I will imagine that I am writing this book for those who are ambitious now and in the past. A person's first task, further, a young person's first task is to be ambitious. Ambition is a grand and lofty ambition, which can be reasonably expressed in many forms. Attila and Napoleon have some lofty ambitions, but the noblest ambition is to leave some lasting value behind them-
On this flat beach, between the ocean and the earth, what should I make or write to stop the night from coming? Tell me the mysterious figure, drink the rough waves, tell me the castle of time and plan a longer day.
Ambition is the driving force behind almost all excellent works in the world. In particular, in fact, all the great contributions to human happiness are made by ambitious people. Give two famous examples. Aren't Liszt and Pasteur such ambitious people? Also, Gillert and Wielaert, who are not as outstanding as them, have made more contributions to mankind recently?
The examples provided by physiology are particularly suitable for us, because the benefits of this discipline to human beings are so obvious. We must be alert to a common fallacy in scientific debate, that is, people who do work beneficial to mankind always think that their work is beneficial to mankind when doing this work. Physiologists, for example, have a particularly noble spirit. In fact, a physiologist may really like to remember that his work is for the benefit of mankind, but the motivation of generating strength and being encouraged to do this work is no different from that of first-class scholars and mathematicians when doing research work.
There are many noble motives that drive people to do a certain research. Among these motives, there are three most important ones. The first thing (without it, the other two things are impossible) is curiosity, that is, the desire to know the truth. Secondly, I am proud of my professional work, satisfied with my achievements, and ashamed to find that my achievements are not commensurate with my talents as a dignified person. The last one is ambition, expecting fame, status and even the power and money that comes with it. When your job brings happiness to others and relieves their pain, you may feel good about yourself, but that's not why you do that job. So, if a mathematician, or a chemist, or even a physiologist really tells me that his motivation for work is the desire to benefit mankind, I won't believe him (if I did, I wouldn't think he was really great). What dominates his motivation is what I described. And what is certain is that no decent person needs to be ashamed of these motives. ?
eight
If rational curiosity, pride and ambition in professional work are the leading motives in research work, then there is no doubt that there is no better opportunity to meet these conditions than to become a mathematician. Mathematicians' research discipline is the most curious of all disciplines. The truth of no subject is as strange as mathematics. Mathematics is the most exquisite and attractive skill, and mathematical research provides an opportunity to show real professional skills. Finally, I want to say that history has fully proved that no matter what the intrinsic value of mathematics is, its achievements are the most lasting of all.
We can see this from the semi-ancient civilization. The civilizations of Babylon and Assyria have been destroyed, and Hammurabi, sargon and Nebuchadnezzar have lost their names, but the mathematics of Babylon is still interesting. Babylonian hexadecimal is still used in astronomy. Of course, the case of Greece is a more convincing example.
For us, the Greeks are the earliest and still "real" mathematicians. Oriental mathematics may only satisfy interest and curiosity, while ancient Greek mathematics is real. The Greeks took the lead in using the mathematical language that modern mathematicians can understand. As Littlewood once told me, Greek mathematicians are not smart and good students at school, nor are they "candidates for scholarships", but "researchers from another university". Therefore, Greek mathematics is "immortal" and even more lasting than Greek literature. When Aeschylus is forgotten, Archimedes will still be remembered, because language will die, but the idea of mathematics will never die. The word "immortality" may not be very clever, but perhaps mathematicians fit its meaning best.
Mathematicians need not worry about being unfair to them in the future. Immortality is usually absurd and cruel: few of us choose to be Og, Ananias and Gaglio. Even in the field of mathematics, history sometimes plays some strange jokes: Raul is famous in the textbook of elementary calculus, but it seems that Raul is as famous as Newton; Farey can't understand the flawless theorem that Haros 14 years ago proved, but he is immortal. The names of five respectable Norwegians still live in Abel's book Life, just because a stupid due diligence has done harm to the greatest figures in their country. However, on the whole, the history of science is fair, especially the history of mathematics. No subject has formed a clear and consistent evaluation standard like mathematics. Most mathematicians remembered by people are worthy of the name. If it can be evaluated in cash, a person's reputation in mathematics will be the most stable and reliable investment.
nine
All these make university teachers deeply gratified, especially math professors. Lawyers, politicians and businessmen sometimes claim that most people who engage in academic careers are cautious and have no ambitions. These people are mainly concerned with comfort and stability. This accusation is unreasonable: university teachers have given up many things, especially the opportunity to make a lot of money-it is difficult for a professor to earn 2000 pounds a year. The stability of work is naturally one of the factors that decide to give up the opportunity to make a lot of money, but this is not the reason why houseman doesn't want to be Sir Simon or a noble in beaverbrook. Houseman turned down some careers because he was ambitious, because he disdained to be a forgotten person after 20 years.
However, how painful it will be for a person to sacrifice all these benefits. I still remember that Bertrand Russell once told me a terrible dream; He is on the top floor of the university library, and a librarian walks up and down the bookshelf, carrying a huge bucket, taking books one by one, scanning them, and then putting them back on the bookshelf or throwing them into the bucket. Finally, he found three volumes of books, and determined that they were the last remaining books of Principles of Mathematics. He picked up one of the volumes, turned over a few pages, seemed to be confused by those strange symbols for a while, then closed the book, took it in his hand and hesitated. ...
10
Mathematicians, like painters and poets, are creators of patterns. Mathematicians' models are longer than those of painters and poets, because mathematicians' models are made up of ideas, painters use shapes and colors to create models, and poets use words and words to shape models. A painting may contain some kind of "artistic conception", but it is usually ordinary and irrelevant; In contrast, poetry is much more important. However, as houseman insisted, people habitually exaggerate the importance of poetry. He said: "I find it hard to believe that there is such a thing as poetry ... poetry is not about what is expressed, but how it is expressed."
Pour out the water from the rivers and seas, and the ointment on the emperor will not wash off.
Is there a better poem than this? But as far as poetry is concerned, what can be more mediocre and absurd than this? The lack of artistic conception does not seem to affect the beauty of this writing pattern. On the other hand, mathematicians have nothing but thoughts, so the mathematician's model is more lasting, because thoughts don't become cliches as quickly as language does.
Just like the models of painters and poets, the models of mathematicians must be beautiful; Just like colors and words, mathematicians' thoughts must be harmonious. Beauty is the first level: ugly mathematics will never have a place in the world. I have to mention a wrong concept here, which is still widely circulated (although it is better than 20 years ago). This is what Whitehead called a "bookworm", that is, he loves mathematics and appreciates its beauty. This is "paranoia confined to a few weirdos in each generation."
It is difficult to find an intellectual who is indifferent to the aesthetic charm of mathematics now. It may be difficult to define the beauty of mathematics, but so is any kind of beauty-we may not know the so-called beauty of a poem, but this does not prevent us from appreciating it in reading. Professor Hogben tried his best to belittle the beauty of mathematics, but even he dared not rashly deny this fact. "There is no doubt that mathematics has an indifferent and unnatural attraction to some people ... This aesthetic charm in mathematics is probably true for these few people." But he also pointed out that these people are "few" and they feel "indifferent" (they are really ridiculous, living in a so-called small place in the university town, avoiding the fresh breeze in a vast space). In these words, Hogben just echoed Whitehead's "bookworm".
However, the fact is that there is no more popular subject than mathematics. All people have some appreciation of mathematics, just as all people can appreciate a beautiful tune; People who are really interested in mathematics are probably more interested than music. On the surface, it may be the opposite, but it is easy to explain. Music can stimulate people's feelings, but math can't; Not knowing music is just a little humiliating. Everyone is so afraid of the name mathematics, and everyone sincerely emphasizes that they have no mathematical cells.
A small rebuttal is enough to reveal the absurdity of "nerd". Every civilized country has thousands of chess players (Russia, these people are educated groups); Every player can taste and appreciate a chess game or the layout of a chess game. However, a layout problem is simply a purely mathematical exercise (the whole game is not necessarily because psychology can also play). Everyone who praises the layout of chess is actually cheering for the beauty of mathematics, although this beauty is relatively low. Chess layout is a mathematical hymn.
A little lower, but for the wider public, we can learn the same content from bridge, even lower, from the quiz games in popular newspapers. Almost all these games are unprecedentedly popular, which is attributed to the attraction of basic mathematics. Excellent creators of intellectual games like Doudney and caliban have no other skills. They know their own career, and what the public needs is nothing more than a little intellectual "stimulus". Nothing is more exciting than math.
What needs to be added is that nothing in the world can make celebrities (and people who despise mathematics) happier than discovering or rediscovering a real mathematical theorem. Spencer republished in his autobiography a theorem about circles that he proved at the age of 20 (he didn't know that Plato had proved this theorem more than 2000 years ago). Recently, Professor Soddy is a more amazing example (although his theorem is actually his own). ⑥