Science,English,and math Ⅲ

【Prime numbers have nver been solved】

〈Is today the day of prime number?〉

If making use of the site, we can judge whether or not the day which we`re worried about is the day of prime number at once.

I doubt whether or not there are the people like that actually, and I won`t be worried about it.

To tell the truth, both the last day of the year in 2020 and the first day of the year in 2021 are the day of prime number.

The last day of the year and its next day which is the first day in the next year are the prime number. They are successive. It happens no more than twice for hundred years...

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【Prime numbers have never been solved】

〈Is today the day of prime number?〉

It happnes no more than twice for hundred years of the 21 century, and the other is the last day of the year in 2029 and the first day of the year in 2030.

〈Look for a huge prime number!〉

Euclid proved that the prime number becomes big infinitively in the Ancient Greece, but it`s hard to find the tremendous prime number actually.

If reading it in history, we can understand it really, especially when Pietro Cataldi found the prime number of six digit, 524287, in 1588, and the number dominated in a position which...

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【A prime number has never been solved】

〈Look for a huge prime number!〉

... and the number dominated a position of the biggest prime number which had been found actually for a long time.

It took 144 years that Euler found the prime number of seven digit in 1732 when his age was 25. Moreover he found the prime number of ten digit after forty years.

And Edouard Lucas found the prime number of 39 digit in 1876, and it`s the biggest prime number which isn`t used by an electric calculator.

August in 2019 when the book which I`ve tried to express in English was written, the biggest prime...

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【A prime number has never been solved】

〈Look for a huge prime number!〉

...the biggest prime number which has been found is beyond our imagination. It`s twenty four million eighty hundred thousand digit. It was found by a computer project which is called GIMPS in 2018. GIMPS is an abbreviation of Great Internet Mersenne Prime Search.

In GIMPS, computers all over the world are connected through a network, and constructs a single computer of high powered in imaginary way. It`s called a distributed computing.

To tell the truth,I`m tired of the prime number. What`s the use of finding such a...

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【A prime number has never been solved】

〈Look for a huge pirme number〉

What is the use of finding such a big prime number? I`m not sure of
it.

I`m going into a new chaper, mathematicians who are beyond our imagination.

【Elements which an elite student has to read in Europe and Ameirca and a mystery on Euclid】

〈Elements which is a marvelous best seller〉

Do you know Elements which was written by Euclid in Ancient Greece?

Elements isn`t only the oldest text on math which was editted around B.C.the third century but it had been used all over the world as textbook until around a hundred...

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【Elements which an elite student in Europe and America has to read and a mystery on Euclid】

〈Elemnts which is a marvelous best seller〉

Elements which hasn`t been edited around the B.C. three century as the eldest textbook on math but had been used in all over the world as textbook on math until a hundred year ago at least as it was. It`s a marvelous best seller in the world.

Except for the Bible, no book than any other Elements which has been read and edited all over the world.

Incidentally, after letterpress printing was invented dy Gutenberg in the 15th century, it was the Elements...

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【Elements which an elite student in Europe and America has to read and a mystery on Euclid】

〈Elements which is a marvelous book〉

Incidentally, after letterpress printing was invented by Gutenberg in the 15th century, it`s the Elements which has been editted as a book with illustration of geometry for the first time.

By the way has the Elements been read in so widely in the world? It has been written only on the way of math but on the way of logic thinking through all the fields.

As to quality and quantity, no similar book than any other Elements which has been expressed well as...

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【Elements on which an elite student in Europe and America has to read and a mystery on Euclid】

〈Elements which is a marvelous best seller〉

As to both quality and quantity, no similar book thna Elements which has been expressed well as example on logical thinking. It means that the Elements is the best book so as to improve our locigcal thinking. Actually the Elements has been indispensabel common knowledge for elites in Europe and America at present.

In Europe and America where tradition on ancient Greek culture has been taken over, logical thinking has been respectd from a long ago.

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【Elements which an elite has to read in Europe and America and a mystery on Euclid】

〈Elements which is a marvelous best seller〉

A way of debating has been learned in Europe and America because they have made much of the logical thinking. They have thought logical thinking which persuades around the people and understands insistence on others which are opposed to rather than an inspiration or a sense on thinking. It means that they`ve thought the logical thinking is an indispensable nature for a leader.

The author said he used to stduy abroad in Vienna so as to be aimed at a conductor at...

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【Elements which an elite in Europe and America has to read and a mystery on Euclid】

〈Elements which is a marvelous best seller〉

The author said he used to go abroad in Vienna in order to be aimed at a conductor at one time.

As to music which they should make much of sensitivity in art, a thing of which happened to think has never been made much of even if it`s novel and attractive when playing music in Europe. The author said he experienced it firsthand.

It`s more important to express it in their own language why they play an musical instrument with its way. If aiming at a conductor....

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【Elements in which an elite in Europe and America has to read and a mystery on Euclid】

〈Elements which is a marvelous best seller〉

If aiming at a conductor which is a leader in an orchestra, being lacking of logical thinking isn`t allowed.

If trying to aim at being a conductor, I`m afraid I`ll set on fire in Vienna.

〈What has been written in Elements?〉

It is natural in Europen and America where that kind of culture has been rooted that the Elements has been indispensable culture so as to improve their logical thinking. A way of logical thinking is written in Elements. It`s piling up...

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【Elements in which an elite in Europe and America has to read and a mystery on Euclid】

〈What has been written in Elements?〉

It`s piling up proposition from a definition and a theorem. If trying to think logically, nothing is removed from them, and nothing has to be added. The author said he is going to show its detail.

The definition is a meaning on a word. If the word which is used for a debate is unclear or misunderstanding, no one can expect rational talk for it.

For example, when trying to discuss a science phobia on children, if the one thinks the children are schoolchilrden in an ...

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【Elements in which an elite in Europe and Ameirca has to read and a mystery on Euclid】

〈What has been written in Elements?〉

...if the one thinks the children are schoolchildren in an elemntary school, and the other they are the whole students in junior high school or high school, their debation will clash.

The theorem is a kind of promise that they recognize it at least as premise.

When trying to discuss whether or not it`s right on talk with a cellphone on a train, there is an insistence that making passengers listen to conversations on the cellphone is something unpleasant and nuisance.

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【Elements in which an elite in Europe and America has to read and a mystery on Euclid】

〈What has been written in Elements?〉

On the other hand there is possible as long as talking with a friend in front of them with the volume which they can listen to, it`s all right. The opposing argument is possible.

However, in the middle of the argument,if someone starts to say why are they forbiddent to make others be trouble? The argument would retreat, so a promise that no one make others be troulbed is necessary at least as premise.

Needless to say, if there is room for something doubtful, we....

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【Elements in which an elite student has to read in Europe and America and on mystery on Euclid】

〈What has been written in Elements?〉

...we have to negotiate on the assumption that a theorem on mutual recognition which is a starting point for a debate should make sure before the negotiation in order to develop the debate efficiently.

The proposition is a one which we can judge whether or not it`s right objectively.

For example, no one can judge objectively whether or not his weight is heavy, so it`s not the proposition. Describing how much its weight is heavy is depending on.

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【Elements in which an elite has to read in Europe and America and a mystery on Euclid】

〈What has been written in Elements?〉

On the other hand his weight is 90 kilogram is the proposition whether or not its right we can judge it objectively, for everyone judges it, its conclusion is the same.

For example, let`s suppose there was a proof like the next.

1 A full fledged employees in X company who earns more than average income a year in Japan are all age which are older than 40.

2 Mr. A works in the X company, and his income a year is high.

3 Mr. A`s age is older than 40.

As to avegage...

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【Elements in which en elite in Europe and Ameirca has to read and a mystery on Euclid】

〈What has been written in Elements?〉

As to average income a year, if we research it, we can know it at once. Roughly speaking it`s nearly four million and a half yen according to research on actual situation of civil income by the Regional Taxation Bureau 国税局.

In short,1 is the proposition which we can judege whether or not it`s right objectively, so it`s right as proposition, but can we conclude to 3 from 1 and 2 ?

As you know, it`s no, for we can`t judge whether or not Mr.A`s income a year is high...

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【Elements in which an elite in Europe and America has to read and a mystery on Euclid】

〈What has been written in Elements?〉

We can`t judege whether or not Mr.A`s income a year is high objectively with the expression on 2 alone.

Possibly he is younger than thirty and his income a year is higher than average before thirty which is three million yen and his income a year may not reach average income on the whole nation, so we can`t conclude 3 is right.

〈A definition → a theorem → a proposition → a conclusion〉

Without depending on a sensitivity nor on an inspiration, winning a deep insight...

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【Elements in which an elite in Europe and America has to read and a mystery on Euclid】

〈A definition → a theorem → a proposition → a conclusion〉

Without depending on a sensitivity nor on an inspiration, winning a deep insight by piling up the debate is the true charm on the logical thinking.

However the one which is able to accumulate is a right proposition alone, a conclusion by accumulating the one which isn`t the proposition or a mistaken proposition isn`t right logically at all.

It is said it`s Plato who said clearly the logical way of a definition → a theorem → a proposition → a....

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【Elements in which an elite in Europe and America has to read and a mystery on Euclid】

〈A definition → a theorem → a proposition → a conclusion〉

It is said it`s Plato of a philosopher who said clearly the way of
Logical thinking a definition → a theorem → a proposition → a conclusion for the first time.

Euclid wrote down a textbook of which center was geometry according to instruction by Plato, and it`s the Elements, but it doesn`t always mean Euclid gathered new facts which he discovered for himself.

His greatest deed is describing the geometry which has developed under him and his...

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【A definition in which an elite in Europe and America has to read and a mystery on Euclid】

〈A definition → a theorem → a proposition → a conclusion〉

His greatest deed is describing the geometry which developed under Pythagoras and his disciples systematically and clearly with a way of Plato`s logical way.

In a way, we should say Uclid was an excellent editor rather than an original mathematician.

〈Euclid is a pen name of a group of editors?〉

A way of logical thinking has been recognized with a start of two books of which title is a technique of expressing, and a technique of thinking...

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【Elements in which an elite in Europe and America has to read and a mystery on Euclid】

〈Euclid is a pen name of a group of editiors?〉

A word of logical thinking has been recognized with a two bestsellers of which title is 『A technique of expressing and a technique of thinking』『Logical thinking』and the word has been paid attention.

When a time has changed from Heisei to Reiwa, AI and learning with a mechanic have swept over the society, it seemst that importance of logical thinking has been heigthened more and more, and the author continued like the next.

However if comparing it with...

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【Elements in which an elite in Europe and Ameirca has to read and a mystery on Euclid】

〈Euclid is a pen name of a group of editors?〉

However if comparing Japan with both Europe and America on the importance of loigical thinking, it doesn`t seem to be filtered into Japan.

And it has something to do with that the Japanese have never read the Elemments, the author said.

Elements is a masterpiece in which each theorem has been organized clearly, but we who have lived at prsent will find it hard to understand.

What is the Elements in detail? If you`re interested in it, please read a book of...

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【Elements in which an elite in Europe and America has to read and a myster on Euclid】

〈Euclid is a pen name of a group of editors?〉

If you`re intersted in the Elements, you should read a book of which title is a miracle by logical thinking for a female student in high school who aimed at being a conductor in an orchestra written by the author, the author said like that.

She acquired a logical thinking through the Elements and her dream of being a conductor came true was described with a form of dialogue.

While Euclid was an author of the book which has influenced over us, almost no one ...

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【Elements in which an elite in Europe and America has to read and a mystery on Euclid】

〈Euclid is a pen name of a group of editors?〉

...almost no one knows on his lifetime including the year when he was born and he was dead.

Some people said that Euclid isn`t a personal name but a name of group of editors

It is certain that even if Euclid was an individual or the name of a group of editors, it didn`t have any ambitions in the least.

If comparing him with other great people in his time, almost none of information has never informed until now, for except for describing on math, Uclid has...

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【Elements in which an elite has to read in Europe and Ameirca and a mystery on Euclid】

〈Euclid is a name of a group of editors?〉

... for except for describing math,Euclid has never done anything special which made his name famous.

By the way what`s his motivation in which he described logical method and made him express 13 volumes? What made him devote himself solely to math?

He believed that thinking logically is a best and most powerful way so as to understand the universe which means the God, doesn`t he?

Instead of by a sense nor an inspiration, he believed the future when the human...

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【Elements in which an elite in Europe and America has to read and a mystery on Euclid】

〈Euclid is a name of a group of editors?〉

Instead of being unable to reach a far away peak by a sense or by an inspiration, he believed that the future when the human being would reach with a logical power.

As a result he must have felt how petty to show off his own honor.

【A male whose brain is excellent like a devil and a theory on a game】

〈A male who Einstein called a genius〉

I`m going to express a male who was the best genius in the world Einstein called. He is John von Neumann. He was born at...

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【A male whose brain is excellent like a devil and a thoery on a game】

〈A male who Einstein called a genius〉

He was born at Budapest in Hungary in 1903. The von is a title which he was from a nobleman. His father was a banker, and his mother was from a wealthy Jew.

He demonstrated his marvelous good memory and linguistic power from his childhood.

Reading once alone, he could learn a book by heart without making any mistakes on any word, or joking with his father in ancient Greek, so everyone thought he was a child prodigy.

He not only entered Budapest university but enrolled at both...

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【A male who is excellent like a devil and a theory on a game】

〈A male who Einstein called a genius〉

He not only entered Budapest university but enrolled both at Berlin and Swiss university, and got a degree on math and chemical industry.

He served as instructor at Berlin university for three years since 1927, and then attained a fame with theses on algebra, set 集合, and quantum mechanics in the world.

He was invited from the Priceton University in the U.S.A.which was the best one in the world then and after three years, he became a member staff there.

As the rise of Nazis persecuted....

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【A male who was excellent like a devil and a theory on game】

〈A male who Einstein called a genius〉

As the Nazis persecuted the Jew, they were forced to defect, and the Princeton university accepted scientists whose anscetry was the Jew positively, and a laboratory where he and Einstein came across.

Neumann was so excellent that he excelled on calculation at a computer which was at dawn then, and a there was a conclusion which was occurred to other mathematician in a few months, but he did it in a few minutes.

He was by far more excellent than any other people that others said he was...

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【A male who was excellent like a devil and a theory on a game】

〈A male who Einstein called a genius〉

He was by far such an excellent one than any other ones that others thought he was from other space and he researched the human being so closely that he could behave himself like the human being. There was an episode for him like that.

On the other hand, it is said that he couldn`t change the position of his cupboard for himself. If he wasn`t interested in anything, he wouldn`t be extremely.

〈A theory on a game in 1926〉

As to a research by Neumann, except for his math by profession, it ...

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【A man who had an excellent brain like a devil and a theory on a game】

〈A man who was called a genius by Einstein〉

...Neumann has influenced over physics, meteorology, economics, psychology, politics and computer science, especially as to him, the most worthy of mention among his achievements was a theory on a game in which he proposed in 1962.

When some players select each strategy on a game, the strategy has influenced how the ones who was involved in the game. He researched a theory on it.

If saying in a plain words, when the players more than two people who have interest each other...

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【A man who had an excellent brain like a devil and a thoery on a game】

〈A theory on a game in 1962〉

...then the theory shows us what`s kind of a result would be caused by the game and how the ones who were involved in the game should deciede each will.

Its player is an individuality, an enterprize, an organization, and even a nation.

After eighteen years from his first announcement on the theory of the game, it was formulated a system of thought by a book that a theory on a game and economic action written by Neumann and economist Oskar Morgensstern for the first time. Its translation ...

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【A man who had an excellent brain like a devil and a theory on a game】

〈A theory on a game in 1962〉

Its translation are five volumes.

Some paraises that it`s one of the best achievements in the first half in the 21th century, or after the general theory by Keynes, it`s the most important achievement in economy were sent, and the book was popular among the people then.

In spite of a short history on the theory of the game which was within a hundred years from its birth, it has been practical into use with a very wide areas of economics, business administration, politics, sociology...

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【A man who had an excellent brain like a devil and a theory on a game】

〈A theory on a game in 1962〉

...it has been practical into use in a very wide area of economics, business administration, politics, sociology, information science, biology, and applied mathematics.

〈A shocking over a dilemma by prisoners〉

As to an applied example on the theory of the game, a dilemma by prisoners is well-known.

There were two suspects on an unforgettable evnet, and they were captured separatedly with a petty offense. Let`s suppose they were a prisoner A and prisoner B.

The prosecution proposed...

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【A man who had an excellent brain like a devil and a theory on a game】

〈A shocking over a dilemma by prisoners〉

The prosecutor proposed a judicial deal with the two prisoners each other. If a suspect disclesed, reducing the prosecution`s demands and shelving prosecution would be done as collateral security.

1 if other one remains silent and you confess, you would be released.

2 if other confesses and you remain silent, you would be sentenced to ten years` imprisonment.

3 if both of them remain silent, both of them would be sentenced to one year`s imprisonment. It`s punishment alone by...

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【A man who had a brain like a devil and a theory on a game】

〈A shocking over a dilemma by prisoners〉

3 it`s punishment alone by petty offense.

4 if both of them confess, they would be sentenced to ten years` imprisonment.

Then two of them were separated, and when being investigated, they couldn`t know what they said and done each other.

If the one remains silent, the other should confess, for the other would be released.

On the other hand, if the one confesses, the other should confess as well, otherwise the other alone would be sentenced to ten years` imprisonment.

In both cases...

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【A man who had a brain like a devil and a theory on a game】

〈A shocking dilemma by prisoners〉

In both cases, confessing makes two of them advantageous, so if judging rationally, they should confess. Then they would be sentenced to five years` imprisonment, but there is a problem in its result.

If they remain silent they would be sentenced to one year`s imprisonment. If they confess, they would be sentenced to five years` imprisonment.

Remaining silent is more advantageous than confessing.

As to dilemma by prisoners, even if they know remains silent is better than confessing, they would...

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【A man who had a brain like a devil and a theory on a game】

〈A shocking over dilemma by prisoners〉

As to dilemma by prisoners, even if the prisoners know remaining silent is more advantageous than confessing, they would confess each other in a condition that the one who would confess is advantageous.

Remaining silent is cooperating each other, and confessing isn't cooperating.

Examples to which the dilemma by prisoners is applied are a lot. For example, a problem on reducing a price in two groups, a problem on dumping garbage, or a problem on posssessing nuclear weapons.

If each of us...

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【A man who had a brain like a devil and a theory on a game】

〈A shocking over a dilemma by prisoners〉

If each of us judge ratioanally and taking into action, being based on the rational judgement, the whole society should go well. It has been accepted by society, but it`s disproved by the dilemma by prisoners.

〈Neumann and an atomic bomb〉

After being in America, Neumann was absorbed in a study on applied mathematics which is useful mathematics in the real world.

As he had a patriotic thought politically, he left to be engaged in job on war gradually as an expert who played a leading...

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【A man who had a brain like a devil and a theory on a game】

〈Neumann and an atomic bomb〉

...he left to be engaged in a job on war gradually as an expert who played a leading part on a shock wave and a explosive wave especially after 1940s. He also took part in planning on Manhattan which was a development on an atomic bomb in 1943.

Neumann put up a theory that exploding befere the bomb dropping on the ground is more serious with regard to a damage by a big bomb, and the theory was made use of for the atomic bomb dropped on Hiroshima and Nagasaki.

A large amount of calculation is...

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【A man who had a brain like a devil and a theory on a game】

〈Neumann and an atomic bomb〉

A large amount of calculation is indispensable so as to forsee a trajectory and power on the bomb, he was gradually completely absorbed in development on a computer.

The first computer which was developed in order to calculate the trajectory was a gigantic one. Its width was 24 meters, height 2,5 meters, and depth 0.9 meters. Its whole weight was 30 ton.

13 mat 畳 room was filled with the big computer, but its ability on calculation was worse than a pocket calculator at present.

In addition....

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【A man who had a brain like a devil and a theory on a game】

〈Neumann and an atomic bomb〉

In addition, whenever doing a new calculation, arrangement and wiring on vacuum tube was assembled from scratch, so when trying to calculate in varied ways, it wasn`t handy to use.

So Neumann proposed a computer inside built-in program, and gave the program a mathematic basic design. A concept of software appeared then.

The software is a program which make the computer work.

On the other hand, the computer itself and other implements around the computer which are visible are called a hardware.

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【A man who had a brain like a devil and a theory on a game】

〈Neumann and an atomic bomb〉

As the software appeared, if rewriting the program, being able to make the computer calculate a new calculation, so the general purpose on the computer made rapid progress.

A computer with a buil-in program is called a Neumann type, and the Neumann type has been a base for all the computers at present.

A document written on a way of built-in program was opne widely among the Ameircan, so the industry on computer has developed.

Neumann died of cancer in Washington D.C.in 1957. Some people said he...

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【A man who had a brain like a devil and a theory on a game】

〈Neumann and an atomic bomb〉

Some people said Neumann was exposed to lots of radiation by Manhattan Project or when making an experiment on the atomci bomb.

〈Conditions on a genius〉

Neumann had an extradordinary ability and warlike politically, though he hated totalitarianism like Nazism and communism because he was a Jew, and he was influenced by it.

By the way, what kind of person is he actually?

The author said he`s come across some geniuses in his life until now. As they are geniuses, so they are very clear-cut personality.

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【A man who had a brain like a devil and a theory on a game】

〈Conditions on a genius〉

On the other hand, they have common nature.

1 they are good at understanding essence on a thing.

2 a speed of learning is incredibly quick.

3 an ability on language is excellent

4 素直

As to 4, I should express in English, but it has various meaning in English, and I have no idea on condition of a genius, so please adopt your favorite English phrase for 素直.

The author said those four things are conditions on the genius. Do they apply for Neumann? He asked us the readers.

【A marvelous inspiration by... 】

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【A marvelous inspiratin by an Indian magician】

〈A genius suddenly showed up〉

When being admired his excellent achievements, Newton who was an English physicist said like that.

If I could take an extensive view of a long distance, it`s just that I was on the shoulder of a giant.

It`s a humble phrase as great scientist, but when reading history on discoveries on physical law in relation to a movement on things supporting Newton`s dynamics, I feel like thinking it`s his real intention.

As taking over great achievements from giants as physics like Copernicus, Galileo, Kepler, and Huygens...

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【A marvelous inspiration of an Indian magician】

〈A genius suddenly turned up〉

As taking over from giants on physics like Copernicus, Galileo, Kepler, and Huygens equally and nameless physicists hidden among history obscurely who tried to solve the truth in the universe, Newton could erect a monumental landmark of classic physics called Newton`s physics, the author said he thought like that.

As to the theory of relative, it is said without Einstein, it is said someone else would discover it within from 10 to 20 years, for as for a discovery on providence of nature, there is a kind of...

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【A marvelous inspiration by an Indian magician】

〈A genius showed up suddenly〉

... there is logical or historical inevitability, but as to a great large number of groups on formulas discovered by Srinivasa Ramanujan who was called a magician in India, there is never inevitability.

Without Ramanujan, they may not have been discovered yet.

He was born in southern area in India in 1887. His father worked in a company which dealt with clothes as a bookkeeper.

His mother was intelligent, cultured, and especially so religious that a prayer meeting was done in her house.

The house of ...

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【A marvelous inspiration by an Indian magician】

〈A genius turned up suddenly〉

The house of Ramanujan was an orthodox Brahman which was the best in a caste of Hindu, so he was trained as proud Brahman and a severe vegetarian who never not only eat meat, but fish nor egg.

As he showed his extraordinary talent on studies since being young, it is said he mastered a content on trigonometry and differential and integral calculus of a textbook which was used by students of university when his age was 13.

〈Coming across a book on mathematics〉

A pure basic applied mathematics summary which ...

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