n
                r
              
              
                )
              
            
          
        
        =
        
          
            
              
                (
              
              
                
                  n
                  −
                  1
                
                r
              
              
                )
              
            
          
        
        +
        
          
            
              
                (
              
              
                
                  n
                  −
                  1
                
                
                  r
                  −
                  1
                
              
              
                )
              
            
          
        
      
    
    {\displaystyle {\tbinom {n}{r}}={\tbinom {n-1}{r}}+{\tbinom {n-1}{r-1}}}
  
, i.e. a prose description of Pascal's triangle, and derived formulae relating to the sums and alternating sums of binomial coefficients. It has been suggested that he may have also discovered the binomial theorem in this context.
3rd century BC: Eratosthenes discovers the Sieve of Eratosthenes.
3rd century BC: Archimedes derives a formula for the volume of a sphere in The Method of Mechanical Theorems.
3rd century BC: Archimedes calculates areas and volumes relating to conic sections, such as the area bounded between a parabola and a chord, and various volumes of revolution.
3rd century BC: Archimedes discovers the sum/difference identity for trigonometric functions in the form of the "Theorem of Broken Chords".
3rd century BC: Archimedes makes use of infinitesimals.
3rd century BC: Archimedes further develops the method of exhaustion into an early description of integration.
3rd century BC: Archimedes calculates tangents to non-trigonometric curves.
3rd century BC: Archimedes uses the method of exhaustion to construct a strict inequality bounding the value of π within an interval of 0.002.
3rd century BC: Archimedes develops the field of statics, introducing notions such as the center of gravity, mechanical equilibrium, the study of levers, and hydrostatics.
3rd century BC: Eratosthenes measures the circumference of the Earth.
260 BC: Aristarchus of Samos proposes a basic heliocentric model of the universe.
200 BC: Apollonius of Perga discovers Apollonius's theorem.
200 BC: Apollonius of Perga assigns equations to curves.
200 BC: Apollonius of Perga develops epicycles. While an incorrect model, it was a precursor to the development of Fourier series.
2nd century BC: Hipparchos discovers the apsidal precession of the Moon's orbit.
2nd century BC: Hipparchos discovers Axial precession.
2nd century BC: Hipparchos measures the sizes of and distances to the Moon and Sun.
190 BC: Magic squares appear in China. The theory of magic squares can be considered the first example of a vector space.
165 BC – 142 BC: Zhang Cang in Northern China is credited with the development of Gaussian elimination.

== 1 AD – 500 AD ==
Mathematics and astronomy flourish during the Golden Age of India (4th to 6th centuries AD) under the Gupta Empire. Meanwhile, Greece and its colonies have entered the Roman period in the last few decades of the preceding millennium, and Greek science is negatively impacted by the Fall of the Western Roman Empire and the economic decline that follows.