The Kepler's three laws, by Isaac Newton (by 1687)

Early proponents of prediction using mathematical calculation were British physicist and mathematician Isaac Newton. He made it feasible to forecast how objects will move through space and time by developing his 'fluxions' in 1665, which is now known as calculus (Gottfried Wilhelm Leibniz independently developed calculus at around the same time).

In order to do this, Newton included concepts from Johannes Kepler's three laws of planetary motion, Galileo Galilei's theories on force and acceleration, Robert Hooke's theories on how a planet's tangential velocity relates to the radial force it experiences, and Galileo Galilei's theories on how the gravitational force is an inverse square law directed towards the Sun.

The 'Speed of Light' equation by James Clerk Maxwell (1865)

By putting Michael Faraday's experimental theories into mathematical form, Scottish physicist James Clerk Maxwell made significant strides in the sciences of electricity and magnetism in 1860 at King's College London in the United Kingdom.A dynamical theory of the electromagnetic field, which was published in 1865, was the result of several works (Philosophical Transactions of the Royal Society of London 155 459). 

In addition to six wave equations—three for each spatial component of the electric field, E, and the magnetic field, B—Maxwell also derived a set of 20 partial differential equations from this data. 

These equations were not yet written down in the vector calculus notation that is familiar to us—Oliver Heaviside did this in 1884.Maxwell's research led him to the conclusion that he could 'barely avoid the inference that light consists in the transverse undulations of the same medium which is the origin of electric and magnetic phenomena' — in other words, he had foreseen that light is an electromagnetic wave.

Mercury's anomalous perihelion precession, by Albert Einstein (1915)

Mercury's orbit was meticulously examined in the 1840s by French astronomer Urbain Le Verrier. He discovered that the planet's elliptical orbit's perihelion, or closest point to the Sun, is not an exact ellipse as Newton's rules would have predicted. Instead, it is moving about the Sun. 

Only 532 arcseconds per century of the change, which is extremely slow, could be attributed to interactions with other planets at the time, leaving 43 arcseconds unaccounted for.Even if it was slight, the disparity alarmed astronomers. A variety of explanations were put out, including an undiscovered planet, an almost microscopic adjustment to Newton's gravitational law, and an oblate Sun, but none of them seemed to work.

Vera Rubin and W Kent Ford Jr.'s book Dark Matter (1970)

The American astronomer Vera Rubin once said in an interview, 'Great astronomers told us it didn't mean anything.She was alluding to their 1970 discovery that the outlying stars in the Andromeda galaxy all revolved around the galactic centre at the same rate. When instructed to continue examining spiral galaxies, the impact continued. 

The rotation curves of the galaxies were 'flat,' seemingly at odds with Kepler's law (the plot of the orbital speed of the visible stars within the galaxy vs their radial distance from the galaxy centre). 

Even more concerning, the stars were orbiting so quickly that they ought to be breaking apart on the galaxies' outer borders.Ford created new observational apparatus under Rubin's direction, including a sophisticated spectrometer based on an electronic photomultiplier tube that enabled the team to accurately record and analyse their astronomical observations.

Brian Josephson's term for it (1962)

As a graduate student at the University of Cambridge, Brian Josephson was taught by Nobel Prize–winning physicist Phillip Anderson, who said of the experience: I can promise you that this was an uncomfortable experience for the professor because he insisted on accuracy or he would approach me and explain it to me after class.

Due to this connection, Josephson was ready to present Anderson with calculations he had done on two superconductors that were separated from one another by a tiny insulating layer or a brief passage of non-superconducting metal. According to his theory, a 'DC supercurrent' made up of electron pairs (Cooper pairs) may tunnel from one superconductor to another without encountering the barrier—a demonstration of a macroscopic quantum effect.