PIERRE DE FERMAT (1601- 65) ANDREW WILES (b.1953)

1637 – France; 1993 – USA

Portrait of PIERRE DE FERMAT

PIERRE DE FERMAT

Fermat’s theorem proves that there are no whole-number solutions of the equation x n + y n = z n for n greater than 2

The problem is based on Pythagoras’ Theorem; in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides; that is x 2 + y 2 = z 2

If x and y are whole numbers then z can also be a whole number: for example 52+ 122 = 132
If the same equation is taken to a higher power than 2, such as x 3 + y 3 = z 3 then z cannot ever be a whole number.

In about 1637, Fermat wrote an equation in the margin of a book and added ‘I have discovered a truly marvelous proof, which this margin is too small to contain’. The problem now called Fermat’s Last Theorem baffled mathematicians for 356 years.

photo of Andrew Wiles in classroom

ANDREW WILES

In 1993, Wiles, a professor of mathematics at Princeton University, finally proved the theorem.

Wiles, born in England, dreamed of proving the theorem ever since he read it at the age of ten in his local library. It took him years of dedicated work to prove it and the 130-page proof was published in the journal ‘Annals of Mathematics‘ in May 1995.

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BENJAMIN FRANKLIN (1706-1790)

1752 – The New World

Portrait of BENJAMIN FRANKLIN ©

BENJAMIN FRANKLIN

‘If you would not be forgotten when you are dead and rotten, either write things worth reading, or do things worth writing about’

Curious about how just about everything works, from governments to lightning rods, Franklin’s legacy, in addition to the many inventions such as lightning conductors, bifocal lenses and street lamps, was one of learning. He established one of the first public libraries as well as one of the first universities in America, Pennsylvania. He established the Democratic Party. Franklin was one of the five signatories of the Declaration of Independence from Great Britain in 1776 and was a later participant in the drafting of the American Constitution.

‘Benjamin Franklin’s choice for the signs of electric charges leads to electric current being positive, even though the charge carriers themselves are negative — thereby cursing electrical engineers with confusing minus signs ever since.
The sign of the charge carriers could not be determined with the technology of Franklin’s time, so this isn’t his fault. It’s just bad luck’

Franklin was a pioneer in understanding the properties and potential of electricity. He undertook studies involving electric charge and introduced the terms ‘positive’ and ‘negative’ in explaining the way substances could be attracted to or repelled by each other according to the nature of their charge. He believed these charges ultimately cancelled each other out so that if something lost electrical charge, another substance would instantly gain the same amount.

 

His work on electricity climaxed with his kite flying experiment of 1752. In order to prove lightning to be a form of electricity, Franklin launched a kite into a thunderstorm on a long piece of conducting string. Tying the string to a capacitor, which became charged when struck by lightning, vindicated his theories.

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BENJAMIN THOMPSON (1753-1814) known as Count Rumford

1798 – England

‘Mechanical work can be converted into heat. Heat is the energy of motion of particles’

Heat is a form of energy associated with the random motion of atoms or molecules. Temperature is a measure of the hotness of an object.

In the eighteenth century, scientists imagined heat as a flow of a fluid substance called CALORIC. Each object contained a certain amount of caloric. If caloric flowed out, the object’s temperature decreased; if more caloric flowed into the object, its temperature increased.

Like PHLOGISTON, caloric was a weightless fluid, a quality that could be transmitted from one substance to another, so that the first warmed the second up. What is being transmitted is heat energy.

Working for the Elector of Bavaria, Rumford investigated the heat generated during the reaming out of the metal core when the bore of a cannon is formed. According to the caloric theory, the heat was released from the shards of metal during boring; Rumford noticed that if the tools were blunt and removed little or no metal, more heat was generated, rather than less.

Rumford postulated that the heat source had to be the work done in drilling the hole. Heat was not an indestructible caloric fluid, as LAVOISIER had argued, but something that could come and go. Mechanical energy could produce heat and heat could lead to mechanical energy.

One analogy he drew was to a bell; heat was like sound, with cold being similar to low notes and hot, to high ones. Temperature was therefore just the frequency of the bell. A hot object would emit ‘calorific rays’, whilst a cold one would emit ‘frigorific rays’ – an idea raised in Plutarch’s De Primo Frigido. Cold was an entity in itself, not simply the absence of heat.

Rumford thought there was no separate caloric fluid and that the heat content of an object was associated with motion or internal vibrations – motion which in the case of the cannon was bolstered by the friction of the tools. He had recognized the relationship between heat energy and the physicists’ concept of ‘work’ – the transfer of energy from a system into the surroundings, caused by the work done, results in a difference in temperature.
This transfer of energy measured as a temperature difference is called ‘heat’.

Half a century was to pass before in 1849, JAMES JOULE established the ‘mechanical equivalent of heat’ and JAMES CLERK MAXWELL launched the kinetic theory. According to Maxwell, the heat content of a body is equivalent to the sum of the individual energies of motion (kinetic energies) of its constituent atoms and molecules.

US born Rumford founded the Royal Institution in London and invented the calorimeter, a device measuring heat.

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THOMAS ALVA EDISON (1847-1931)

1875 – USA

‘We don’t know one millionth of one percent of anything’

photo portrait of THOMAS ALVA EDISON ©

THOMAS ALVA EDISON

‘Genius is one percent inspiration and ninety-nine percent perspiration’
Scorning high-minded theoretical and mathematical methods was the basis of Edison’s trial and error approach to scientific enquiry and the root of his genius.

1877 – Patents the carbon button transmitter, still in use in telephones today.
1877 – Invents the phonograph.
1879 – Invents the first commercial incandescent light after more than 6000 attempts at finding the right filament and finally settling on carbonized bamboo fibre.

Edison held 1093 patents either jointly or singularly and was responsible for inventing the Kinetograph and the Kinetoscope (available from 1894) the Dictaphone, the mimeograph, the electronic vote-recording machine and the stock ticker.

His laboratory was established at Menlo Park in 1876, establishing dedicated research and development centres full of inventors, engineers and scientists. In 1882 he set up a commercial heat, light and power company in Lower Manhattan, which became the company General Electric.

Experimenting with light bulbs, in 1883 one of his technicians found that in a vacuüm, electrons flow from a heated element – such as an incandescent lamp filament – to a cooler metal plate.
The electrons can flow only from the hot element to the cool plate, but never the other way. When English physicist JOHN AMBROSE FLEMING heard of this ‘Edison effect’ he used the phenomenon to convert an alternating electric current into a direct current, calling his device a valve. Although the valve has been replaced by diodes, the principle is still used.

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ALEXANDER GRAHAM BELL (1847-1922)

1875 – USA

‘The inventor of the telephone, Bell devoted much of his life to working with the deaf’

After emigrating to Canada from Scotland in 1870, Bell met Thomas Watson, who would help Bell’s theoretical ideas become physical reality. Bell believed that if the right apparatus could be devised, sound waves from the mouth could be converted into electric current, which could then be sent down a wire relatively simply and converted into sound at the other end using a suitable device. Bell’s telephone was patented in 1876.

Bell used the money brought in from his invention to found his company AT & T and the Bell Laboratories.
Just as THOMAS EDISON improved the viability of Bell’s telephone, so Bell enhanced Edison’s phonograph.

Bell spent some time educating Helen Keller and was instrumental in founding the journal ‘Science‘.

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ALBERT EINSTEIN (1879-1955)

1905 – Switzerland

  1. ‘the relativity principle: All laws of science are the same in all frames of reference.
  2. constancy of the speed of light: The speed of light in a vacuüm is constant and is independent of the speed of the observer’
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EINSTEIN

The laws of physics are identical to different spectators, regardless of their position, as long as they are moving at a constant speed in relation to each other. Above all the speed of light is constant. Classical laws of mechanics seem to be obeyed in our normal lives because the speeds involved are insignificant.

Newton’s recipe for measuring the speed of a body moving through space involved simply timing it as it passed between two fixed points. This is based on the assumptions that time is flowing at the same rate for everyone – that there is such a thing as ‘absolute’ time, and that two observers would always agree on the distance between any two points in space.
The implications of this principle if the observers are moving at different speeds are bizarre and normal indicators of velocity such as distance and time become warped. Absolute space and time do not exist. The faster an object is moving the slower time moves. Objects appear to become shorter in the direction of travel. Mass increases as the speed of an object increases. Ultimately nothing may move faster than or equal to the speed of light because at that point it would have infinite mass, no length and time would stand still.

‘The energy (E) of a body equals its mass (m) times the speed of light (c) squared’

This equation shows that mass and energy are mutually convertible under certain conditions.

The mass-energy equation is a consequence of Einstein’s theory of special relativity and declares that only a small amount of atomic mass could unleash huge amounts of energy.

Two of his early papers described Brownian motion and the ‘photoelectric’ effect (employing PLANCK’s quantum theory and helping to confirm Planck’s ideas in the process).

1915 – Germany

‘Objects do not attract each other by exerting pull, but the presence of matter in space causes space to curve in such a manner that a gravitational field is set up. Gravity is the property of space itself’

From 1907 to 1915 Einstein developed his special theory into a general theory that included equating accelerating forces and gravitational forces. This implies light rays would be bent by gravitational attraction and electromagnetic radiation wavelengths would be increased under gravity. Moreover, mass and the resultant gravity, warps space and time, which would otherwise be ‘flat’, into curved paths that other masses (e.g. the moons of planets) caught within the field of the distortion follow. The predictions from special and general relativity were gradually proven by experimental evidence.

Einstein spent much of the rest of his life trying to devise a unified theory of electromagnetic, gravitational and nuclear fields.

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NIKOLA TESLA (1856-1943)

1888 – USA

‘The transmission of high voltage alternating current (AC) over long distances is more efficient than the transmission of direct current (DC)’

DC transmission is no longer used anywhere in the world.

Early photograph of NikolaTesla ©

NIKOLA TESLA

In the 1880s THOMAS EDISON (1847-1931) developed DC generation and set up his Edison light company to build power plants. DC loses much of its energy when transmitted through wires at long distances and DC power plants had to be close to cities.

In 1888 Tesla came up with an idea involving a rotating magnetic field in an induction motor, which would generate an ‘alternating current’. He invented the AC induction motor and suggested that the transmission of AC power is more efficient.

On 16th November 1896 the AC power plant at Niagara Falls built by George Westinghouse (1864-1914) became the first power plant to transmit electric power between two cities (from Niagara Falls to Buffalo).

Tesla’s development of AC power led to the invention of induction motors, dynamos, transformers, condensers, bladeless turbines, mechanical rev. counters, automobile speedometers, gas discharge lamps (forerunners of fluorescent lights), radio broadcasting and hundreds of other things. His patents number over 700.

The tesla (T), the SI unit of magnetic flux density, for measuring magnetism, is named in his honour.

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