Timeline of scientific discoveries

The timeline below shows the date of publication of possible major scientific breakthroughs, theories and discoveries, along with the discoverer. For the purposes of this article, we do not regard mere speculation as discovery, although imperfect reasoned arguments, arguments based on elegance/simplicity, and numerically/experimentally verified conjectures qualify (as otherwise no scientific discovery before the late 19th century would count). We begin our timeline at the Bronze Age, as it is difficult to estimate the timeline before this point, such as of the discovery of counting, natural numbers and arithmetic.

See also: Timeline of historic inventions

To avoid overlap with Timeline of historic inventions, we do not list examples of documentation for manufactured substances and devices unless they reveal a more fundamental leap in the theoretical ideas in a field.

Bronze Age

Many early innovations of the Bronze Age were requirements resulting from the increase in trade, and this also applies to the scientific advances of this period. For context, the major civilizations of this period are Egypt, Mesopotamia, and the Indus Valley, with Greece rising in importance towards the end of the third millennium BC. It is to be noted that the Indus Valley script remains undeciphered and there are very little surviving fragments of its writing, thus any inference about scientific discoveries in the region must be made based only on archaeological digs.

Numbers, measurement and arithmetic
  • Around 3000 BC: Units of measurement are developed in the major Bronze Age civilisations: Egypt, Mesopotamia, Elam and the Indus Valley. The Indus Valley may have been the major innovator on this, as the first measurement devices (rulers, protractors, weighing scales) were invented in Lothal in Gujarat, India.[1][2][3][4]
  • 1800 BC: Fractions were first studied by the Egyptians in their study of Egyptian fractions.

Geometry and trigonometry

Algebra
  • 2100 BC: Quadratic equations, in the form of problems relating the areas and sides of rectangles, are solved by Babylonians.[5]

Number theory and discrete mathematics
  • 2000 BC: Pythagorean triples are first discussed in Babylon and Egypt, and appear on later manuscripts such as the Berlin Papyrus 6619.[7]

Numerical mathematics and algorithms
  • 2000 BC: Multiplication tables in Babylon.[8]
  • 1800 BC – 1600 BC: A numerical approximation for the square root of two, accurate to 6 decimal places, is recorded on YBC 7289, a Babylonian clay tablet believed to belong to a student.[9]
  • 19th to 17th century BCE: A Babylonian tablet uses ​25⁄8 as an approximation for π, which has an error of 0.5%.[10][11][12]
  • Early 2nd millennium BCE: The Rhind Mathematical Papyrus (a copy of an older Middle Kingdom text) contains the first documented instance of inscribing a polygon (in this case, an octagon) into a circle to estimate the value of π.[13][14]

Notation and conventions
  • 3000 BC: The first deciphered numeral system is that of the Egyptian numerals, a sign-value system (as opposed to a place-value system).[15]
  • 2000 BC: Primitive positional notation for numerals is seen in the Babylonian cuneiform numerals.[16] However, the lack of clarity around the notion of zero made their system highly ambiguous (e.g. 13200 would be written the same as 132).[17]

Astronomy
  • Early 2nd millennium BC: The periodicity of planetary phenomenon is recognised by Babylonian astronomers.

Biology and anatomy
  • Early 2nd millennium BC: Ancient Egyptians study anatomy, as recorded in the Edwin Smith Papyrus. They identified the heart and its vessels, liver, spleen, kidneys, hypothalamus, uterus, and bladder, and correctly identified that blood vessels emanated from the heart (however, they also believed that tears, urine, and semen, but not saliva and sweat, originated in the heart, see Cardiocentric hypothesis).[18]

Iron Age

Geometry and trigonometry
  • c. 700 BC: The Pythagoras theorem is discovered by Baudhayana in the Hindu Shulba Sutras in Upanishadic India.[19] However, Indian mathematics, especially North Indian mathematics, generally did not have a tradition of communicating proofs, and it is not fully certain that Baudhayana or Apastamba knew of a proof.

Number theory and discrete mathematics
  • c. 700 BC: Pell's equations are first studied by Baudhayana in India, the first diophantine equations known to be studied.[20]

Geometry and trigonometry

Biology and anatomy
  • 600 BC – 200 BC: The Sushruta Samhita (3.V) shows an understanding of musculoskeletal structure (including joints, ligaments and muscles and their functions).[21]
  • 600 BC – 200 BC: The Sushruta Samhita refers to the cardiovascular system as a closed circuit.[22]
  • 600 BC – 200 BC: The Sushruta Samhita (3.IX) identifies the existence of nerves.[21]

Linguistics

500 BC – 1 BC

The Greeks make numerous advances in mathematics and astronomy through the Archaic, Classical and Hellenistic periods.

Logic and proof
  • 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.[23][24]
  • c. 300 BC: Greek mathematician Euclid in the Elements describes a primitive form of formal proof and axiomatic systems. However, modern mathematicians generally believe that his axioms were highly incomplete, and that his definitions were not really used in his proofs.

Numbers, measurement and arithmetic
  • 4th century BC: Eudoxus of Cnidus states the Archimedean property.[25]
  • 4th-3rd century BC: In Mauryan India, The Jain mathematical text Surya Prajnapati draws a distinction between countable and uncountable infinities.[26]
  • 3rd century BC: Pingala in Mauryan India studies binary numbers, making him the first to study the radix (numerical base) in history.[27]

Algebra
  • 5th century BC: Possible date of the discovery of the triangular numbers (i.e. the sum of consecutive integers), by the Pythagoreans.[28]
  • c. 300 BC: Finite geometric progressions are studied by Euclid in Ptolemaic Egypt.[29]
  • 3rd century BC: Archimedes relates problems in geometric series to those in arithmetic series, foreshadowing the logarithm.[30]
  • 190 BC: Magic squares appear in China. The theory of magic squares can be considered the first example of a vector space.
  • 165-142 BC: Zhang Cang in Northern China is credited with the development of Gaussian elimination.[31]

Number theory and discrete mathematics
  • c. 500 BC: Hippasus, a Pythagorean, discovers irrational numbers.[32][33]
  • 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.
  • 3rd century BC: Pingala in Mauryan India describes the Fibonacci sequence.[34][35]
  • c. 300 BC: Euclid proves the infinitude of primes.[36]
  • c. 300 BC: Euclid proves the Fundamental Theorem of Arithmetic.
  • c. 300 BC: Euclid discovers the Euclidean algorithm.
  • 3rd century BC: Pingala in Mauryan India discovers the binomial coefficients in a combinatorial context and the additive formula for generating them ,[37][38] 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.[39]
  • 3rd century BC: Eratosthenes discovers the Sieve of Eratosthenes.[40]

Geometry and trigonometry
  • 5th century BC: The Greeks start experimenting with straightedge-and-compass constructions.[41]
  • 4th century BC: Menaechmus discovers conic sections.[42]
  • 4th century BC: Menaechmus develops co-ordinate geometry.[43]
  • c. 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.[44]
  • 3rd century BC: Archimedes derives a formula for the volume of a sphere in The Method of Mechanical Theorems.[45]
  • 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.[46]
  • 3rd century BC: Archimedes discovers the sum/difference identity for trigonometric functions in the form of the "Theorem of Broken Chords".[44]
  • c. 200 BC: Apollonius of Perga discovers Apollonius's theorem.
  • c. 200 BC: Apollonius of Perga assigns equations to curves.

Analysis

Numerical mathematics and algorithms
  • 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.

Astronomy
  • 5th century BC: The earliest documented mention of a spherical Earth comes from the Greeks in the 5th century BC.[51] It is known that the Indians modeled the Earth as spherical by 300 BC[52]
  • 500 BC: Anaxagoras identifies moonlight as reflected sunlight.[53]
  • 260 BC: Aristarchus of Samos proposes a basic heliocentric model of the universe.[54]
  • c. 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.[55]
  • 2nd century BC: Hipparchos discovers Axial precession.

Mechanics
  • 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.
  • 350-50 BC: Clay tablets from (possibly Hellenistic-era) Babylon describe the mean speed theorem.[56]

Optics
  • 4th century BC: Mozi in China gives a description of the camera obscura phenomenon.
  • c. 300 BC: Euclid's Optics introduces the field of geometric optics, making basic considerations on the sizes of images.

Thermal physics
  • 460 BC: Empedocles describes thermal expansion.[57]

Biology and anatomy
  • 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.[58] Graeco-Roman physician Galen would later use the term "myopia" for near-sightedness.

Social science
Pāṇini's Aṣṭādhyāyī, an early Indian grammatical treatise that constructs a formal system for the purpose of describing Sanskrit grammar.

Economics
  • Late 4th century BC: Kautilya establishes the field of economics with the Arthashastra (literally "Science of wealth"), a prescriptive treatise on economics and statecraft for Mauryan India.[59]

Linguistics
  • 4th century BC: Pāṇini develops a full-fledged formal grammar (for Sanskrit).

Astronomical and geospatial measurements
  • 3rd century BC: Eratosthenes measures the circumference of the Earth.[60]
  • 2nd century BC: Hipparchos measures the sizes of and distances to the moon and sun.[61]

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.

Numbers, measurement and arithmetic
Example of the early Greek symbol for zero (lower right corner) from a 2nd-century papyrus

Algebra
  • 499 AD: Aryabhata discovers the formula for the square-pyramidal numbers (the sums of consecutive square numbers).[64]
  • 499 AD: Aryabhata discovers the formula for the simplicial numbers (the sums of consecutive cube numbers).[64]

Number theory and discrete mathematics

Geometry and trigonometry
  • c. 60 AD: Heron's formula is discovered by Hero of Alexandria.[66]
  • c. 100 AD: Menelaus of Alexandria describes spherical triangles, a precursor to non-Euclidean geometry.[67]
  • 4th to 5th centuries: The modern fundamental trigonometric functions, sine and cosine, are described in the Siddhantas of India.[68] This formulation of trigonometry is an improvement over the earlier Greek functions, in that it lends itself more seamlessly to polar co-ordinates and the later complex interpretation of the trigonometric functions.

Numerical mathematics and algorithms
  • By the 4th century AD: a square root finding algorithm with quartic convergence, known as the Bakhshali method (after the Bakhshali manuscript which records it), is discovered in India.[69]
  • 499 AD: Aryabhata describes a numerical algorithm for finding cube roots.[70][71]
  • 499 AD: Aryabhata develops an algorithm to solve the Chinese remainder theorem.[72]
  • 1st to 4th century AD: A precursor to long division, known as "galley division" is developed at some point. Its discovery is generally believed to have originated in India around the 4th century AD,[73] although Singaporean mathematician Lam Lay Yong claims that the method is found in the Chinese text The Nine Chapters on the Mathematical Art, from the 1st century AD.[74]

Notation and conventions
Diophantus' Arithmetica (pictured: a Latin translation from 1621) contained the first known use of symbolic mathematical notation. Despite the relative decline in the importance of the sciences during the Roman era, several Greek mathematicians continued to flourish in Alexandria.
  • c. 150 AD: The Almagest of Ptolemy contains evidence of the Hellenistic zero. Unlike the earlier Babylonian zero, the Hellenistic zero could be used alone, or at the end of a number. However, it was usually used in the fractional part of a numeral, and was not regarded as a true arithmetical number itself.
  • 3rd century AD: Diophantus uses a primitive form of algebraic symbolism, which is quickly forgotten.[75]
  • By the 4th century AD: The present Hindu–Arabic numeral system with place-value numerals develops in Gupta-era India, and is attested in the Bakhshali Manuscript of Gandhara.[76] The superiority of the system over existing place-value and sign-value systems arises from its treatment of zero as an ordinary numeral.
  • By the 5th century AD: The decimal separator is developed in India,[77] as recorded in al-Uqlidisi's later commentary on Indian mathematics.[78]
  • By 499 AD: Aryabhata's work shows the use of the modern fraction notation, known as bhinnarasi.[79]

Astronomy
  • c. 150 AD: Ptolemy's Almagest contains practical formulae to calculate latitudes and day lengths.
  • 2nd century AD: Ptolemy formalises the epicycles of Apollonius.
  • By the 5th century AD: The elliptical orbits of planets are discovered in India by at least the time of Aryabhata, and are used for the calculations of orbital periods and eclipse timings.[80]
  • 499 AD: Historians speculate that Aryabhata may have used an underlying heliocentric model for his astronomical calculations, which would make it the first computational heliocentric model in history (as opposed to Aristarchus's model in form).[81][82][83] This claim is based on his description of the planetary period about the sun (śīghrocca), but has been met with criticism.[84]

Optics
  • 2nd century - Ptolemy publishes his Optics, discussing colour, reflection, and refraction of light, and Including the first known table of refractive angles.

Biology and anatomy
  • 2nd century AD: Galen studies the anatomy of pigs.[85]

Astronomical and geospatial measurements
  • 499 AD: Aryabhata creates a particularly accurate eclipse chart. As an example of its accuracy, 18th century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations (based on Aryabhata's computational paradigm) of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[86]

500 AD – 1000 AD
The age of Imperial Karnataka was a period of significant advancement in Indian mathematics.

The Golden Age of Indian mathematics and astronomy continues after the end of the Gupta empire, especially in Southern India during the era of the Rashtrakuta, Western Chalukya and Vijayanagara empires of Karnataka, which variously patronised Hindu and Jain mathematicians. In addition, the Middle East enters the Islamic Golden Age through contact with other civilisations, and China enters a golden period during the Tang and Song dynasties.

Numbers, measurement and arithmetic

Algebra

Number theory and discrete mathematics

Geometry and trigonometry

Analysis
  • 10th century AD: Manjula in India discovers the derivative, deducing that the derivative of the sine function is the cosine.[90]

Probability and statistics
  • 9th century AD: Al-Kindi's Manuscript on Deciphering Cryptographic Messages contains the first use of statistical inference.[91]

Numerical mathematics and algorithms
  • 628 AD: Brahmagupta discovers second-order interpolation, in the form of Brahmagupta's interpolation formula.
  • 629 AD: Bhāskara I produces the first approximation of a transcendental function with a rational function, in the sine approximation formula that bears his name.
  • 816 AD: Jain mathematician Virasena describes the integer logarithm.[92]
  • 9th century AD: Algorisms (arithmetical algorithms on numbers written in place-value system) are described by al-Khwarizmi in his kitāb al-ḥisāb al-hindī (Book of Indian computation) and kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī (Addition and subtraction in Indian arithmetic).
  • 9th century AD: Mahāvīra discovers the first algorithm for writing fractions as Egyptian fractions,[93] which is in fact a slightly more general form of the Greedy algorithm for Egyptian fractions.

Notation and conventions
  • 628 AD: Brahmagupta invents a symbolic mathematical notation, which is then adopted by mathematicians through India and the Near East, and eventually Europe.

Astronomy
  • 6th century AD: Varahamira in the Gupta empire is the first to describe comets as astronomical phenomena, and as periodic in nature.[94]

Mechanics
  • c. 525 AD: John Philoponus in Byzantine Egypt describes the notion of inertia, and states that the motion of a falling object does not depend on its weight.[95] His radical rejection of Aristotlean orthodoxy lead him to be ignored in his time.

Optics

Astronomical and geospatial measurements

1000 AD – 1500 AD

Algebra
  • 11th century: Alhazen discovers the formula for the simplicial numbers defined as the sums of consecutive quartic powers.

Number theory and discrete mathematics

Geometry and trigonometry
  • 15th century: Parameshvara discovers a formula for the circumradius of a quadrilateral.[104]

Analysis

Numerical mathematics and algorithms
  • 12th century AD: al-Tusi develops a numerical algorithm to solve cubic equations.
  • 1380 AD: Madhava of Sangamagrama solves transcendental equations by iteration.[107]
  • 1380 AD: Madhava of Sangamagrama discovers the most precise estimate of π in the medieval world through his infinite series, a strict inequality with uncertainty 3e-13.

Astronomy
  • 1058 AD: al-Zarqālī in Islamic Spain discovers the apsidal precession of the sun.
  • c. 1500 AD: Nilakantha Somayaji develops a model similar to the Tychonic system. His model has been described as mathematically more efficient than the Tychonic system due to correctly considering the equation of the centre and latitudinal motion of Mercury and Venus.[90][110]

Mechanics
  • 12th century AD: Jewish polymath Baruch ben Malka in Iraq formulates a qualitative form of Newton's second law for constant forces.[111][112]

Optics
  • 11th century: Alhazen systematically studies optics and refraction, which would later be important in making the connection between geometric (ray) optics and wave theory.
  • 11th century: Shen Kuo discovers atmospheric refraction and provides the correct explanation of rainbow phenomenon
  • c1290 - Eye Glasses are invented in Northern Italy,[113] possibly Pisa, demonstrating knowledge of human biology and optics, to offer bespoke works that compensate for an individual human disability.

Astronomical and geospatial measurements

Economics
  • 1295 AD: Scottish priest Duns Scotus writes about the mutual beneficence of trade.[114]
  • 14th century AD: French priest Jean Buridan provides a basic explanation of the price system.

Philosophy of science
  • 1220s - Robert Grosseteste writes on optics, and the production of lenses, while asserting models should be developed from observations, and predictions of those models verified through observation, in a precursor to the scientific method.[115]
  • 1267 - Roger Bacon publishes his Opus Majus, compiling translated Classical Greek, and Arabic works on mathematics, optics, and alchemy into a volume, and details his methods for evaluating the theories, particularly those of Ptolemy's 2nd century Optics, and his findings on the production of lenses, asserting “theories supplied by reason should be verified by sensory data, aided by instruments, and corroborated by trustworthy witnesses", in a precursor to the peer reviewed scientific method.

16th century

The Scientific Revolution occurs in Europe around this period, greatly accelerating the progress of science and contributing to the rationalization of the natural sciences.

Numbers, measurement and arithmetic

Algebra

Probability and statistics
  • 1564: Gerolamo Cardano is the first to produce a systematic treatment of probability.[120]

Numerical mathematics and algorithms

Notation and conventions

Various pieces of modern symbolic notation were introduced in this period, notably:

Astronomy
  • 1543: Nicolaus Copernicus develops a heliocentric model, which assuming Aryabhata did not use a heliocentric model, would be the first quantitative heliocentric model in history.
  • Late 16th century: Tycho Brahe proves that comets are astronomical (and not atmospheric) phenomena.

Biology and anatomy
  • 1543 – Vesalius: pioneering research into human anatomy

Economics
  • 1517: Nicolaus Copernicus develops the quantity theory of money and states the earliest known form of Gresham's law: ("Bad money drowns out good").[124]

17th century

18th century

19th century

20th century

21st century
See also: List of years in science § 2000s, and Breakthrough of the Year § Breakthrough of the Year
  • 2001 – The first draft of the Human Genome Project is published.
  • 2003 – Grigori Perelman presents proof of the Poincaré Conjecture.
  • 2004 – Andre Geim and Konstantin Novoselov isolated graphene, a monolayer of carbon atoms, and studied its quantum electrical properties.
  • 2005 – Grid cells in the brain are discovered by Edvard Moser and May-Britt Moser.
  • 2010 – The first Self-Replicating, Synthetic Bacterial Cells are Constructed.[127]
  • 2010 – The Neanderthal Genome Project presented preliminary genetic evidence that interbreeding did likely take place and that a small but significant portion of Neanderthal admixture is present in modern non-African populations.
  • 2012 – Higgs boson is discovered at CERN (confirmed to 99.999% certainty)
  • 2012 – Photonic molecules are discovered at MIT
  • 2014 – Exotic hadrons are discovered at the LHCb
  • 2015 – Traces of liquid water discovered on Mars[128] (Since refuted in NASA report from 2017!)[129]
  • 2016 – The LIGO team detected gravitational waves from a black hole merger.
  • 2017 – Gravitational wave signal GW170817 was observed by the LIGO/Virgo collaboration. This was the first instance of a gravitational wave event that was observed to have a simultaneous electromagnetic signal when space telescopes like Hubble observed lights coming from the event, thereby marking a significant breakthrough for multi-messenger astronomy.[130][131][132]
  • 2019 – The first ever image of a black hole was captured, using eight different telescopes taking simultaneous pictures, timed with extremely precise atomic clocks.
  • 2020 – NASA and SOFIA (Stratospheric Observatory of Infrared Astronomy) discovered about 12oz of surface water in one of the moon's largest visible crater. This has sparked new motivation to venture into space. We continue to discover water is more common than we originally thought.[133]
  • 2020 - In response to the COVID-19 pandemic, biotechnology companies, national governments, and universities work to accelerate progression to an effective COVID-19 vaccine.
Further information: 2020 in science and 2021 in science

References
  1. Whitelaw, p. 14.
  2. S. R. Rao (1985). Lothal. Archaeological Survey of India. pp. 40–41.
  3. Rao (July 1992). "A Navigational Instrument of the Harappan Sailors" (PDF). Marine Archaeology. 3: 61–66. Notes: protractor described as "compass" in article.
  4. Petruso, Karl M (1981). "Early Weights and Weighing in Egypt and the Indus Valley". M Bulletin. 79: 44–51. JSTOR 4171634.
  5. Friberg, Jöran (2009). "A Geometric Algorithm with Solutions to Quadratic Equations in a Sumerian Juridical Document from Ur III Umma". Cuneiform Digital Library Journal. 3.
  6. Maor, Eli (1998). Trigonometric Delights. Princeton University Press. p. 20. ISBN 978-0-691-09541-7.
  7. Richard J. Gillings, Mathematics in the Time of the Pharaohs, Dover, New York, 1982, 161.
  8. Jane Qiu (7 January 2014). "Ancient times table hidden in Chinese bamboo strips". Nature News. doi:10.1038/nature.2014.14482. S2CID 130132289.
  9. Beery, Janet L.; Swetz, Frank J. (July 2012), "The best known old Babylonian tablet?", Convergence, Mathematical Association of America, doi:10.4169/loci003889
  10. Romano, David Gilman (1993). Athletics and Mathematics in Archaic Corinth: The Origins of the Greek Stadion. American Philosophical Society. p. 78. ISBN 9780871692061. A group of mathematical clay tablets from the Old Babylonian Period, excavated at Susa in 1936, and published by E.M. Bruins in 1950, provide the information that the Babylonian approximation of π was 3 1/8 or 3.125.
  11. Bruins, E. M. (1950). "Quelques textes mathématiques de la Mission de Suse" (PDF).
  12. Bruins, E. M.; Rutten, M. (1961). Textes mathématiques de Suse. Mémoires de la Mission archéologique en Iran. XXXIV.
  13. Imhausen, Annette (2007). Katz, Victor J. (ed.). The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. ISBN 978-0-691-11485-9.
  14. Rossi (2007). Corinna Architecture and Mathematics in Ancient Egypt. Cambridge University Press. ISBN 978-0-521-69053-9.
  15. "Egyptian numerals". Retrieved 25 September 2013.
  16. Stephen Chrisomalis (2010). Numerical Notation: A Comparative History. p. 248. ISBN 9780521878180.
  17. Lamb, Evelyn (31 August 2014), "Look, Ma, No Zero!", Scientific American, Roots of Unity
  18. Porter, Roy (17 October 1999). The Greatest Benefit to Mankind: A Medical History of Humanity (The Norton History of Science). W. W. Norton. pp. 49–50. ISBN 9780393319804. Retrieved 17 November 2013.
  19. Thibaut, George (1875). "On the Śulvasútras". The Journal of the Asiatic Society of Bengal. 44: 227–275.
  20. Seshadri, Conjeevaram (2010). Seshadri, C. S (ed.). Studies in the History of Indian Mathematics. New Delhi: Hindustan Book Agency. pp. 152–153. doi:10.1007/978-93-86279-49-1. ISBN 978-93-80250-06-9.
  21. Bhishagratna, Kaviraj KL (1907). An English Translation of the Sushruta Samhita in Three Volumes. Archived from the original on 4 November 2008. Alt URL
  22. Patwardhan, Kishor (2012). "The history of the discovery of blood circulation: Unrecognized contributions of Ayurveda masters". Advances in Physiology Education. 36 (2): 77–82. doi:10.1152/advan.00123.2011. PMID 22665419.
  23. Bhate, S. and Kak, S. (1993) Panini and Computer Science. Annals of the Bhandarkar Oriental Research Institute, vol. 72, pp. 79-94.
  24. Kadvany, John (2007), "Positional Value and Linguistic Recursion", Journal of Indian Philosophy, 35 (5–6): 487–520, CiteSeerX 10.1.1.565.2083, doi:10.1007/s10781-007-9025-5, S2CID 52885600.
  25. Knopp, Konrad (1951). Theory and Application of Infinite Series (English 2nd ed.). London and Glasgow: Blackie & Son, Ltd. p. 7. ISBN 0-486-66165-2.
  26. Ian Stewart (2017). Infinity: a Very Short Introduction. Oxford University Press. p. 117. ISBN 978-0-19-875523-4. Archived from the original on 3 April 2017.
  27. Van Nooten, B. (1 March 1993). "Binary numbers in Indian antiquity". Journal of Indian Philosophy. 21 (1): 31–50. doi:10.1007/BF01092744. S2CID 171039636.
  28. Eves, Howard. "Webpage cites AN INTRODUCTION TO THE HISTORY OF MATHEMATICS". Mathcentral. Retrieved 28 March 2015.
  29. Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements (2nd ed. [Facsimile. Original publication: Cambridge University Press, 1925] ed.). New York: Dover Publications.
  30. Ian Bruce (2000) "Napier’s Logarithms", American Journal of Physics 68(2):148
  31. Needham, Joseph (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth (Vol. 3), p 24. Taipei: Caves Books, Ltd.
  32. Kurt Von Fritz (1945). "The Discovery of Incommensurability by Hippasus of Metapontum". The Annals of Mathematics.
  33. James R. Choike (1980). "The Pentagram and the Discovery of an Irrational Number". The Two-Year College Mathematics Journal..
  34. Singh, Parmanand (1985), "The So-called Fibonacci numbers in ancient and medieval India", Historia Mathematica, 12 (3): 229–44, doi:10.1016/0315-0860(85)90021-7
  35. Knuth, Donald (1968), The Art of Computer Programming, 1, Addison Wesley, p. 100, ISBN 978-81-7758-754-8, Before Fibonacci wrote his work, the sequence Fn had already been discussed by Indian scholars, who had long been interested in rhythmic patterns... both Gopala (before 1135 AD) and Hemachandra (c. 1150) mentioned the numbers 1,2,3,5,8,13,21 explicitly [see P. Singh Historia Math 12 (1985) 229–44]" p. 100 (3d ed)...
  36. Ore, Oystein (1988) [1948], Number Theory and its History, Dover, p. 65
  37. A. W. F. Edwards. Pascal's arithmetical triangle: the story of a mathematical idea. JHU Press, 2002. Pages 30–31.
  38. Edwards, A. W. F. (2013), "The arithmetical triangle", in Wilson, Robin; Watkins, John J. (eds.), Combinatorics: Ancient and Modern, Oxford University Press, pp. 166–180
  39. Amulya Kumar Bag (6 January 1966). "Binomial theorem in Ancient India" (PDF). Indian J. Hist. Sci.: 68–74.
  40. Hoche, Richard, ed. (1866), Nicomachi Geraseni Pythagorei Introductionis arithmeticae libri II, Leipzig: B.G. Teubner, p. 31
  41. Bold, Benjamin. Famous Problems of Geometry and How to Solve Them, Dover Publications, 1982 (orig. 1969).
  42. Boyer (1991). "The age of Plato and Aristotle". A History of Mathematics. p. 93. It was consequently a signal achievement on the part of Menaechmus when he disclosed that curves having the desired property were near at hand. In fact, there was a family of appropriate curves obtained from a single source – the cutting of a right circular cone by a plane perpendicular to an element of the cone. That is, Menaechmus is reputed to have discovered the curves that were later known as the ellipse, the parabola, and the hyperbola. [...] Yet the first discovery of the ellipse seems to have been made by Menaechmus as a mere by-product in a search in which it was the parabola and hyperbola that proffered the properties needed in the solution of the Delian problem.
  43. Boyer, Carl B. (1991). "The Age of Plato and Aristotle". A History of Mathematics (Second ed.). John Wiley & Sons, Inc. pp. 94–95. ISBN 0-471-54397-7. Menaechmus apparently derived these properties of the conic sections and others as well. Since this material has a strong resemblance to the use of coordinates, as illustrated above, it has sometimes been maintained that Menaechmus had analytic geometry. Such a judgment is warranted only in part, for certainly Menaechmus was unaware that any equation in two unknown quantities determines a curve. In fact, the general concept of an equation in unknown quantities was alien to Greek thought. It was shortcomings in algebraic notations that, more than anything else, operated against the Greek achievement of a full-fledged coordinate geometry.
  44. Boyer, Carl Benjamin (1991). "Greek Trigonometry and Mensuration". A History of Mathematics. pp. 158–159. Trigonometry, like other branches of mathematics, was not the work of any one man, or nation. Theorems on ratios of the sides of similar triangles had been known to, and used by, the ancient Egyptians and Babylonians. In view of the pre-Hellenic lack of the concept of angle measure, such a study might better be called "trilaterometry", or the measure of three sided polygons (trilaterals), than "trigonometry", the measure of parts of a triangle. With the Greeks we first find a systematic study of relationships between angles (or arcs) in a circle and the lengths of chords subtending these. Properties of chords, as measures of central and inscribed angles in circles, were familiar to the Greeks of Hippocrates' day, and it is likely that Eudoxus had used ratios and angle measures in determining the size of the earth and the relative distances of the sun and the moon. In the works of Euclid there is no trigonometry in the strict sense of the word, but there are theorems equivalent to specific trigonometric laws or formulas. Propositions II.12 and 13 of the Elements, for example, are the laws of cosines for obtuse and acute angles respectively, stated in geometric rather than trigonometric language and proved by a method similar to that used by Euclid in connection with the Pythagorean theorem. Theorems on the lengths of chords are essentially applications of the modern law of sines. We have seen that Archimedes' theorem on the broken chord can readily be translated into trigonometric language analogous to formulas for sines of sums and differences of angles.
  45. Archimedes (1912), The method of Archimedes recently discovered by Heiberg; a supplement to the Works of Archimedes, Cambridge University Press
  46. Eves, Howard (1963), A Survey of Geometry (Volume One), Boston: Allyn and Bacon
  47. Archimedes, The Method of Mechanical Theorems; see Archimedes Palimpsest
  48. O'Connor, J.J. & Robertson, E.F. (February 1996). "A history of calculus". University of St Andrews. Retrieved 7 August 2007.
  49. K., Bidwell, James (30 November 1993). "Archimedes and Pi-Revisited". School Science and Mathematics. 94 (3).
  50. Boyer, Carl B. (1991). "Archimedes of Syracuse". A History of Mathematics (2nd ed.). Wiley. pp. 127. ISBN 978-0-471-54397-8. Greek mathematics sometimes has been described as essentially static, with little regard for the notion of variability; but Archimedes, in his study of the spiral, seems to have found the tangent to a curve through kinematic considerations akin to differential calculus. Thinking of a point on the spiral 1=r = aθ as subjected to a double motion — a uniform radial motion away from the origin of coordinates and a circular motion about the origin — he seems to have found (through the parallelogram of velocities) the direction of motion (hence of the tangent to the curve) by noting the resultant of the two component motions. This appears to be the first instance in which a tangent was found to a curve other than a circle.
    Archimedes' study of the spiral, a curve that he ascribed to his friend Conon of Alexandria, was part of the Greek search for the solution of the three famous problems.
  51. Dicks, D.R. (1970). Early Greek Astronomy to Aristotle. Ithaca, N.Y.: Cornell University Press. pp. 68. ISBN 978-0-8014-0561-7.
  52. E. At. Schwanbeck (1877). Ancient India as described by Megasthenês and Arrian; being a translation of the fragments of the Indika of Megasthenês collected by Dr. Schwanbeck, and of the first part of the Indika of Arrian. p. 101.
  53. Warmflash, David (20 June 2019). "An Ancient Greek Philosopher Was Exiled for Claiming the Moon Was a Rock, Not a God". Smithsonian Mag. Retrieved 10 March 2020.
  54. Draper, John William (2007) [1874]. "History of the Conflict Between Religion and Science". In Joshi, S. T. (ed.). The Agnostic Reader. Prometheus. pp. 172–173. ISBN 978-1-59102-533-7.
  55. Jones, A., Alexander (September 1991). "The Adaptation of Babylonian Methods in Greek Numerical Astronomy" (PDF). Isis. 82 (3): 440–453. Bibcode:1991Isis...82..441J. doi:10.1086/355836.
  56. Ossendrijver, Mathieu (29 January 2016). "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph". Science. 351 (6272): 482–484. Bibcode:2016Sci...351..482O. doi:10.1126/science.aad8085. PMID 26823423. S2CID 206644971.
  57. Valleriani, Matteo (3 June 2010). Galileo Engineer. Springer Science and Business Media.
  58. Spaide RF, Ohno-Matsui KM, Yannuzzi LA, eds. (2013). Pathologic Myopia. Springer Science & Business Media. p. 2. ISBN 978-1461483380.
  59. Mabbett, I. W. (1964). "The Date of the Arthaśāstra". Journal of the American Oriental Society. American Oriental Society. 84 (2): 162–169. doi:10.2307/597102. ISSN 0003-0279. JSTOR 597102.
  60. D. Rawlins: "Methods for Measuring the Earth's Size by Determining the Curvature of the Sea" and "Racking the Stade for Eratosthenes", appendices to "The Eratosthenes–Strabo Nile Map. Is It the Earliest Surviving Instance of Spherical Cartography? Did It Supply the 5000 Stades Arc for Eratosthenes' Experiment?", Archive for History of Exact Sciences, v.26, 211–219, 1982
  61. Bowen A.C., Goldstein B.R. (1991). "Hipparchus' Treatment of Early Greek Astronomy: The Case of Eudoxus and the Length of Daytime Author(s)". Proceedings of the American Philosophical Society 135(2): 233–254.
  62. Struik, page 32–33. "In these matrices we find negative numbers, which appear here for the first time in history."
  63. Luke Hodgkin (2005). A History of Mathematics: From Mesopotamia to Modernity. Oxford University Press. p. 88. ISBN 978-0-19-152383-0. Liu is explicit on this; at the point where the Nine Chapters give a detailed and helpful 'Sign Rule'
  64. (Boyer 1991, "The Mathematics of the Hindus" p. 207) "He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes."
  65. Bibhutibhushan Datta and Avadhesh Narayan Singh (1962). History of Hindu Mathematics A source Book Part II. Asia Publishing House. p. 92.
  66. Heath, Thomas L. (1921). A History of Greek Mathematics (Vol II). Oxford University Press. pp. 321–323.
  67. Boyer, Carl Benjamin (1991). "Greek Trigonometry and Mensuration". A History of Mathematics. p. 163. In Book I of this treatise Menelaus establishes a basis for spherical triangles analogous to that of Euclid I for plane triangles. Included is a theorem without Euclidean analogue – that two spherical triangles are congruent if corresponding angles are equal (Menelaus did not distinguish between congruent and symmetric spherical triangles); and the theorem A + B + C > 180° is established. The second book of the Sphaerica describes the application of spherical geometry to astronomical phenomena and is of little mathematical interest. Book III, the last, contains the well known "theorem of Menelaus" as part of what is essentially spherical trigonometry in the typical Greek form – a geometry or trigonometry of chords in a circle. In the circle in Fig. 10.4 we should write that chord AB is twice the sine of half the central angle AOB (multiplied by the radius of the circle). Menelaus and his Greek successors instead referred to AB simply as the chord corresponding to the arc AB. If BOB' is a diameter of the circle, then chord A' is twice the cosine of half the angle AOB (multiplied by the radius of the circle).
  68. Boyer, Carl Benjamin (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.
  69. Bailey, David; Borwein, Jonathan (2012). "Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics" (PDF). American Mathematical Monthly. 119 (8). pp. 646–657. Retrieved 14 September 2017.
  70. 37461 Aryabhata at the Encyclopædia Britannica
  71. Parakh, Abhishek (2006). "Aryabhata's Root Extraction Methods". arXiv:math/0608793.
  72. Kak 1986
  73. Cajori, Florian (1928). A History of Elementary Mathematics. Science. 5. The Open Court Company, Publishers. pp. 516–7. doi:10.1126/science.5.117.516. ISBN 978-1-60206-991-6. PMID 17758371. It will be remembered that the scratch method did not spring into existence in the form taught by the writers of the sixteenth century. On the contrary, it is simply the graphical representation of the method employed by the Hindus, who calculated with a coarse pencil on a small dust-covered tablet. The erasing of a figure by the Hindus is here represented by the scratching of a figure.
  74. Lay-Yong, Lam (1966). "On the Chinese Origin of the Galley Method of Arithmetical Division". The British Journal for the History of Science. 3: 66–69. doi:10.1017/S0007087400000200.
  75. Kurt Vogel, "Diophantus of Alexandria." in Complete Dictionary of Scientific Biography, Encyclopedia.com, 2008. Quote: The symbolism that Diophantus introduced for the first time, and undoubtedly devised himself, provided a short and readily comprehensible means of expressing an equation... Since an abbreviation is also employed for the word ‘equals’, Diophantus took a fundamental step from verbal algebra towards symbolic algebra.
  76. Pearce, Ian (May 2002). "The Bakhshali manuscript". The MacTutor History of Mathematics archive. Retrieved 24 July 2007.
  77. Reimer, L., and Reimer, W. Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Vol. 2. 1995. pp. 22-22. Parsippany, NJ: Pearson ducation, Inc. as Dale Seymor Publications. ISBN 0-86651-823-1.
  78. Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". In Katz, Victor J. (ed.). The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. p. 530. ISBN 978-0-691-11485-9.
  79. Miller, Jeff (22 December 2014). "Earliest Uses of Various Mathematical Symbols". Archived from the original on 20 February 2016. Retrieved 15 February 2016.
  80. Hayashi (2008), Aryabhata I
  81. The concept of Indian heliocentrism has been advocated by B. L. van der Waerden, Das heliozentrische System in der griechischen, persischen und indischen Astronomie. Naturforschenden Gesellschaft in Zürich. Zürich:Kommissionsverlag Leeman AG, 1970.
  82. B.L. van der Waerden, "The Heliocentric System in Greek, Persian and Hindu Astronomy", in David A. King and George Saliba, ed., From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E. S. Kennedy, Annals of the New York Academy of Science, 500 (1987), pp. 529–534.
  83. Hugh Thurston (1996). Early Astronomy. Springer. p. 188. ISBN 0-387-94822-8.
  84. Noel Swerdlow, "Review: A Lost Monument of Indian Astronomy," Isis, 64 (1973): 239–243.
  85. Pasipoularides, Ares (1 March 2014). "Galen, father of systematic medicine. An essay on the evolution of modern medicine and cardiology". International Journal of Cardiology. 172 (1): 47–58. doi:10.1016/j.ijcard.2013.12.166. PMID 24461486.
  86. Ansari, S.M.R. (March 1977). "Aryabhata I, His Life and His Contributions". Bulletin of the Astronomical Society of India. 5 (1): 10–18. Bibcode:1977BASI....5...10A. hdl:2248/502.
  87. Henry Thomas Colebrooke. Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara, London 1817, p. 339 (online)
  88. Plofker (2007, pp. 428–434)
  89. Tabak, John (2009), Algebra: Sets, Symbols, and the Language of Thought, Infobase Publishing, p. 42, ISBN 978-0-8160-6875-3
  90. Joseph, G. G. (2000), The Crest of the Peacock: The Non-European Roots of Mathematics, Princeton, NJ: Princeton University Press, 416 pages, ISBN 978-0-691-00659-8
  91. Broemeling, Lyle D. (2011). "An Account of Early Statistical Inference in Arab Cryptology". The American Statistician. 65 (4): 255–257. doi:10.1198/tas.2011.10191. S2CID 123537702.
  92. Gupta, R. C. (2000), "History of Mathematics in India", in Hoiberg, Dale; Ramchandani, Indu (eds.), Students' Britannica India: Select essays, Popular Prakashan, p. 329
  93. Kusuba 2004, pp. 497–516
  94. Kelley, David H. & Milone, Eugene F. (2011). Exploring Ancient Skies: A Survey of Ancient and Cultural Astronomy (2nd ed.). Springer Science+Business Media. p. 293. doi:10.1007/978-1-4419-7624-6. ISBN 978-1-4419-7624-6. OCLC 710113366.
  95. Morris R. Cohen and I. E. Drabkin (eds. 1958), A Source Book in Greek Science (p. 220), with several changes. Cambridge, MA: Harvard University Press, as referenced by David C. Lindberg (1992), The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450, University of Chicago Press, p. 305, ISBN 0-226-48231-6
  96. http://spie.org/etop/2007/etop07fundamentalsII.pdf," R. Rashed credited Ibn Sahl with discovering the law of refraction [23], usually called Snell’s law and also Snell and Descartes’ law."
  97. Smith, A. Mark (2015). From Sight to Light: The Passage from Ancient to Modern Optics. University of Chicago Press. p. 178. ISBN 9780226174761.
  98. Bina Chatterjee (introduction by), The Khandakhadyaka of Brahmagupta, Motilal Banarsidass (1970), p. 13
  99. Lallanji Gopal, History of Agriculture in India, Up to C. 1200 A.D., Concept Publishing Company (2008), p. 603
  100. Kosla Vepa, Astronomical Dating of Events & Select Vignettes from Indian History, Indic Studies Foundation (2008), p. 372
  101. Dwijendra Narayan Jha (edited by), The feudal order: state, society, and ideology in early medieval India, Manohar Publishers & Distributors (2000), p. 276
  102. Katz (1998), p. 255
  103. Florian Cajori (1918), Origin of the Name "Mathematical Induction", The American Mathematical Monthly 25 (5), p. 197-201.
  104. Radha Charan Gupta (1977) "Parameshvara's rule for the circumradius of a cyclic quadrilateral", Historia Mathematica 4: 67–74
  105. (Katz 1995)
  106. J J O'Connor and E F Robertson (2000). "Madhava of Sangamagramma". MacTutor History of Mathematics archive. School of Mathematics and Statistics, University of St Andrews, Scotland. Archived from the original on 14 May 2006. Retrieved 8 September 2007.
  107. Ian G. Pearce (2002). Madhava of Sangamagramma. MacTutor History of Mathematics archive. University of St Andrews.
  108. Roy 1990, pp. 101–102
  109. Brink, David (2015). "Nilakantha's accelerated series for π". Acta Arithmetica. 171 (4): 293–308. doi:10.4064/aa171-4-1.
  110. Ramasubramanian, K.; Srinivas, M. D.; Sriram, M. S. (1994). "Modification of the earlier Indian planetary theory by the Kerala astronomers (c. 1500 AD) and the implied heliocentric picture of planetary motion". Current Science. 66: 784–790.
  111. Crombie, Alistair Cameron, Augustine to Galileo 2, p. 67.
  112. Pines, Shlomo (1970). "Abu'l-Barakāt al-Baghdādī , Hibat Allah". Dictionary of Scientific Biography. 1. New York: Charles Scribner's Sons. pp. 26–28. ISBN 0-684-10114-9.
    (cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory", Journal of the History of Ideas 64 (4), p. 521-546 [528].)
  113. "The invention of spectacles". The College of Optometrists. The College of Optometrists. Retrieved 9 May 2020.
  114. Mochrie, Robert (2005). Justice in Exchange: The Economic Philosophy of John Duns Scotus
  115. "Robert Grosseteste". Stanford Encyclopaedia of Philosophy. Stanford.edu. Retrieved 6 May 2020.
  116. Kline, Morris. A history of mathematical thought, volume 1. p. 253.
  117. Katz, Victor J. (2004), "9.1.4", A History of Mathematics, Brief Version, Addison-Wesley, ISBN 978-0-321-16193-2
  118. Burton, David. The History of Mathematics: An Introduction (7th (2010) ed.). New York: McGraw-Hill.
  119. Bruno, Leonard C (2003) [1999]. Math and mathematicians: the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 60. ISBN 0787638137. OCLC 41497065.
  120. Westfall, Richard S. "Cardano, Girolamo". The Galileo Project. rice.edu. Archived from the original on 28 July 2012. Retrieved 2012-07-19.
  121. Beckmann, Petr (1971). A history of π (2nd ed.). Boulder, CO: The Golem Press. pp. 94–95. ISBN 978-0-88029-418-8. MR 0449960.
  122. Jourdain, Philip E. B. (1913). The Nature of Mathematics.
  123. Robert Recorde, The Whetstone of Witte (London, England: John Kyngstone, 1557), p. 236 (although the pages of this book are not numbered). From the chapter titled "The rule of equation, commonly called Algebers Rule" (p. 236): "Howbeit, for easie alteration of equations. I will propounde a fewe examples, bicause the extraction of their rootes, maie the more aptly bee wroughte. And to avoide the tediouse repetition of these woordes: is equalle to: I will sette as I doe often in worke use, a paire of paralleles, or Gemowe [twin, from gemew, from the French gemeau (twin / twins), from the Latin gemellus (little twin)] lines of one lengthe, thus: = , bicause noe .2. thynges, can be moare equalle." (However, for easy manipulation of equations, I will present a few examples in order that the extraction of roots may be more readily done. And to avoid the tedious repetition of these words "is equal to", I will substitute, as I often do when working, a pair of parallels or twin lines of the same length, thus: = , because no two things can be more equal.)
  124. Volckart, Oliver (1997). "Early beginnings of the quantity theory of money and their context in Polish and Prussian monetary policies, c. 1520–1550". The Economic History Review. Wiley-Blackwell. 50 (3): 430–49. doi:10.1111/1468-0289.00063. ISSN 0013-0117. JSTOR 2599810.
  125. "John Napier and logarithms". Ualr.edu. Retrieved 12 August 2011.
  126. "The Roslin Institute (University of Edinburgh) – Public Interest: Dolly the Sheep". www.roslin.ed.ac.uk. Retrieved 14 January 2017.
  127. "JCVI: First Self-Replicating, Synthetic Bacterial Cell Constructed by J. Craig Venter Institute Researchers". jcvi.org. Retrieved 12 August 2018.
  128. Anderson, Gina (28 September 2015). "NASA Confirms Evidence That Liquid Water Flows on Today's Mars". NASA. Retrieved 14 January 2017.
  129. "Recurring Martian Streaks: Flowing Sand, Not Water?". 21 November 2017.
  130. Landau, Elizabeth; Chou, Felicia; Washington, Dewayne; Porter, Molly (16 October 2017). "NASA Missions Catch First Light from a Gravitational-Wave Event". NASA. Retrieved 17 October 2017.
  131. "Neutron star discovery marks breakthrough for 'multi-messenger astronomy'". csmonitor.com. 16 October 2017. Retrieved 17 October 2017.
  132. "Hubble makes milestone observation of gravitational-wave source". slashgear.com. 16 October 2017. Retrieved 17 October 2017.
  133. "NASA's SOFIA Discovers Water on Sunlit Surface of Moon". AP NEWS. 26 October 2020. Retrieved 3 November 2020.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.