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The Genius Nicola Tesla and Mathematics

by Liliana Usvat


"Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality." (Nikola Tesla)

One day man will connect his apparatus to the very wheel work of the universe ...
and the very forces that motivate the planets in their orbits and cause them to rotate will rotate his own machinery. (Nikola Tesla)

"The scientific man does not aim at an immediate result.
He does not expect that his advanced ideas will be readily taken up.
His work is like that of the planter - for the future.
His duty is to lay the foundation for those who are to come, and point the way.
He lives and labors and hopes." (Nikola Tesla)

"Perhaps it is better in this present world of ours that a revolutionary idea or invention instead of being helped and patted, be hampered and ill-treated in its adolescence - by want of means, by selfish interest, pedantry, stupidity and ignorance; that it be attacked and stifled; that it pass through bitter trials and tribulations, through the heartless strife of commercial existence. So do we get our light. So all that was great in the past was ridiculed, condemned, combated, suppressed - only to emerge all the more powerfully, all the more triumphantly from the struggle." (Nikola Tesla)

Nikola Tesla (10 July 1856 – 7 January 1943) was a Serbian Americaninventor, electrical engineer, mechanical engineer, physicist, and futurist best known for his contributions to the design of the modern alternating current (AC) electricity supply system.

Eidetic memory

Tesla read many works, memorizing complete books, and supposedly possessed a photographic memory. He was a polyglot, speaking eight languages: Serbo-Croatian, Czech, English, French, German, Hungarian, Italian, and Latin.

Tesla related in his autobiography that he experienced detailed moments of inspiration. During his early life, Tesla was stricken with illness time and time again. He suffered a peculiar affliction in which blinding flashes of light would appear before his eyes, often accompanied by visions.

Often, the visions were linked to a word or idea he might have come across; at other times they would provide the solution to a particular problem he had encountered. Just by hearing the name of an item, he would be able to envision it in realistic detail.

Tesla would visualize an invention in his mind with extreme precision, including all dimensions, before moving to the construction stage, a technique sometimes known as picture thinking.

He typically did not make drawings by hand but worked from memory. Beginning in his childhood, Tesla had frequent flashbacks to events that had happened previously in his life

Tesla noticed that he could clearly visualize his discoveries, he didn’t need experiments, models or drawings . In such a way he developed his own methods to give material form to his creative ideas. Tesla sharply distinguished ideas, which were coming into his mind as visions, and those, which appear due to analytical mind clearance. Tesla explained:

The moment when somebody designs an imaginary device and is connected with a problem of transfer from raw idea to the practice. That is why any discovery made this way has lack of details, and usually it is inferior .

Tesla used another method, entirely. He did not hurry nor follow with an empirical check. When an idea appeared, he immediately began to elaborate on it in his imagination. He would change its design, improving it -and would “switch on” the device to begin its operation in his head. For him, it did not matter whether he tested his invention in the laboratory or in his mind. He could notice if something would prevent his invention from working properly… in the same way he could develop a perfect idea without any physical touch. Only then would he give a concrete look for this final product of his mind. All his inventions were developed by this method - with no exceptions, during twenty years…

"There is hardly any scientific discovery that can't be foreseen mathematically, without visualization… Introduction of unfinished, crude ideas to the practice is always a waste of energy and time.

According to Tesla, certain conclusions were born in his mind spontaneously, in the form of geometric images. Then followed the understanding of the discovery and its physical interpretation. Only then, mathematical formalization took place, followed by finding the necessary technical properties and material essential for a continuous operation of the constructed physical model. The work he understood at first as a struggle for mental clarification, i.e. elimination of secondary ideas and sensible details, which blur imaging principles and complicate the approach to the real nature of relations between fundamental geometrical elements.

According to Tesla, the principle was considered finished and ready to apply, when the connection between geometrical objects was stated. Thus, discovery appeared at the moment when correspondence of the elements and their physical manifestations was defined, so we can find a physical law, which rules in the real world, in the algorithm itself. For Tesla, an idea found its manifestation in the act of creative thinking.

Only then, the operating parameters of a specific device took place, following from general understanding. The result can be a design of an inductive engine or a model of rotating magnetic field.

As he told  it, a method of mental improvement was polished to such great extent, making even minute corrections of the discovery in my mind, without any physical check, would assure it correct operation. It can open an illusive secret to his work, amounting to a great volume, taking into consideration all of his scientific and technical innovation; it is a remarkable fact.


Tesla used simple the mathematics of Ancient Greek mathematician Archimedes, first making an analogy between mechanics and electromagnetism. It is not possible to fully evaluate the significance of such method of thinking, which directly points out the necessity of full physical interpretation of elementary mathematical notions.

Tesla’s physics requires a quite different understanding of mathematics, in some extent it is sacral in the spirit of Pythagoras. Pythagoras considered that numbers and subjects are interrelated. They correspond to each other in property due to informational and mathematical aspects of matter existing as one of the manifestations of the Divine Logos.

Attentive researchers can immediately notice that there are no infinitesimal or differentials in Tesla’s works. Tesla knew James Maxwell, creator of the theoretical electromagnetism. He told (Maxwell) that his elegant differential equations are as poetry. One could find Maxwell’s works in Tesla’s library; these works were published when Tesla was twenty and he was a student in Graatz.


In 1928, Tesla received his last patent, U.S. Patent 1,655,114, for a biplane capable of taking off vertically (VTOL aircraft) and then be "gradually tilted through manipulation of the elevator devices" in flight until it was flying like a conventional plane.

Tesla obtained around 300 patents worldwide for his inventions. Some of Tesla's patents are not accounted for, and various sources have discovered some that have lain hidden in patent archives.

There are a minimum of 278 patents issued to Tesla in 26 countries that have been accounted for. Many of Tesla's patents were in the United States, Britain, and Canada, but many other patents were approved in countries around the globe. Many inventions developed by Tesla were not put into patent protection.

Family and Education

His father, Milutin Tesla was a Serbian Orthodox Priest and his mother Djuka Mandic was an inventor in her own right of household appliances. Tesla studied at the Realschule, Karlstadt in 1873, the Polytechnic Institute in Graz, Austria and the University of Prague.

At first, he intended to specialize in physics and mathematics, but soon he became fascinated with electricity. He began his career as an electrical engineer with a telephone company in Budapest in 1881.


Tesla gained experience in telephony and electrical engineering before emigrating to the United States in 1884 to work for Thomas Edison.

Young Nikola Tesla came to the United States in 1884 with an introduction letter from Charles Batchelor to Thomas Edison: "I know two great men,” wrote Batchelor, "one is you and the other is this young man.” Tesla spent the next 59 years of his productive life living in New York. Tesla set about improving Edison’s line of dynamos while working in Edison’s lab in New Jersey. It was here that his divergence of opinion with Edison over direct current versus alternating current began. This disagreement climaxed in the war of the currents as Edison fought a losing battle to protect his investment in direct current equipment and facilities.

His childhood dream was to come to America to harness the power of Niagara Falls.

He soon struck out on his own with financial backers, setting up laboratories and companies to develop a range of electrical devices. His patented AC induction motor and transformer were licensed by George Westinghouse, who also hired Tesla as a consultant to help develop a power system using alternating current.

Tesla is also known for his high-voltage, high-frequency power experiments in New York and Colorado Springs which included patented devices and theoretical work used in the invention of radio communication, for his X-ray experiments, and for his ill-fated attempt at intercontinental wireless transmission in his unfinished Wardenclyffe Tower project.

Nikola Tesla developed polyphase alternating current system of generators, motors and transformers and held 40 basic U.S. patents on the system, which George Westinghouse bought, determined to supply America with Tesla system.

In February 1882, Tesla discovered rotating magnetic field, a fundamental principle in physics and the basis of nearly all devices that use alternating current.

Tesla's A-C induction motor is widely used throughout the world in industry and household appliances.  This motor started the industrial revolution at he turn of the century.  Electricity today is generated, transmitted and converted to mechanical power by means of his inventions.  Tesla's greatest achievement is his polyphase alternating current system, which is today lighting the entire globe.

Tesia astonished the world by demonstrating the wonders of alternating current electricity at the World Columbian Exposition in Chicago in 1893.

Alternating current became standard power in the 20th century.  This accomplishment changed the world.  He designed the first hydroelectric powerplant in Niagara Falls in 1895, which was the final victory of alternating current.  The achievement was covered widely in the world press and Tesla was praised as a hero worldwide.  The King Nikola of Montenegro conferred upon him the Order of Danilo.

Tesla built an experimental station in Colorado Springs, Colorado in 1899, to experiment with high voltage, high frequency electricity and other phenomena.

As early as 1892, Nikola Tesla created a basic design for radio. On November 8, 1898 he patented a radio controlled robot-boat.  Tesla used this boat which was controlled by radio waves  in the Electrical Exhibition in 1898, Madison Square Garden.

Tesla's robot-boat was constructed with an antenna, which transmitted the radio waves coming from the command post where Tesla was standing.  Those radio waves were received by a radio sensitive device called coherer, which transmitted the radio waves into mechanical movements of the propellers on the boat. 

Dynamic theory of gravity

When he was eighty-one, Tesla challenged Albert Einstein's theory of relativity, announcing he was working on a dynamic theory of gravity and argued that a field of force was a better concept and did away with the curvature of space. Unfortunately the theory was never published, but Tesla may have been developing a theory about gravity waves. This theory provides a basis for plasma cosmology.


Tesla, aged 40. c. 1896

Tesla was 6 ft 2 in (1.88 m) tall and weighed 142 pounds (64 kg), with almost no weight variance from 1888 to about 1926. He was an elegant, stylish figure in New York City, meticulous in his grooming, clothing, and regimented in his daily activities.

"This was not because of personal vanity. Neatness and fastidiousness in clothes were entirely in harmony with every other phase of his personality.

He did not maintain a large wardrobe and he wore no jewelry of any kind ... He observed, however, that in the matter of clothes the world takes a man at his own valuation, as expressed in his appearance, and frequently eases his way to his objective through small courtesies not extended to less prepossessing individuals."

Time Travel

Tesla wrote from Colorado Springs to his New York friend Johnson that he found a thought in a “scribble” of high-frequency electromagnetic discharge and soon Johnson would be able to read his poetry personally to Homer, whereas Tesla would discuss his discoveries with Archimedes. In the same way, we can find a detailed description of "green" electromagnetic waves in his research journal. These waves looked like a fog, which appeared when the warship in Philadelphia disappeared.

When Tesla returned to Colorado Springs, he told journalists that he made a connection with extraterrestrial civilizations. Few people regarded this claim seriously, however, there is evidence that Tesla continued his research on "parallel worlds" alone and silently without publishing the results. To all appearances, he made a device to tune the electromagnetic oscillations of his own brain, in other words, to control his mental activity. Thus, he could communicate with realities displaced in time (parallel worlds) without any problems.

Sleep habits

Tesla claimed to never sleep more than two hours. However, Tesla did admit to "dozing" from time to time "to recharge his batteries".

During his second year of study at Graz, Tesla developed a passion for (and became very proficient at) billiards, chess and card-playing, sometimes spending more than 48 hours in a stretch at a gaming table. On one occasion at his laboratory, Tesla worked for a period of 84 hours without sleep or rest.

Literary works

Tesla wrote a number of books and articles for magazines and journals. Among his books are My Inventions: The Autobiography of Nikola Tesla, compiled and edited by Ben Johnston; The Fantastic Inventions of Nikola Tesla, compiled and edited by David Hatcher Childress; and The Tesla Papers.

Many of Tesla's writings are freely available on the web,including the article "The Problem of Increasing Human Energy," published in The Century Magazine in 1900,and the article "Experiments With Alternate Currents Of High Potential And High Frequency," published in his book Inventions, Researches and Writings of Nikola Tesla.



"Chance favors the prepared mind." - Louis Pasteur