Famous sayings in mathematics reading (70 articles)

First of all, the simple combination of integers has been the source of new life in mathematics for centuries.

Second, the great structure of the universe is now beginning to appear as a pure mathematician.

Third, ecology is essentially a mathematics.

Fourth, mathematics is symbol plus logic.

5. New mathematical methods and concepts are often more important than solving mathematical problems.

Six, the first is mathematics, the second is mathematics, and the third is mathematics.

Seven, do more exercises and develop good problem-solving habits.

Eight, mathematics has a high reputation, another reason is that mathematics makes natural science theorem, giving natural science a certain degree of reliability.

Nine, pure mathematics is the magician's real wand.

Ten, the main goal of mathematics is the public interest and the explanation of natural phenomena.

We can expect that with the development of education and entertainment, more people will like music and painting. However, few people can really appreciate mathematics.

Twelve, there is a law in teaching, and there is no fixed law in teaching.

Thirteen, mathematicians are fascinated by nature, and there is no mathematics without fascination.

Fourteen, the science of pure mathematics, in its modern development stage, can be said to be the most primitive creation of human spirit.

15. Specialization and generalization are important sources of useful auxiliary problems.

Sixteen, mathematics is the theory of studying abstract structures.

History makes people wise, poetry makes them elegant, mathematics makes them noble, natural philosophy makes them deep, morality makes them steady, and ethical rhetoric makes them able to contend.

Eighteen, it is not intuitive when missing numbers, and it is difficult to be nuanced when missing numbers. In addition, there are two necessary processes to lay a good foundation of mathematics: first, learning and accepting "from thin to thick"; Digestion and refining "from coarse to fine".

Nineteen, in mathematics, it is very important to distinguish what is important and what is not.

Twenty, infinity! No other problem has touched the human mind so deeply.

Twenty-one, as long as a branch of science can ask a lot of questions, it is full of vitality, and no problems indicate the termination or decline of independent development.

In the field of mathematics, the art of asking questions is more important than the art of answering questions.

23. Just because you can use mathematical formulas doesn't mean you can do mathematics.

24. Mathematics is an evolving culture.

25. Mathematics is the key to science.

Twenty-six, the universe is big, the particles are tiny, the speed of rockets, the cleverness of chemical industry, the change of the earth, the mystery of biology, the complexity of daily use, and mathematics is everywhere.

27. Non-mathematical induction plays an indispensable role in mathematics learning.

I always try my best to get rid of that heavy and monotonous calculation.

Twenty-nine, some beautiful theorems in mathematics have such characteristics: it is easy to sum up from facts, but the proof is extremely profound.

One of the values of a good question is that it can produce other good questions.

Only with the vigorous development of mathematics can a country show its national strength. The development and perfection of mathematics are closely related to the prosperity of the country.

32. Pursuing that goal in the best time of my life ... The book has been written. It doesn't matter whether modern people read it or future generations read it. It may take a hundred years to get readers.

Mathematicians are as happy when they derive equations and formulas as when they see statues, beautiful scenery and beautiful tunes.

34. It is found that every new group is mathematical in form, because we can't have other guidance.

35. This is a reliable rule. When the author of a mathematical or philosophical work writes with vague and abstruse words, he is talking nonsense.

36. Mathematics is a clever art. ..

37. Mathematics is an infinite science. Herman Weil.

Anyone who doesn't know that the diagonal side of a square is an incommensurable quantity is not worthy of this title.

39. Mathematics is a variety of proof skills.

The essence of mathematics lies in freedom.

Forty-one, mathematics, queen of science; Number theory, the queen of mathematics.

42. Mathematics is the highest form of all knowledge.

Forty-three, the driving force of mathematical invention is not reasoning, but imagination.

44. Mathematics is an infinite science.

45. God created integers, and the rest are man-made.

46. Mathematics is the brightest pearl in the crown of human wisdom.

Any branch of mathematics, no matter how abstract, will be applied to the real world one day.

Forty-eight, learn mathematics to do more exercises, thinking while doing. Predict what it is and then know why.

Forty-nine, mathematics is gymnastics to exercise the mind.

Fifty, mathematical methods permeate and dominate all theoretical branches of natural science. It has increasingly become the main symbol of measuring scientific achievements.

51. Abstract mathematical knowledge is based on the perception of images, while static teaching theory is based on dynamic experience, perception and thinking.

52. Mathematics is a rational spirit, which enables human thinking to be applied to the most perfect degree.

53. Mathematics has made an important contribution to the observation of nature. It explains the simple primitive elements in the regular structure, with which celestial bodies are built.

Fifty-four, stones can be broken, but not strong; Dan can grind, but he can't win red.

55. The incomparable eternity and omnipotence of mathematics, as well as its independence in time and cultural background, are the direct consequences of its essence.

56. Observation may lead to discovery, and observation may reveal some laws, patterns or rules.

57. A mathematician who is not a poet will never be a complete mathematician.

58. In mathematics, the main tools for us to find truth are induction and simulation.

59. Mathematics is the highest achievement of human thinking.

Sixty, give me five coefficients, and I will draw an elephant; Give me six coefficients and the elephant will wag its tail.

6 1. Mathematics is a tool of knowledge and the source of other knowledge tools. All the sciences that study order and measurement are related to mathematics.

The more detached a mathematician is, the better.

Sixty-three, mathematics is the study of quantitative relations and spatial forms in real life.

Number theory is the oldest branch of human knowledge, but some of his deepest secrets are closely related to his most ordinary truth.

What pleases me most about mathematics is what can be proved.

66. Instead of talking about novel problem-solving methods, it is better to keep the conventional problem-solving methods in mind.

Think of yourself as a fool, ask if you don't understand, and learn more.

Sixty-eight, mathematics is the symbol of God's description of nature.

Sixty-nine, the ruler is short; Every inch has its advantages. Insufficient things; I can't think clearly.

In the field of mathematics, the art of asking questions is more important than the art of answering questions. Kangel

Reading of Confucius and Mencius (70)

1. Courtesy, tolerance, faithfulness, sensitivity and benefit: courtesy does not insult people, tolerates people's hearts, believes in responsibility, is sensitive and active, and benefits are enough to make people.

Second, correct, and then know the weight; Degree, then know the length.

Third, praise his poems and read his books. I don't know who he is, but what? So, it is a business friend.

Fourth, for example, if it's a mountain, it's not a success, so I'll stop. For example, the flat land, although full of fat, I will go if I enter.

Fifth, a gentleman should be loyal to his thoughts and make up for it. He will spare the beauty and save his evil, so that he can date each other from top to bottom.

Six, a gentleman has three pleasures, but the king of the world does not exist. Parents are there, and brothers are happy for no reason; Yang is worthy of the sky, regardless of people, but also happy; It is three pleasures to be educated by talents in the world.

Seven, a threesome, there must be my teacher: do the good ones and replace the bad ones.

Eight, promising, such as digging wells; Digging a well in nine days is not as good as a spring, but it is still abandoning the well.

Nine, just, resolute, plain, close to benevolence.

Ten, you treat me like a brother, then I will take care of you; If you treat me like a dog or a horse, then I will treat you like a Chinese; If you treat me like dirt, then I treat you like an enemy.

1 1. Cultivating talents is the foundation of the country.

Twelve, cold, and then know the pine and cypress carving.

Thirteen, the road is impassable, take a trip to the sea and follow your own reasons!

Fourteen, the master said, in my heart.

Fifteen, a gentleman has four methods. It respects people, respects things, benefits the people and serves the people.

Sixteen, quality is better than literature, quality is better than history, gentle, and then a gentleman.

Seventeen, knowing is not as good as being good, and being good is not as good as being happy.

Eighteen, outstanding.

Nineteen, hearsay, abandon morality!

Twenty, angry and forget food, happy and forget worry, I don't know that old age is coming.

Twenty-one, wealth can't be lewd, poverty can't be moved, and power can't be bent. This is called a gentleman.

Twenty-two, those who gain the Tao help more, and those who lose the Tao help less. When there is little help, relatives will be there; Help more, and the world will be at peace.

People who study hard can always realize their wishes.

Twenty-four, benevolence wins ruthlessness, water wins fire. Today, if you are kind, you will still save a car with a glass of water. If you don't let it out, you will say that the water is too hot, which is the same as those heartless people who will eventually die.

Twenty-five, old but not old; Young, young, young.

Twenty-six, the world's talents and education.

Twenty-seven, poor is immune, rich is helpful.

Twenty-eight, the three armies can win the handsome, but the ordinary man can't win the ambition!

Twenty-nine, I start with others, listen to their words and believe their actions; Today, I am a man. I listen to his words and watch his actions.

Thirty, if you don't change it, too much!

Thirty-one, no hidden heart, inhuman; No shame, no humanity; It is inhuman to have an unyielding heart.

With your father's knowledge, you can't be a scholar.

Thirty-three, don't be angry, don't be angry, don't be angry, don't give a horn, don't take three horns, and you won't have it anymore.

34. It is said that it is 40 miles away in the Shanhaiguan Pass on the outskirts of the city. Anyone who kills its elk is guilty of homicide.

35. A gentleman's business lies in filial piety, so loyalty and righteousness can move you. Things are old, and the dragon can be moved. Home management, so governance can move officials. Based on behavior, the name stands behind.

Thirty-six, the Tao is based on morality and is ashamed of courtesy.

37. Being rich and expensive is what people want. You can't go anywhere unless you take the main road. Poverty and meanness are human evils.

Thirty-eight, by, teach you what you know! A person's real knowledge lies in knowing what he knows and what he doesn't know.

Diligence is good training, and one point of hard work is one point.

Forty, don't complain, don't treat people, go to school.

41. Never tire of learning and never tire of teaching.

Forty-two, I try not to eat for a day and stay up all night. It's no use thinking, it's better to learn.

Forty-three, five out of ten, determined to learn, standing at thirty, not confused at forty, knowing the destiny at fifty, listening at sixty, and doing what I want at seventy, not exceeding the moment.

Forty-four, the use of courtesy, harmony is expensive. Wang Zhidao is the first beauty. Small and big, there are problems. Knowing peace without courtesy won't work.

45. If you don't advance, you will retreat. Only what. A person will make progress if he is clean, but he may not be able to walk if he is clean.

Forty-six, the beneficiary has three friends: friends are straight, friends understand, and friends listen more.

Forty-seven, money can be sought, although I am a whip, I will do it. If you can't ask, just do as I say.

Forty-eight, sensitive and eager to learn, not ashamed to ask questions.

Forty-nine, don't learn manners, can't stand it.

Fifty, unreasonable, can't make an appointment for a long time, can't be happy. The benevolent is benevolent, and the knowledgeable is benevolent.

The more you learn, the more you find yourself ignorant.

52. Don't be angry or jealous.

Fifty-three, give up on yourself, not with words; Give up on yourself, and do nothing.

Fifty-four, the father is watching his ambition, and the father is not watching his actions; Three years without changing your father's ways can be described as filial piety.

Fifty-five, eating sparsely, drinking water, and being happy are among them. Unjust wealth is like a cloud to me.

56. devote yourself to the leisure of mountain paths, but use them to build a road. If you don't use it for leisure, it will be blocked.

57. The foundation of the world, the foundation of the country is at home, and the foundation of the home is in the body.

Fifty-eight, people know each other, you know each other, you know each other.

Fifty-nine, there is a road in the world, and you are martyred. There is no way in the world, you are a martyr.

Sixty, a gentleman is nothing more than being kind to others.

Sixty-one, so the sky will fall on the Sri Lankan people. We must first suffer from their minds, their bones and muscles, starve their bodies and skin, and mess with their actions. Therefore, we must be patient and get what we can't.

Sixty-two, xing, people. Success is fun.

Sixty-three, benevolent people are benevolent, there is no harm in saving, and there is benevolence in death.

Sixty-four, do not follow the rules, can not be round.

Sixty-five, a thousand times the country, respecting things and believing, saving the people and loving the people, making the people timely.

Sixty-six, the knife is not fast, the stone mill. People can't learn from the world.

Sixty-seven, xian zai, retreat! A spoonful of food, a spoonful of drink, in a mean alley, it is unbearable to see. I won't change my fun back.

If you don't study for six or eight days, you will feel disgusting and tasteless.

Sixty-nine, praise his poems, read his books, I don't know who he is? It is based on its world.

Seventy, different ways, no common goal.

Excerpts from classic reading quotations (70)

First, familiar reading method, step by step, familiar reading and careful thinking. -Zhu

Second, the son of heaven values heroes, and the article teaches Cao. Everything is inferior, only reading is high. -"prodigy poetry, exhortation"

Third, don't complain about the sky, don't be rude to others, and go to school. -The Analects of Confucius

Fourth, if a worker wants to do a good job, he must sharpen his tools first. -Confucius

5. Sunrise illuminates the earth, and reading clears the mind. -(Mongolian) proverb

Sixth, finally, we must build a new country and study hard. —— Guo Moruo

Seven, jade does not peck, abrasive; People don't learn or know. -Book of Rites

Learn once, learn for a long time, but don't be lazy. -(Qing) Peng Ruishu

Bad books, like bad friends, will corrupt us. Fielding

Ten, books are the president of human knowledge. -Shakespeare

1 1. It is better to make a friend who reads thousands of books than to make a friend who can't read. -"aphorisms are interlocking"

A person who loves books will never lack a faithful friend, a good tutor, a lovely companion and a gentle comforter. Isaac barrow

Thirteen, the bright light is always a partner; Yi Shu is often a friend. -"Couplets Collection"

Fourteen, everywhere is a place of creation, every day is a time of creation, and everyone is a creator. -Tao Xingzhi

15. People who can't use time the least will complain that they don't have enough time. -Labroue Yale.

Sixteen, learning to read is to light the torch. Hugo

Seventeen, the night light is five more chickens, which is the time for men to study. Black hair doesn't know how to study early, but when you study, you will regret it! -Yan Zhenqing

Eighteen, curious people, only made five kinds of fools; He who is ashamed to ask questions is a fool all his life. anonymous

Nineteen, husband Taoism and hidden in books, learning and advancing in vibration, waste in poverty. —— Wang Fu

Books make some people knowledgeable, but they also make some people crazy. -Petrarch [Italian poet]

Twenty-one, give an outline to see, solve a volume and make it public. -Zheng Xuan

Twenty-two, familiar with 300 Tang poems, can sing without writing poems. -Sun Zhu's Preface to 300 Tang Poems

Twenty-three, a good book is never tired of reading, and you will know it when you are familiar with it. -Su Shi

Twenty-four, reading thousands of books, without a master in my heart, is like a storm. -Liezi

Twenty-five, when we read a good book for the first time, we seemed to find a friend; When we read this book again, it seems that we have met our old friends again. -Voltaire

Twenty-six, no one found that the communication between people is just some empty talk, some empty talk, no one knows who, no one wants to know who. Gorky

Twenty-seven, the book is the ladder of human progress. Gorky

Reading without thinking is eating without digesting. -Polk (British writer)

Twenty-nine, reading is learning, using is also learning, and more importantly, learning. Mao Zedong

When reading, think deeply and ask more questions. If you just read and don't think, you may follow suit and become a slave to books; Or take a look at the flowers, and you get little. -Wang Zikun

3 1. Learning is not imitating anything, but mastering skills and methods. Gorky

A person who loves reading will never lack a loyal friend, a good teacher, a lovely companion and a warm comforter. -Barrow

The wider a person's knowledge, the more perfect he is. Gorky

Thirty-four, the pen is shocked by the wind and rain, and the poem becomes a cry. -Du Fu

Thirty-five years old, my husband needs ambition to learn. If you don't learn, you can't be versatile, and if you don't want to learn, you can't succeed. -Zhuge Liang

Thirty-six, reading affairs should be gradual; You can't read books until they are ripe, so don't wait hastily, although it's useless. -Hu [Ming]

At the age of 37, I jumped at books, just like a hungry man jumped at bread. Gorky

Thirty-eight, where to find the pleasure of reading, count plum blossoms. -Zhu

39. Great achievements are directly proportional to efforts. Work hard and you will get something. If you accumulate from less to more, miracles can be created. -Lu Xun

40. Wise people ask smart questions, fools ask stupid questions. -Tao Xingzhi

Forty-one, people can go without food for twelve days, and books can be safe for one day. -Lu you

Forty-two, I dare not forget my country, but I still want to cover my coffin. -Lu You's Disease

43. Books are good teachers for us. We don't need whipping and beating, words and scolding, tuition fees and informal forms. The love of books is the love of wisdom. -Durbeyfield

44. The kungfu of learning is the kungfu of chewing slowly. Just like eating, it's good for the human body to chew until it's chewed. mould

Forty-five, the soul of the whole past lies in the book. -Carlisle

46. It's better not to read a book that doesn't suit you. We must learn the skills of choosing the most valuable and appropriate reading materials. -belinsky

Forty-seven, reading thousands of books, writing like a god-Du Fu

48. People are alive and books are dead. The living can read the dead book and live it. If you read the living from the dead, you can read people to death. —— Guo Moruo

Forty-nine, a day without books, everything goes to waste. -Chen Shou

Fifty, be reasonable about what you want to study. -Zhang Weiping

Fifty-one, a threesome, there must be my teacher. Choose the good and follow it, change the bad. -Confucius

52. Books are inseparable life companions and mentors of young people. Gorky

53. Never tire of learning and never tire of teaching. Confucius

Fifty-four, I dare not do anything, just because I have read the script. -Tao Zongyi

55. Reading is to wisdom what gymnastics is to body. -Addison

56. Books are the nourishment of the whole world. Life without books is like life without sunshine. Wisdom without books is like a bird without wings. -Shakespeare

Fifty-seven, books or medicine, good reading can cure fools. -Liu Xiang

58. Books that you intend to burn but are reluctant to put down are useful. -Stop Johnson.

Fifty-nine, studious is old, enduring, can avoid good troubles. -Shen Hanguang

60. Tian Ge's achievements have their origins. Who is the registered surname? -Guizhuang

Sixty-one, reading is not much, just as it means, it is unknown. Enough is enough, don't learn, enough is enough, don't learn. -Han Yu's Persuasion Poems

Sixty-two, therefore, the day will drop to a great post, and people must first suffer their minds, their bones and muscles, starve their bodies, empty their bodies, and mess with their actions, so their perseverance has benefited their bodies. -Mencius

Sixty-three, study hard, not seek erudition. —— (Song) Huang Tingjian

Sixty-four, learning from time to time is unpleasant! Confucius

Sixty-five, reading is also like mining. —— Zhao Shuli

66. Learn without learning. I'd rather fish without nets. -Ge Hong

It is a good idea to study hard when it is precious. Cai Shangsi

A good book is a good friend, and today and tomorrow will last forever. -Tapa (UK)

69. Don't do to others what you don't want them to do to you. -Confucius

A book, like a ship, leads us from a narrow place to an infinite ocean of life. Keller

Complete works of famous sayings about diligent study and reading (70 articles)

Don't go to bed when you can't tell yourself what you learned today. Fort Lee Heaton

As we all know, it is much more difficult to turn words into actions than actions into words. Gorky

Third, reading a hundred times is self-evident. Chen Yu

Fourth, cleverness lies in diligence, and genius lies in accumulation. -Hua

Reading a good book means talking to many noble people. -Goethe

6. Throughout the ages, all those who have achieved their careers and made a difference to mankind are the results of down-to-earth and hard climbing. -Qian Sanqiang

Learning is an extremely precious thing, and it is not shameful to absorb it from any source. -Abu Ri Faraz

Eight, do not participate in the struggle to change society, the ideal will always be a mirage. Wu Yunduo

Do you want to be a happy person? I hope you can learn first and understand that you can bear hardships. -Turgenev

No animal is more diligent than an ant, but it is the most taciturn. Franklin

Eleven, the human brain and limbs are the same. If you use it too much, it will work; if you don't use it, it will be useless. -Mao Yisheng

12. Learning is an extremely precious thing, and it is not shameful to absorb it from any source. -Abu Ri Faraz

Thirteen, if you want to know what's going on in the world, you must read ancient books. -Feng Menglong

Time is like water in a sponge, it is always there as long as you are willing to squeeze it. -Lu Xun

A diligent person will be praised, even if his insight or mental freshness and creativity will be damaged by his diligence. -Nietzsche

Genius is the infinite ability to work hard. -Carlisle

Seventeen, the gentleman's learning must be good at asking, asking and learning, learning from each other's strengths. Non-learning, no doubt; Don't ask, don't learn. -Liu Kai

Any achievements I have made in science are only due to long-term thinking, patience and diligence. -Darwin

19. Faith has no boundaries between land and language. It is brothers and friends who support the truth. Heinrich Mann

The trick to learning a lot is not to learn a lot at once. -Locke

Twenty-one, the three conditions for reading are: more observation, more hardship, and more research. Garfield

Whoever studies as hard as I do will be as successful as I am. -Mozart

Nothing is more valuable than time. Without time, we will accomplish nothing. Mendeleev

24. Without double diligence, there is neither talent nor genius. Mendeleev

25. Cleverness comes from diligence, and genius lies in accumulation. -Hua

No one will become a wise man because of learning. Learning may come from diligence, but wit and wisdom are lazy to talent. John Selden

27. Faith is what people need. People who don't believe in anything will not be happy. Hugo

28. I didn't get any other benefits from my efforts, but I became more and more aware of my ignorance. Descartes

Twenty-nine, poetry and books are diligent, not diligent and empty. -Han Yu

Being thirty years old and enjoying reading is equivalent to turning the lonely Guang Chen in life into a moment of great enjoyment. -Montesquieu

3 1, doing things too fast is one of the biggest dangers-bacon

Thirty-two, the so-called genius is the power of hard work. Dwight

33. A person's activities are useless and insignificant if they are not inspired by noble thoughts. Chernyshevski

Love makes diligence, and diligence makes genius. —— Guo Moruo

35. Prudence and diligence bring good luck. -England

Science is for studious people, while poetry is for learned people. -Joseph Lou

Thirty-seven, diligent people forget to eat and sleep, lazy people always have no time. -Japan

38. Empty talk, etc. Not long, and there is nothing to say. It has always been reflected in the mirror of facts and dragged away. -Lu Xun

All my excellent qualities are attributed to books. Gorky

Genius should never despise diligence. -Pliny Jr.

Forty-one, learning is labor, and it is full of ideas. -ushinski

42. Do you want to be a happy person? I hope you learn to suffer first. -Turgenev

Forty-three, the time should be allocated accurately, so that every year, every month, every day and every hour has its special tasks. Descartes

Forty-four, diligent, do not waste time; Do something useful at any time and give up all unnecessary actions. Franklin

History makes people wise, poetry makes them wise, mathematics makes them exact, philosophy makes them deep, ethics makes them grave, and logic makes them able to contend. bacon

Genius is one percent inspiration and ninety-nine percent diligence. Edison

Forty-seven, reading thousands of books, writing like a god. -Du Fu

Forty-eight, after a hard day, you can have a good sleep; If you work hard all your life, you can sleep happily. -Leonardo da Vinci

Forty-nine, life is diligent and does not ask for anything in return. -Zhang Heng

50. Hobbies make diligence, and diligence makes genius. —— Guo Moruo

Fifty-one, where there is a genius, I use the kung fu of others drinking coffee at work. -Lu Xun

Fifty-two, a hard day, you can have a good sleep; If you live hard, you will have a pleasant sleep. -Leonardo da Vinci

53. The first sign of an educated mind is being good at asking questions. -plekhanov

Genius is nothing more than hard work and diligence. -Bifeng

55. Diligence should be the decisive factor in the formation of genius. —— Guo Moruo

56. The road to art is full of thorns, which is also a good thing. Ordinary people are discouraged, except the strong-willed. Hugo

Fifty-seven, courage and belief in winning can often make the battle come to a successful end. -Engels

58. The progress of a country lies in everyone's efforts, just as the decline of a country lies in everyone's laziness, selfishness and depravity. -Smal.

Fifty-nine, the industry is good at diligence and barren in drama; Doing things in thought; Destroy with ... -Han Yu

Faith is an oasis in the heart, and the camels of thought will never get there. Gibran

A person who doesn't pay attention to small things will never succeed in big things. Carnegie

62. Learning at leisure is not better than learning at leisure. Joe Bells

Sixty-three, each of us has a key to self-study, that is: ideal, diligence, perseverance, modesty and scientific method. -Hua

64. It is often more important to ask a question than to solve it. -Einstein

Sixty-five, the land is not cultivated, and no matter how fertile it is, it will not bear fruit; People who don't read, no matter how clever, can't read. -Cicero

Diligence and wisdom are twins, laziness and stupidity are brothers. -Folk proverbs

Sixty-seven, the industry is diligent and wasteful, and the line is destroyed by thinking. -Han Yu

A new book is like a ship, leading us from a narrow place to the infinite ocean of life. Helen Keller

Sixty-nine, when the book is used, hate less, nothing is difficult, nothing is impossible to a willing heart. —— Chen Tingzhuo

70. Strong will cannot be defeated by imaginary fate. Franklin