如果能回到你學術生涯的起點,你會給那時的自己一些什麼建議呢?關於讀博,關於平衡課業與科研、生活與學術,關於科研方法,關於心態,關於找教職,甚至關於轉行與工業界。

雖然我自己是工程學科背景,今年開始在UCLA讀碩士,已經做過一些研究了有四篇小文章。想聽聽大家的故事,但是不限學科背景,無論成果多少,也不在於國內國外,謝謝!


學術界的形勢年年都在變化。我覺得,對初入行者,最重要的是想清楚自己做科研的動機,或者,用時下時髦的詞來說,初心是什麼?自己是否有做科研的大心臟,做到「舉世譽之而不加勸,舉世非之而不加沮」?自己對以後人生道路的期待到底怎麼樣,是不是「起碼得在本科學校任教纔算滿意」?——學術界前輩聽了這種話當然會想笑,也可能是苦笑,不過說實話,社會上很多人,包括博士新生的一些親人,甚至博士生自己,真就是這麼想的。自己是否真的不太在乎周圍人的想法?——很多學生以為自己不在乎周圍人的想法,實際上過年回家被親戚問工作情況問收入問婚育情況的時候還是會沮喪。

如果你看了這麼幾句話覺得很沉重,晚上都睡不著覺,那還是儘早準備去業界上班吧。如果你覺得這些也沒啥,我更關心科研本身的內容,那可以進這一行試試。據我觀察,學術界做得好的人,一般都有一種「舉重若輕」的氣質。他們也瞭解這些世俗的現實問題,但他們不會讓焦慮支配自己的情緒,他們仍然能有心情有精力去做科研上該做的事情。


  1. 學術的經濟模式和娛樂圈很像,前2%的人會有90%的資源。
  2. 塞翁失馬,焉知非福,錯過了就錯過了,下次機會會有的。學術界是知識的邊緣,機會很多,你只需要撿到一個。
  3. 你的學術聲望比一切都重要,圈子就那麼大,抬頭不見低頭見,不要為了芝麻不擇手段,丟了西瓜。
  4. 被拒絕是正常的,是常態,很輕易被接受纔是不正常的,不要讓拒絕影響自己。畢竟一篇論文的發表只需要被接受一次。
  5. 接受人的不同,觀點的不同,追求的不同,習慣的不同。接受他人,才能合作,纔能有碰撞和好結果。
  6. 戰略上不要懶惰,多參加社交,多跨界,多看。好的工作很少是靠時間堆出來的。
  7. 焦慮是正常的,焦慮使人思考,是好事,歡迎自己的焦慮。
  8. 教職的標準是獨立,博士博後的標準是執行力。若目標是教職,做好本職工作是不夠的,請提前計劃。

2020-05-17補充

兩句簡單的話,但是是我收到的最好的建議。

9. 永遠不要當大海里的一滴水。

10. 永遠比別人期望的多做一點點。不需要很多,只需要多一點點。


前段時間偶然獲得數學家 Rota 的兩篇小短文,講述了混跡數學界的一些經驗,並給予了一些忠告。在此發給大家,希望對大家有一定的啟發作用。

一代數學大師 ROTA 的經驗與忠告

義大利裔的美籍數學家 Gian-Carlo Rota(1932 年 4 月 27 日 – 1999 年 4 月 18 日)是一位傑出的組合學家。他曾是研究泛函分析(Functional Analysis)出身,後來由於個人興趣的轉移,成為了一位研究組合數學(Combinatorial Mathematics)的學者。Rota 的職業生涯大部分都在麻省理工學院(MIT)度過,曾擔任 MIT 的數學教授與哲學教授。

1970 年的 Rota

從數學家族譜(Mathematics Genealogy Project)上面可以看到:Gian-Carlo Rota 的導師是 Jacob T. Schwartz,Rota 於 1956 年在耶魯大學獲得數學博士學位,其博士論文的題目是 Extension Theory of Differential Operators。

Rota 的數學族譜

在 1997 年,Rota 發表了兩篇關於人生經驗和忠告的文章,分別是 「Ten Lessons I wish I Had Been Taught」 和 「Ten Lessons for the Survival of a Mathematics Department「。下面就來逐一分享這兩篇文章中的一些觀點。

Ten Lessons I wish I Had Been Taught

講座(Lecturing)

每次講座或者分享的時候都有幾個需要注意的事情。

(a)每次講座都應該只有一個重點。(Every lecture should make only one main point.)

Every lecture should state one main point and repeat it over and over, like a theme with variations. An audience is like a herd of cows, moving slowly in the direction they are being driven towards. If we make one point, we have a good chance that the audience will take the right direction; if we make several points, then the cows will scatter all over the field. The audience will lose interest and everyone will go back to the thoughts they interrupted in order to come to our lecture.

(b)不要超時。(Never run overtime.)

Running overtime is the one unforgivable error a lecturer can make. After fifty minutes (one micro-century as von Neumann used to say) everybody』s attention will turn elsewhere even if we are trying to prove the Riemann hypothesis. One minute overtime can destroy the best of lectures.

(c)提及聽眾的成果。(Relate to your audience.)

As you enter the lecture hall, try to spot someone in the audience with whose work you have some familiarity. Quickly rearrange your presentation so as to manage to mention some of that person』s work. In this way, you will guarantee that at least one person will follow with rapt attention, and you will make a friend to boot.

Everyone in the audience has come to listen to your lecture with the secret hope of hearing their work mentioned.

(d)給聽眾一些值得回憶的東西。(Give them something to take home.)

Most of the time they admit that they have forgotten the subject of the course and all the mathematics I thought I had taught them. However, they will gladly recall some joke, some anecdote, some quirk, some side remark, or some mistake I made.

板書技巧(Blackboard Technique)

(a)開講前保持黑板乾淨(Make sure the blackboard is spotless.)

By starting with a spotless blackboard you will subtly convey the impression that the lecture they are about to hear is equally spotless.

(b)從黑板的左上角開始書寫(Start writing on the top left-hand corner.

What we write on the blackboard should correspond to what we want an attentive listener to take down in his notebook. It is preferable to write slowly and in a large handwriting, with no abbreviations.

When slides are used instead of the blackboard, the speaker should spend some time explaining each slide, preferably by adding sentences that are inessential, repetitive, or superfluous, so as to allow any member of the audience time to copy our slide. We all fall prey to the illusion that a listener will find the time to read the copy of the slides we hand them after the lecture. This is wishful thinking.

多次公佈同樣的結果(Publish the Same Result Several Times)

The mathematical community is split into small groups, each one with its own customs, notation, and terminology. It may soon be indispensable to present the same result in several versions, each one accessible to a specific group; the price one might have to pay otherwise is to have our work rediscovered by someone who uses a different language and notation and who will rightly claim it as his own.

說明性的工作反而更有可能被記得(You Are More Likely to Be Remembered by Your Expository Work)

When we think of Hilbert, we think of a few of his great theorems, like his basis theorem. But Hilbert』s name is more often remembered for his work in number theory, his Zahlbericht, his book Foundations of Geometry, and for his text on integral equations.

每個數學家只有少數的招數(Every Mathematician Has Only a Few Tricks)

You admire Erdo?s』s contributions to mathematics as much as I do, and I felt annoyed when the older mathematician flatly and definitively stated that all of Erdo?s』s work could be 「reduced」 to a few tricks which Erdo?s repeatedly relied on in his proofs. What the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks which they use over and over. But on reading the proofs of Hilbert』s striking and deep theorems in invariant theory, it was surprising to verify that Hilbert』s proofs relied on the same few tricks. Even Hilbert had only a few tricks!

別害怕犯錯(Do Not Worry about Your Mistakes)

There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.

使用費曼的方法(Use the Feynman Method)

You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, 「How did he do it? He must be a genius!」

不要吝嗇你的讚美(Give Lavish Acknowledgments)

I have always felt miffed after reading a paper in which I felt I was not being given proper credit, and it is safe to conjecture that the same happens to everyone else.

寫好摘要(Write Informative Introductions)

If we wish our paper to be read, we had better provide our prospective readers with strong motivation to do so. A lengthy introduction, summarizing the history of the subject, giving everybody his due, and perhaps enticingly outlining the content of the paper in a discursive manner, will go some of the way towards getting us a couple of readers.

為老年做好心理準備(Be Prepared for Old Age)

You must realize that after reaching a certain age you are no longer viewed as a person. You become an institution, and you are treated the way institutions are treated. You are expected to behave like a piece of period furniture, an architectural landmark, or an incunabulum.

Ten Lessons for the Survival of a Mathematics Department

不要在其他系講自己系同事的壞話(Never wash your dirty linen in public)

Departments of a university are like sovereign states: there is no such thing as charity towards one another.

別越級打報告(Never go above the head of your department)

Your letter will be viewed as evidence of disunity in the rank and file of mathematicians. Human nature being what it is, such a dean or provost is likely to remember an unsolicited letter at budget time, and not very kindly at that.

不要進行領域評價(Never Compare Fields)

You are not alone in believing that your own field is better and more promising than those of your colleagues. We all believe the same about our own fields. But our beliefs cancel each other out. Better keep your mouth shut rather than make yourself obnoxious. And remember, when talking to outsiders, have nothing but praise for your colleagues in all fields, even for those in combinatorics. All public shows of disunity are ultimately harmful to the well-being of mathematics.

別看不起別人使用的數學(Remember that the grocery bill is a piece of mathematics too)

The grocery bill, a computer program, and class field theory are three instances of mathematics. Your opinion that some instances may be better than others is most effectively verbalized when you are asked to vote on a tenure decision. At other times, a careless statement of relative values is more likely to turn potential friends of mathematics into enemies of our field. Believe me, we are going to need all the friends we can get.

善待擅長教學的老師(Do not look down on good teachers)

Mathematics is the greatest undertaking of mankind. All mathematicians know this. Yet many people do not share this view. Consequently, mathematics is not as self-supporting a profession in our society as the exercise of poetry was in medieval Ireland. Most of our income will have to come from teaching, and the more students we teach, the more of our friends we can appoint to our department. Those few colleagues who are successful at teaching undergraduate courses should earn our thanks as well as our respect. It is counterproductive to turn up our noses at those who bring home the dough.

學會推銷自己的數學成果(Write expository papers)

When I was in graduate school, one of my teachers told me, 「When you write a research paper, you are afraid that your result might already be known; but when you write an expository paper, you discover that nothing is known.」

It is not enough for you (or anyone) to have a good product to sell; you must package it right and advertise it properly. Otherwise you will go out of business.

When an engineer knocks at your door with a mathematical question, you should not try to get rid of him or her as quickly as possible.

不要把提問者拒之門外(Do not show your questioners to the door)

What the engineer wants is to be treated with respect and consideration, like the human being he is, and most of all to be listened to with rapt attention. If you do this, he will be likely to hit upon a clever new idea as he explains the problem to you, and you will get some of the credit.

Listening to engineers and other scientists is our duty. You may even learn some interesting new mathematics while doing so.

聯合陣線(View the mathematical community as a United Front)

Grade school teachers, high school teachers, administrators and lobbyists are as much mathematicians as you or Hilbert. It is not up to us to make invidious distinctions. They contribute to the well-being of mathematics as much as or more than you or other mathematicians. They are right in feeling left out by snobbish research mathematicians who do not know on which side their bread is buttered. It is our best interest, as well as the interest of justice, to treat all who deal with mathematics in whatever way as equals. By being united we will increase the probability of our survival.

把科學從不可靠中拯救出來(Attack Flakiness)

Flakiness is nowadays creeping into the sciences like a virus through a computer, and it may be the present threat to our civilization. Mathematics can save the world from the invasion of the flakes by unmasking them and by contributing some hard thinking. You and I know that mathematics is not and will never be flaky, by definition.

This is the biggest chance we have had in a long while to make a lasting contribution to the well-being of Science. Let us not botch it as we did with the few other chances we have had in the past.

善待所有人(Learn when to withdraw)

Let me confess to you something I have told very few others (after all, this message will not get around much): I have written some of the papers I like the most while hiding in a closet. When the going gets rough, we have recourse to a way of salvation that is not available to ordinary mortals: we have that Mighty Fortress that is our Mathematics. This is what makes us mathematicians into very special people. The danger is envy from the rest of the world.

When you meet someone who does not know how to differentiate and integrate, be kind, gentle, understanding. Remember, there are lots of people like that out there, and if we are not careful, they will do away with us, as has happened many times before in history to other Very Special People.

參考資料:

  1. Rota, Gian-Carlo. 「Ten lessons I wish I had been taught.」 Indiscrete thoughts. Birkh?user, Boston, MA, 1997. 195-203.
  2. Rota, Gian-Carlo. 「Ten Lessons for the Survival of a Mathematics Department.」 Indiscrete Thoughts. Birkh?user, Boston, MA, 1997. 204-208.


謝謝邀請。

學術圈勸退文章和回答已經夠多了,勸退依據主要是性價比不高。在此也不重複。

除了錢和生活的原因外,還要考慮的一個問題是學術圈現在基本都是實行的是團隊課題組制度,這種制度下的大老闆對團隊下的每個成員職業發展影響很大,不管是博士生還是職工。實際上這種制度就是科研圈的資本主義制度(甚至可以說是封建地主制度也沒問題),團隊裏的每一個人都被老闆剝削著剩餘價值。

找科研條件好,老闆人品好的團隊加入,這其實只是很小的一方面。如果想在科研領域有一番天地,一個更加準確的說法是:在自己確有科研能力的基礎上,找到一個願意成全你的老闆

什麼意思呢,很多課題組成立之初,老闆的目的就是為自己謀取利益出發的(尤其是工科),根本沒有考慮過培養出比自己更加優秀的科研人員。

可以想像一下,一個願意成全你的老闆應該具有怎樣的品質:

1首先這個老闆得慧眼識珠。(這個比例不算低但也不高)

2其次這個老闆願意承認有員工比自己厲害的。(這很難)

3老闆願意為了你的學術前途犧牲掉自己的部分利益(花錢送你去上暑期學校,讓你去開會等等),甚至大部分利益(把你送給學術實力更強的地方學習)。工科大部分老闆不把你當廉價勞動力就不錯了,非親非故誰會考慮手下打工員工前途。(這很難)

在現有科研資本主義制度下,滿足上述條件的老闆可謂是科研圈的聖賢了。

但如果真的滿足上述條件,那就不要辜負導師的期望。


我看到很多人說混學術圈要找到一個大腿。此話倒是不假,但是很多學術大佬只是把你當他的一兵一卒,並不是要支持你發展,因此並不是進入一個大組就有所謂的學術前途了。


針對應用/實用型研究,兩個建議:

一,不要通過論文來學習知識;

二,去學習研究方向的「元學科」。

解釋:

很多科研新人,因為剛接觸科研前沿,很容易被手裡的幾十篇論文迷糊了眼睛。通常來說,他們在閱讀這些論文之後,往往會做一個比較詳細的綜述,之後就把視野侷限在了這些論文中,而後續的研究工作也只是基於這些論文的微創新。

這會帶來三個嚴重的問題:第一,他們的知識是完全碎片化的,沒有學科框架,因為論文與論文之間本身就是碎片化的;第二,知識面狹窄,因為僅通過論文學習知識,自然而然就把視野侷限在了論文所涉及的知識面上;第三,層次低,因為論文往往是把某個已有的東西做了微小改進,那麼你再去啃這些論文,等同於喫二手飯,層次很低。

因此,對於一個有心學術的人,首先應該去系統地學習正經教材。只有這些教材能幫你建立完備的學科架構。其次,應該學習元學科教材,進一步拓展視野。譬如,假如你是做天文數據處理的學生,那麼元學科就可以是數據科學和統計學;假如你是控制理論的學生,那麼數學裡關於非線性和動態的部分就是元學科;假如是微電子類學生,那麼半導體物理和半導體器件物理學則應該作為元學科。當然,這些元學科只是我限於個人的理解,並不一定準確,但思路可以總結為:去尋找當前研究課題或方向的「根源」學科,拓展視野。

總體來說,除去研究工作佔用的時間,剩下的時間都可以用來學習。而這部分所能擠出來的學習時間,應該把其中的大部分用於專業教材的學習和鞏固;把其中的一部分用於元學科的學習,拓展視野;最後把其中較少的部分用於閱讀頂刊和頂會論文。論文閱讀應當少且精。也就是說,按重要性來講,學科專業書籍&>元學科書籍&>&>論文。


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