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On November 8, 1895, physicist Wilhelm Conrad Röntgen (1845-1923) becomes the first person to observe X-rays, a significant scientific advancement that would ultimately benefit a variety of fields, most of all medicine, by making the invisible visible.

Röntgen's discovery occurred accidentally in his Wurzburg, Germany, lab, where he was testing whether cathode rays could pass through glass when he noticed a glow coming from a nearby chemically coated screen. He dubbed the rays that caused this glow X-rays because of their unknown nature.

X-rays are electromagnetic energy waves that act similarly to light rays, but at wavelengths approximately 1,000 times shorter than those of light. Röntgen holed up in his lab and conducted a series of experiments to better understand his discovery. He learned that X-rays penetrate human flesh but not higher-density substances such as bone or lead and that they can be photographed.

Röntgen's discovery was labeled a medical miracle and X-rays soon became an important diagnostic tool in medicine, allowing doctors to see inside the human body for the first time without surgery. In 1897, X-rays were first used on a military battlefield, during the Balkan War, to find bullets and broken bones inside patients.

Scientists were quick to realize the benefits of X-rays, but slower to comprehend the harmful effects of radiation. Initially, it was believed X-rays passed through flesh as harmlessly as light. However, within several years, researchers began to report cases of burns and skin damage after exposure to X-rays, and in 1904, Thomas Edison’s assistant, Clarence Dally, who had worked extensively with X-rays, died of skin cancer. Dally’s death caused some scientists to begin taking the risks of radiation more seriously, but they still weren’t fully understood.

During the 1930s, 40s and 50s, in fact, many American shoe stores featured shoe-fitting fluoroscopes that used X-rays to enable customers to see the bones in their feet; it wasn’t until the 1950s that this practice was determined to be risky business.

Wilhelm Röntgen received numerous accolades for his work, including the first Nobel Prize in physics in 1901, yet he remained modest and never tried to patent his discovery. Today, X-ray technology is widely used in medicine, material analysis and devices such as airport security scanners.

## Scientist Discovers X-rays - HISTORY

**ARIE CURIE'S CHOICE** of a thesis topic was influenced by two recent discoveries by other scientists. In December 1895, about six months after the Curies married, German physicist Wilhelm Roentgen discovered a kind of ray that could travel through solid wood or flesh and yield photographs of living people's bones. Roentgen dubbed these mysterious rays X-rays, with X standing for unknown. In recognition of his discovery, Roentgen in 1901 became the first Nobel laureate in physics.

In early 1896, only a few of months after Roentgen's discovery, French physicist Henri Becquerel reported to the French Academy of Sciences that uranium compounds, even if they were kept in the dark, emitted rays that would fog a photographic plate. He had come upon this discovery accidentally. Despite Becquerel's intriguing finding, the scientific community continued to focus its attention on Roentgen's X-rays, neglecting the much weaker Becquerel rays or uranium rays.

**HE IGNORED URANIUM RAYS** appealed to Marie Curie. Since she would not have a long bibliography of published papers to read, she could begin experimental work on them immediately. The director of the Paris Municipal School of Industrial Physics and Chemistry, where Pierre was professor of physics, permitted her to use a crowded, damp storeroom there as a lab.

“Instead of making these bodies act upon photographic plates, I preferred to determine the intensity of their radiation by measuring the conductivity of the air exposed to the action of the rays.”

This device for precise electrical measurement, invented by Pierre Curie and his brother Jacques, was essential for Marie's work. (Photo ACJC)

**ARIE'S SIMPLE HYPOTHESIS** would prove revolutionary. It would ultimately contribute to a fundamental shift in scientific understanding. At the time scientists regarded the atom--a word meaning *undivided* or *indivisible* -- as the most elementary particle. A hint that this ancient idea was false came from the discovery of the electron by other scientists around this same time. But nobody grasped the complex inner structure or the immense energy stored in atoms. Marie and Pierre Curie themselves were not convinced that radioactive energy came from within atoms--maybe, for example, the earth was bathed in cosmic rays, whose energy certain atoms somehow caught and radiated? Marie's real achievement was to cut through the complicated and obscure observations with a crystal-clear analysis of the set of conclusions that, however unexpected, were logically possible.

Marie tested all the known elements in order to determine if other elements or minerals would make air conduct electricity better, or if uranium alone could do this. In this task she was assisted by a number of chemists who donated a variety of mineral samples, including some containing very rare elements. In April 1898 her research revealed that thorium compounds, like those of uranium, emit Becquerel rays. Again the emission appeared to be an atomic property. To describe the behavior of uranium and thorium she invented the word “radioactivity” --based on the Latin word for ray.

## History: German scientist discovers X-rays in 1895

** **

On this day in 1895, physicist Wilhelm Conrad Rontgen (1845-1923) becomes the first person to observe X-rays, a significant scientific advancement that would ultimately benefit a variety of fields, most of all medicine, by making the invisible visible. Rontgen’s discovery occurred accidentally in his Wurzburg, Germany, lab, where he was testing whether cathode rays could pass through glass when he noticed a glow coming from a nearby chemically coated screen. He dubbed the rays that caused this glow X-rays because of their unknown nature.

Rontgen’s discovery was labeled a medical miracle and X-rays soon became an important diagnostic tool in medicine, allowing doctors to see inside the human body for the first time without surgery. In 1897, X-rays were first used on a military battlefield, during the Balkan War, to find bullets and broken bones inside patients.

## Welcome to the World of X-ray Astronomy

X-rays were first observed and documented in 1895 by Wilhelm Conrad Röntgen, a German scientist who found them quite by accident when experimenting with vacuum tubes. A week later, he took an X-ray photograph of his wife's hand which clearly revealed her wedding ring and her bones. The photograph electrified the general public and aroused great scientific interest in the new form of radiation. Röntgen called it "X" to indicate it was an unknown type of radiation. The name stuck, although (over Röntgen's objections), many of his colleagues suggested calling them Röntgen rays. They are still occasionally referred to as Röntgen rays in German-speaking countries.

In June 1990, the United States launched a new German-built satellite to record X-rays from the sky. This joint U.S./German/U.K. program was named Röntgen Satellite in his honor (though it is almost always referred to as ROSAT).

## How Astronomers Observe X-rays Emitted by Cosmic Sources

Although the more energetic X-rays (E > 30 keV) can penetrate the air for distances of at least a few meters (otherwise, Röntgen would never have observed them, and medical X-ray machines would not work), the Earth's atmosphere is thick enough that virtually none are able to penetrate from outer space all the way to the Earth's surface. X-rays in the 0.5 - 5 keV range, where most celestial sources give off the bulk of their energy, can be stopped by a few sheets of paper ninety percent of the photons in a beam of 3 keV X-rays are absorbed by traveling through just 10 cm of air!

To observe X-rays from the sky, the X-ray detectors must be flown above most of the Earth's atmosphere. There are at present three methods of doing so:

### Rocket flights

A detector is placed in the nose cone section of the rocket and launched above the atmosphere. This was first done at White Sands missile range in New Mexico with a V2 rocket in 1949. X-rays from the Sun were detected by the Navy's experiment on board. An Aerobee 150 rocket launched in June of 1962 detected the first X-rays from other celestial sources. The experiment package contained in this rocket is pictured at right. The largest drawback to rocket flights is their very short duration (just a few minutes above the atmosphere before the rocket falls back to Earth) and their limited field of view. A rocket launched from the United States will not be able to see sources in the southern hemisphere sky a rocket launched from Australia will not be able to see sources in the northern hemisphere sky.

### Balloons

Balloon flights can carry instruments to altitudes of 35 kilometers above sea level, where they are above the bulk of the Earth's atmosphere. Unlike a rocket where data are collected during a brief few minutes, balloons are able to stay aloft for much longer. However, even at such altitudes, much of the X-ray spectrum is still absorbed. X-rays with energies less than 35 keV cannot even reach balloons. One balloon-borne experiment was called the High Resolution Gamma-ray and Hard X-ray Spectrometer (HIREGS). It was launched in 1994 from the Antarctic where steady winds carried the balloon on a circumpolar flight lasting for almost two months! A picture of the launch of HIREGS can be seen at right. The instrument is at the bottom end of the balloon tether.

### Satellites

A detector is placed on a satellite which is taken up to an orbit well above the Earth's atmosphere. Unlike balloons, instruments on satellites are able to observe the full range of the X-ray spectrum. Unlike rockets, they can collect data for as long as the instruments continue to operate. In one instance, the Vela 5B satellite, the X-ray detector remained functional for over ten years!

## The Kinds of Objects in the Universe that X-ray Astronomers Observe

There are a variety of different kinds of astronomical sources which emit electromagnetic radiation in the X-ray regime. These include:

## History: German scientist discovers X-rays in 1895

** **

On this day in 1895, physicist Wilhelm Conrad Rontgen (1845-1923) becomes the first person to observe X-rays, a significant scientific advancement that would ultimately benefit a variety of fields, most of all medicine, by making the invisible visible. Rontgen’s discovery occurred accidentally in his Wurzburg, Germany, lab, where he was testing whether cathode rays could pass through glass when he noticed a glow coming from a nearby chemically coated screen. He dubbed the rays that caused this glow X-rays because of their unknown nature.

Rontgen’s discovery was labeled a medical miracle and X-rays soon became an important diagnostic tool in medicine, allowing doctors to see inside the human body for the first time without surgery. In 1897, X-rays were first used on a military battlefield, during the Balkan War, to find bullets and broken bones inside patients.

## This Month in Physics History

Few scientific breakthroughs have had as immediate an impact as Wilhelm Conrad Roentgen's discovery of X-rays, a momentous event that instantly revolutionized the fields of physics and medicine. The X-ray emerged from the laboratory and into widespread use in a startlingly brief leap: within a year of Roentgen's announcement of his discovery, the application of X-rays to diagnosis and therapy was an established part of the medical profession.

Roentgen's scientific career was one beset with difficulties. As a student in Holland, he was expelled from the Utrecht Technical School for a prank committed by another student. His lack of a diploma initially prevented him from obtaining a position at the University of Würzburg even after he received his doctorate, although he eventually was accepted. His experiments at Würzburg focused on light phenomena and other emissions generated by discharging electrical current in so-called "Crookes tubes," glass bulbs with positive and negative electrodes, evacuated of air, which display a fluorescent glow when a high voltage current is passed through it. He was particularly interested in cathode rays and in assessing their range outside of charged tubes.

On November 8, 1895, Roentgen noticed that when he shielded the tube with heavy black cardboard, the green fluorescent light caused a platinobarium screen nine feet at away to glow - too far away to be reacting to the cathode rays as he understood them. He determined the fluorescence was caused by invisible rays originating from the Crookes tube he was using to study cathode rays (later recognized as electrons), which penetrated the opaque black paper wrapped around the tube. Further experiments revealed that this new type of ray was capable of passing through most substances, including the soft tissues of the body, but left bones and metals visible. One of his earliest photographic plates from his experiments was a film of his wife Bertha's hand, with her wedding ring clearly visible.

To test his observations and enhance his scientific data, Roentgen plunged into seven weeks of meticulous planned and executed experiments. On December 28, he submitted his first "provisional" communication, "On a New Kind of Rays," in the Proceedings of the Würzburg Physico-Medical Society. In January 1896 he made his first public presentation before the same society, following his lecture with a demonstration: he made a plate of the hand of an attending anatomist, who proposed the new discovery be named "Roentgen's Rays."

The news spread rapidly throughout the world. Thomas Edison was among those eager to perfect Roentgen's discovery, developing a handheld fluoroscope, although he failed to make a commercial "X-ray lamp" for domestic use. The apparatus for producing X-rays was soon widely available, and studios opened to take "bone portraits," further fueling public interest and imagination. Poems about X-rays appeared in popular journals, and the metaphorical use of the rays popped up in political cartoons, short stories, and advertising. Detectives touted the use of Roentgen devices in following unfaithful spouses, and lead underwear was manufactured to foil attempts at peeking with "X-ray glasses."

As frivolous as such reactions may seem, the medical community quickly recognized the importance of Roentgen's discovery. By February 1896, X-rays were finding their first clinical use in the US in Dartmouth, MA, when Edwin Brant Frost produced a plate of a patient's Colles fracture for his brother, a local doctor. Soon attempts were made to insert metal rods or inject radio-opaque substances to give clear pictures of organs and vessels, with mixed results. The first angiography, moving-picture X-rays, and military radiology, were performed in early 1896.

In addition to the diagnostic powers of X-rays, some experimentalists began applying the rays to treating disease. Since the early 19th century, electrotherapy had proved popular for the temporary relief of real and imagined pains. The same apparatus could generate X-rays. In January 1896, only a few days after the announcement of Roentgen's work, a Chicago electrotherapist named Emil Grubbe irradiated a woman with a recurrent cancer of the breast, and by the end of the year, several researchers had noted the palliative effects of the rays on cancers. Others found remarkable results in the treatment of surface lesions and skin problems while others investigated the possible bacterial action of the rays. X-rays even found cosmetic uses in depilatory clinics set up in the US and France.

Roentgen was awarded the first Nobel Prize in physics in 1901 for his discovery. When asked what his thoughts were at the moment of discovery, he replied, true to form, "I didn't think, I investigated." Today, Roentgen is widely recognized as a brilliant experimentalist who never sought honors or financial profits for his research. He rejected a title that would have given him entry into the German nobility, and donated his Nobel Prize money to his university. While he accepted the honorary degree of doctor of medicine offered to him by his own university, he never took out any patents on X-rays, to ensure that the world could freely benefit from his work. His altruism came at considerable personal cost: at the time of his death in 1923, Roentgen was nearly bankrupt from the inflation following World War I.

**©1995 - 2021, AMERICAN PHYSICAL SOCIETY**

APS encourages the redistribution of the materials included in this newspaper provided that attribution to the source is noted and the materials are not truncated or changed.

## Contents

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.

### Mathematics Edit

#### Numbers, measurement and arithmetic Edit

- 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 Edit

- 2100 BC: The concept of area is first recognised in Babylonian clay tablets, [5] and 3-dimensional volume is discussed in an Egyptian papyrus. This begins the study of geometry.
- Early 2nd millennium BC: Similar triangles and side-ratios are studied in Egypt (e.g. in the Rhind Mathematical Papyrus, a copy of an older Middle Kingdom text) for the construction of pyramids, paving the way for the field of trigonometry. [6]

#### Algebra Edit

- 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 Edit

- 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 Edit

- 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 Edit

- 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. 13 200 would be written the same as 132 ). [17]

### Astronomy Edit

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

### Biology and anatomy Edit

- 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]

### Mathematics Edit

#### Geometry and trigonometry Edit

- 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 Edit

- 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 Edit

### Biology and anatomy Edit

- 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]

### Social science Edit

#### Linguistics Edit

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

### Mathematics Edit

#### Logic and proof Edit

- 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 Edit

- 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 Edit

- 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 Edit

- 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 ( n r ) = ( n − 1 r ) + ( n − 1 r − 1 )
>=< binom >+< binom >> , [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 Edit

- 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 Edit

- Late 5th century BC: Antiphon discovers the method of exhaustion, foreshadowing the concept of a limit.
- 3rd century BC: Archimedes makes use of infinitesimals. [47]
- 3rd century BC: Archimedes further develops the method of exhaustion into an early description of integration. [48][49]
- 3rd century BC: Archimedes calculates tangents to non-trigonometric curves. [50]

#### Numerical mathematics and algorithms Edit

- 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.

### Physics Edit

#### Astronomy Edit

- 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 Edit

- 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 Edit

- 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 Edit

### Biology and anatomy Edit

- 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 Edit

#### Economics Edit

- 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 Edit

### Astronomical and geospatial measurements Edit

- 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]

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.

### Mathematics Edit

#### Numbers, measurement and arithmetic Edit

- 210 AD: Negative numbers are accepted as numeric by the late Han-era Chinese text
*The Nine Chapters on the Mathematical Art*. [62] Later, Liu Hui of Cao Wei (during the Three Kingdoms period) writes down laws regarding the arithmetic of negative numbers. [63]

#### Algebra Edit

- 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 Edit

- 3rd century AD: Diophantus discusses linear diophantine equations.
- 499 AD: Aryabhata discovers Bezout's identity, a foundational result to the theory of principal ideal domains. [65]
- 499 AD: Aryabhata develops Kuṭṭaka, an algorithm very similar to the Extended Euclidean algorithm. [65]

#### Geometry and trigonometry Edit

- 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 Edit

- 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 Edit

- 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]

### Physics Edit

#### Astronomy Edit

- 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 Edit

- 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 Edit

### Astronomical and geospatial measurements Edit

- 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]

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.

### Mathematics Edit

#### Numbers, measurement and arithmetic Edit

- 628 AD: Brahmagupta states the arithmetic rules for addition, subtraction, and multiplication with zero, as well as the multiplication of negative numbers, extending the basic rules for the latter found in the earlier The Nine Chapters on the Mathematical Art. [87]

#### Algebra Edit

- 628 AD: Brahmagupta provides an explicit solution to the quadratic equation. [88]
- 9th century AD: Jain mathematician Mahāvīra writes down a factorisation for the difference of cubes. [89]

#### Number theory and discrete mathematics Edit

- 628 AD: Brahmagupta writes down Brahmagupta's identity, an important lemma in the theory of Pell's equation.
- 628 AD: Brahmagupta produces an infinite (but not exhaustive) number of solutions to Pell's equation.
- c. 850 AD: Mahāvīra derives the expression for the binomial coefficient in terms of factorials, ( n r ) = n ! r ! ( n − r ) !
>=< frac >> . [38] - c. 975 AD: Halayudha organizes the binomial coefficients into a triangle, i.e. Pascal's triangle. [38]

#### Geometry and trigonometry Edit

#### Analysis Edit

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

#### Probability and statistics Edit

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

#### Numerical mathematics and algorithms Edit

- 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 Edit

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

### Physics Edit

#### Astronomy Edit

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

#### Mechanics Edit

- 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 Edit

### Astronomical and geospatial measurements Edit

### Mathematics Edit

#### Algebra Edit

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

#### Number theory and discrete mathematics Edit

- c. 1000 AD: al-Karaji uses mathematical induction. [102]
- 12th century AD: Bhāskara II develops the Chakravala method, solving Pell's equation. [103]

#### Geometry and trigonometry Edit

#### Analysis Edit

- 1380 AD: Madhava of Sangamagrama develops the Taylor series, and derives the Taylor series representation for the sine, cosine and arctangent functions, and uses it to produce the Leibniz series for π . [105]
- 1380 AD: Madhava of Sangamagrama discusses error terms in infinite series in the context of his infinite series for π . [106]
- 1380 AD: Madhava of Sangamagrama discovers continued fractions and uses them to solve transcendental equations. [107]
- 1380 AD: The Kerala school develops convergence tests for infinite series. [105]
- c. 1500 AD: Nilakantha Somayaji discovers an infinite series for π . [108][109]

#### Numerical mathematics and algorithms Edit

- 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.
- 1480 AD: Madhava of Sangamagrama found pi and that it was infinite.

### Physics Edit

#### Astronomy Edit

- 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 Edit

- 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 Edit

- 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 - Eyeglasses are invented in Northern Italy, [113] possibly Pisa, demonstrating knowledge of human biology [
*citation needed*] and optics, to offer bespoke works that compensate for an individual human disability.

### Astronomical and geospatial measurements Edit

- 11th century: Shen Kuo discovers the concepts of true north and magnetic declination.
- 11th century: Shen Kuo develops the field of geomorphology and natural climate change.

### Social science Edit

#### Economics Edit

- 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 Edit

- 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.

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

### Mathematics Edit

#### Numbers, measurement and arithmetic Edit

#### Algebra Edit

- c. 1500: Scipione del Ferro solves the special cubic equation x 3 = p x + q
=px+q> . [118][119] - 16th century: Gerolamo Cardano solves the general cubic equation (by reducing them to the case with zero quadratic term).
- 16th century: Lodovico Ferrari solves the general quartic equation (by reducing it to the case with zero quartic term).
- 16th century: François Viète discovers Vieta's formulas.

#### Probability and statistics Edit

#### Numerical mathematics and algorithms Edit

#### Notation and conventions Edit

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

## The Shy Scientist Who Could See Through Skin

N o one was initially more skeptical of the existence of X-rays than Wilhelm Roentgen &mdash the man who discovered them.

One day in late 1895, the German physicist was preparing to begin an experiment with cathode rays, the glowing beams of electrons that pass through a vacuum tube when electricity is applied, which were a popular fixture in physics at the time. In his darkened lab, he covered the tube with black cardboard to hide its glow, but noticed a glimmer of light on a fluorescent screen across the room.

Curious, Roentgen &ldquoplaced a sheet of black cardboard between the screen and the tube, then another, then a book of 1000 pages, then a wooden shelf board more than two and a half centimeters thick,&rdquo according to a story in the journal *Physics Today*. &ldquoThe glimmer remained.&rdquo

At some point, he held up a small lead disk, and cast a terrifying shadow on the screen: the dark shape of the disk itself, along with the skeletal outline of the bones in his hand.

According to *Physics Today*, Roentgen was very late to dinner with his family that night. When he did show up, &ldquohe did not speak, ate little, and then left abruptly&rdquo to return to his lab. Afraid that he might have imagined the whole thing, he cautiously told a friend, as quoted by the journal *Resonance*, &ldquoI have discovered something interesting, but I do not know whether or not my observations are correct.&rdquo Eventually he summoned the courage to tell his wife what he&rsquod seen, and enlisted her help in a follow-up experiment. Just before Christmas that year, he replaced the fluorescent screen with photographic paper and took the world&rsquos first X-ray, a clear image of the bones and wedding ring on his wife&rsquos left hand. She found the experience as unnerving as he had, exclaiming, &ldquoI have seen my death.&rdquo

When news of Roentgen&rsquos discovery was published in an Austrian newspaper on this day, Jan. 5, in 1896, the monumental implications for science and medicine quickly became apparent. The New York *Times* picked up the story two weeks later, but couched it in skepticism that echoed Roentgen&rsquos own, reporting his &ldquoalleged discovery of how to photograph the invisible.&rdquo

While the *Times* eventually wrote more glowingly of Roentgen&rsquos discovery, neither it nor any other newspaper revealed much about the scientist himself. Notoriously publicity-shy, he turned down countless speaking engagements and stipulated that when he died, his letters and journals should be destroyed.

He eschewed fortune as well as fame: He never patented X-rays, which he thought should be freely available to other researchers and the medical community, and, according to TIME’s brief notice at the time of his death, donated the money that came with his 1901 Nobel Prize (about $40,000) to a scientific society.

Roentgen&rsquos generosity caught up with him near the end of his life, however. By the time he died, in 1923, his unwillingness to profit from his discovery &mdash coupled with the economic conditions that followed World War I &mdash had left him nearly penniless.

* Read TIME’s 1956 examination of the safety of X-rays*: X-Ray Danger

## The Discovery of DNA's Structure

Taken in 1952, this image is the first X-ray picture of DNA, which led to the discovery of its molecular structure by Watson and Crick. Created by Rosalind Franklin using a technique called X-ray crystallography, it revealed the helical shape of the DNA molecule. Watson and Crick realized that DNA was made up of two chains of nucleotide pairs that encode the genetic information for all living things.

**Credits:** Photo of Rosalind Franklin courtesy of Vittorio Luzzati. Photo of x-ray crystallography (Exposure 51) courtesy of King's College Archives. King's College London.

**Topics Covered:**

Evolution Since Darwin

They were hardly modest, these two brash young scientists who in 1953 declared to patrons of the Eagle Pub in Cambridge, England, that they had "found the secret of life." But James Watson and Francis Crick's claim was a valid one, for they had in fact discovered the structure of DNA, the chemical that encodes instructions for building and replicating almost all living things. The stunning find made possible the era of "new biology" that led to the biotechnology industry and, most recently, the deciphering of the human genetic blueprint.

Watson and Crick's discovery didn't come out of the blue. As early as 1943 Oswald Avery proved what had been suspected: that DNA, a nucleic acid, carries genetic information. But no one knew how it worked.

By the early 1950s, at least two groups were hot on the trail. Crick, a British graduate student, and Watson, an American research fellow, were in the hunt at Cambridge University.

At King's College in London, Rosalind Franklin and Maurice Wilkins were studying DNA. Wilkins and Franklin used X-ray diffraction as their main tool -- beaming X-rays through the molecule yielded a shadow picture of the molecule's structure, by how the X-rays bounced off its component parts.

Franklin, a shy and inward young woman, suffered from patronizing attitudes and sexism that forced her to do much of her work alone. And her senior partner, Wilkins, showed some of Franklin's findings to Watson in January 1953 without her knowledge.

Referring to Franklin's X-ray image known as "Exposure 51," James Watson is reported to have said, "The instant I saw the picture, my mouth fell open and my pulse began to race." Shortly after, Watson and Crick made a crucial advance when they proposed that the DNA molecule was made up of two chains of nucleotides paired in such a way to form a double helix, like a spiral staircase. This structure, announced in their famous paper in the April 1953 issue of Nature, explained how the DNA molecule could replicate itself during cell division, enabling organisms to reproduce themselves with amazing accuracy except for occasional mutations.

For their work, Watson, Crick, and Wilkins received the Nobel Prize in 1962. Despite her contribution to the discovery of DNA's helical structure, Rosalind Franklin was not named a prize winner: She had died of cancer four years earlier, at the age of 37.

## NASA researchers discover first X-rays from Uranus

#### NASA rocket passes key test for Artemis mission

Acting NASA Administrator Steve Jurczyk provides insight on ‘FOX News Live.’

Astronomers at NASA's Chandra X-ray Observatory have detected X-rays from the planet Uranus for the first time.

Researchers used observations of the ice giant taken in 2002 and 2017 to detect the radiation as part of a new study published Tuesday in the Journal of Geophysical Research.

In an examination and with further analysis, they saw clear detection of X-rays from the first observation and possible flare of X-rays from those 15 years later.

The scientists believe that the sun could be the driving force causing Uranus to emit the X-rays.

Uranus at approximately the same orientation as it was during the 2002 Chandra observations. 2017 HRC Composite Image (Credit: X-ray: NASA/CXO/University College London/W. Dunn et al Optical: W.M. Keck Observatory) (NASA)

Astronomers have previously observed that both Jupiter and Saturn scatter X-ray light from the sun.

However, while the study's authors say they believe the X-rays detected would also be from "scattering," another source of X-rays is also likely.

Like Saturn, they say, Uranus' rings could be producing the X-rays itself or even the planet's aurora -- a phenomenon created when high-energy particles interact with the atmosphere.

"Uranus is surrounded by charged particles such as electrons and protons in its nearby space environment," the Chandra X-ray Observatory wrote in a release. "If these energetic particles collide with the rings, they could cause the rings to glow in X-rays."

X-rays are emitted in Earth’s auroras and Jupiter has auroras, as well, though X-rays from auroras on Jupiter come from two sources.

However, a nearly identical NASA release notes that researchers remain uncertain about what causes the auroras on Uranus.

The agency wrote that the unusual orientations of its spin axis and magnetic field may cause the planet's auroras to be "unusually complex and variable."

The rotation axis of Uranus is nearly parallel to its path around the sun -- unlike the axes of other planets in the solar system -- and while Uranus is tilted on its side, its magnetic field is tiled by a different amount.

"Determining the sources of the X-rays from Uranus could help astronomers better understand how more exotic objects in space, such as growing black holes and neutron stars, emit X-rays," NASA wrote.

Uranus is the seventh planet from the sun in the solar system. It has two sets of rings around its equator. Its diameter is four times that of Earth.

Because Voyager 2 was the only spacecraft to ever fly by Uranus, astronomers rely on telescopes like Chandra to learn more about the cold planet that is made up almost entirely of hydrogen and helium.

## Just Months After Its Discovery, the X-Ray Was in Use in War

Photography of any kind was still a relatively new technology in 1895—imagine what it must have felt like to learn you could take a photograph of a living person’s bones.

### Related Content

On this day in 1895, scientist Wilhelm Conrad Röntgen published a paper called ‘On a New Kind of Rays.’ It was the first scientific paper to describe x-rays. Only six days earlier, he took the x-ray that was published with the paper: his wife’s hand, her wedding ring visible on the fourth finger. Although we don’t think about it much now, the x-ray gave people an entirely new ability: to see inside a living person without cutting them open first.

The English translation of Röntgen's paper appeared in the January 23, 1896 edition of *Nature*. He describes conducting an experiment by firing electricity through a vacuum tube. He’d covered the tube in black cardboard to block the light this produced, but even though the tube was covered he noticed that a fluorescent screen more than a meter away was glowing, writes Hannah Waters for *The Scientist*. (One of the earliest x-ray tubes is in the collection of The National Museum of American History.)

Röntgen dubbed these mysterious rays capable of passing through glass “X” (for unknown) and subsequently tried to block them with a variety of materials—aluminum, copper, even the walls of his lab—to no avail,” she writes. When he tried it with a piece of lead, she writes, it blocked the rays, “but he was shocked to see his own flesh glowing around his bones on the fluorescent screen behind his hand.” The step from here to an x-ray photograph was short.

The ability of the new rays to image the bones within a living hand interested the general public for some six months,” writes researcher Arne Hessenbruch. Newspapers published long explorations of how the x-ray worked and what its consequences might be, while humorists produced cartoons and theaters wrote x-ray plays. The prospect of total nakedness, as shown by early x-rays of hands, was understandably titillating to the general public.

But while the public was laughing, the x-ray was immediately useful to doctors. The first x-ray machine was used to take images of patients just a month after the publication of Röntgen's paper, reports one 2011 study. Within just a few months, it was being used by battlefield doctors, writes Dan Schlenoff for *Scientific American*. Before the x-ray, there was no reliable way to tell precisely what was going on inside someone’s body. The exact location of a break in a bone, a bullet, or a piece of shrapnel was a mystery.

Over the next few years, Schlenoff writes, they were used in the Greco-Turkish War, the Russo-Japanese War and the Balkan Wars. “Mobile units were developed to keep up with field hospitals,” he writes. “If surgery could be performed, x-rays became vital.” By the time WWI began, x-ray technology was well-established.

Civilian doctors were as quick to see the technology’s usefulness. “Within a year, the first radiology department opened in a Glasgow hospital,” Waters writes, “and the department head produced the first pictures of a kidney stone and a penny lodged in a child’s throat.”

X-rays are light, like any other light, but they’re not in the visible spectrum. And their properties meant that early x-rays were very damaging to people’s bodies. Barely two weeks after Rӧntgen’s discovery, a dentist used himself as a guinea pig and shot the first dental radiograph, write K. Sansare, V. Khanna and F. Karjodkar in the journal *DentoMaxilloFacial Radiology*. The exposure took 25 minutes, which he later described as torture, although he didn’t elaborate. But he continued to experiment with radiation—on his patients, not himself.

Many other early medical uses of x-rays resulted in patients getting burns. A 2011 study of an early x-ray machine found that its use would expose the skin to 1,500 times the amount of radiation present in a modern x-ray.

###### About Kat Eschner

Kat Eschner is a freelance science and culture journalist based in Toronto.