我 23 岁了,我现在面临一些选择. 是时候好好回顾一下过去,细致地梳理一下我的理想,给人生定个方向了.
我曾经以为我的人生会很顺利,非常非常顺利的那种. 我以为我永远不会面临这个问题,永远不需要写这种文章,我把未来看得也过于简单了. 于是,在第一次考研失败后,甚至早在第一次考研上考场之前,我都还对未来充满了希望,早就计划好要考第二次. 第一次考研结束的那一天是刚刚过了 2018 年冬至的第一天,冬至对于北半球来说是黑夜最长、白昼最短的一天. 考完试后我对自己说,从今天开始,白天就越来越长了.
我报考的是北京大学数学系基础数学方向,能继续做基础数学是我的理想. 北京大学的数学系实力很强,与北京国际数学研究中心资源互通,聚集了来自全世界的各个方向的数学人才,每年基础数学方向招收研究生 10 - 15 人,推免人数占了绝大多数,留给考研的名额只有 2 - 3 人,而报名考研的人数每年都有 100 多人. 第一次考研时,我有个朋友本来也想报考北大的,最后还是换成了中科院,他觉得北大的报录比太大了,报名的那么多人里只要有那么 2 个特别特别厉害的,其他人就算是白考了,考再好也没用. 不过我还是毅然决然地报了,当时我的理由非常简单:
第一,北大第一年不分导师,不用担心自己感兴趣的老师已经招满了推免生.
第二,据往年数据,每年过线的平均只有 1 - 2 个,而政治和英语过线不难,卡住 99% 的人的是两门专业课——数学分析、高等代数和解析几何. 因此政治英语不需要特别花时间去准备,只要把全部精力投入到数学上,最后两门专业课都过线(达到 90 分)就基本可以确定获得了复试机会,也基本可以确定一只脚踏进了北大的大门.
第一次考研失败了,一遍书都没有复习完. 不过我知道是自己开始得晚,再考一次就没问题了. 寒假过完开学后先办理了降级手续,这样我便又是应届毕业生了,而且可以住宿舍、吃食堂、进图书馆、选一些课去上. 有了第一次的经验,我给自己规划好,决定暑假一开始就全身心准备考研,春季学期好好学习一些高级的数学课程,这样到时候进到北大的面试也更有底气. 那一学期我旁听了研究生的表示论课程,上了半学期的椭圆曲线研究生讨论班,选了我校荣誉学院数学方向的同调代数讨论班,还旁听学了一学期法语. 学期中,一位老师介绍给我一个关于数论和代数几何的学术会议,允许一些本科生参加,不过本科生要想获得资助(报销路费和安排住宿)需要做一个 25 min 左右的 talk. 为了得到资助,我准备了一个介绍 Taniyama-Shimura-Weil 猜想(定理)的 talk. 这次活动对我影响很大,我认识了十多位比我优秀得多的各大高校的本科生,他们已经人均能对代数几何侃侃而谈了.
学期结束,暑假开始,我再次投入到考研的复习中. 8 月到 10 月的复习推进得很快,高等代数和解析几何已经复习完一轮了,剩下一个多月做做题就好了;数学分析没能按计划进行,一轮复习没有按时完成,不过考研报名时我还是没有犹豫,我觉得我再努努力,可以把一轮课本复习与二轮做题结合到一起搞,边复习边做题,肯定能复习完. 那是十月份,我还是对考上北大比较有自信. 然而实际情况是,我一开始做题,便觉得题做不完了. 谢惠民等人的《数学分析习题课讲义》是一本比我想象中好太多太多的书,我甚至觉得最开始就不应该去看课本. 网上的经验说看课本、回归课本、课本是最好的,但我看了谢惠民就觉得还是不如直接看谢惠民. 然而时间不够看完谢惠民的了,我就尽量更快地看它,觉得能多看一点是一点,尽量快的意思是,不做练习题了,例题只稍微想 20 分钟就行了,想不出来就马上看解答好了. 这样看了挺多,却全都埋下了祸患. 直到最后临考试一个星期时,我打算再复习一下之前看过的内容,却发现当初看得快、懂得快的那些,也都很快就忘记了. 这在数学分析的考试中给了我足够的惩罚——有几道题,我明知道我学过,我看过,然而就是不知道该怎么在考场上把它解出来,那感觉比第一次考研难受多了. 我明知数学应该怎么学,却没有那么学. 好在下午第二门专业课高等代数和解析几何我做得还不错,让我不至于太自卑.
第二次考研结束的那天是冬至,我感到那一天的黑夜是我人生中最漫长的一个. 第二次考研前确实有人建议我换一个报考,比如报考中科院,但我没有听. 那时我想的是,即便是北大,不也就是上午做 10 道题下午做 10 道题么,如果我复习 5 个月却有一个科目连 6 道题都做不出来,那也许我不适合学数学;如果我考不上中国最好的数学系,那我又怎么保证以后一定能写得出文章、解决得了问题,怎么保证以后能拿到教职、在数学界继续待下去呢?如果考不上北大,我就趁早转行好了,趁早去工作,去过平凡的人生.
考完后我却无比后悔,要是报考中科院也许还有希望、也许还有学上,无论它是不是最理想的地方,无论是否能选自己想做的方向,至少把学术的道路先维持下去——真的一想到去工作,我不甘心. 我想做数学,那是我的理想.
我其实并没有非常幸运,幸运到从一开始就想做数学,真正学习数学还是在大学以后. 我的爸爸妈妈从来没有给我指定过方向,他们尊重我的所有决定,鼓励我勇敢去尝试,寻找属于自己的道路. 小时候我很有虚荣心,想做最厉害的人,那时我以为当上国家主席就是最厉害的,甚至没把科学家放在眼里. 再大一些我听说了联合国,又把志愿改成了当联合国秘书长. 这样的志气让我有勇气在小学各种比赛各种活动中举手报名参加. 从那时开始,一切都顺风顺水:学习好,得到了老师的关注;被推荐参加各种比赛,拿奖,得到更多老师的关注;被少先队老师选为大队长,又获得更多荣誉——我被卷入了一个良性循环,它裹挟着我,让我以为生活就是一帆风顺,我只管努力成长,一切荣誉自然都会到来.
良性循环继续被我带到了初中——在初中的分班考试中我很意外地拿到了第一名,于是我刚上初中时整个年级的老师都知道了我的名字,我直接被班主任老师任命为班长,然后过于顺利地成为了学生会主席. 初中的环境就比小学要复杂一些,班长和学生会的工作经历就开始有点锻炼人了,我的情商在那时得到了极大的提升,同时也体会到了人际交往中的疲惫. 这时年级组长老师和我进行了谈话,她觉得我严谨、较真的精神很可贵,希望我不要变得油滑事故,希望我不要对政治过于上心,可以试着走学术的道路. 正好到初三就卸任了一切职务,一心学习准备中考,每天没有烦心事还是更快乐一些. 年级组长老师对我的影响还是很大,那是她第一次在我心里给我埋下了学术的种子.
高中时我顺利得到一个机会在某高校一位老师的指导下完成了一次科研体验. 这一次科研体验对我来说很重要,它帮我排除了这类实验学科科研的人生道路. 这次科研是在一个微生物的实验室进行的,总的来说不是很有意思,课题是已经确定好的,需要用到的知识不多,高中的基础再简单学一学就可以上手做了,设计好实验,然后就是机械地执行计划:配置培养基,接种微生物,放到摇床里(因为是比较大规模的培养,用的液态培养基),定时给它们喂糖,然后进行和课题有关的东西,进行化学检测,我俨然成为了“实验民工”. 我觉得这样的生活不会是我想要的,即便是我没有接触到的关于如何确定课题的那一部分,想必也不会很困难,而且看上去没有很大的自由. 更重要的是——我觉得这种实验科学的科研过程有点不严谨.
我并不排斥发现问题并解决问题,关键是有时候解决问题的过程中不明不白地就解决了问题. 尽管科学的研究方法已经尽最大努力保证解决问题的每一步都不会出现大的问题了,但每一步仍然有不严谨的自由——甚至有人为操纵的自由. 毕导在评论曹雪涛疑似造假的文章⧉中的一段话比较能说明这个问题:
生医里面的玄学因素实在太多了,P个图根本看不出来. 还有些科研人员,会先想好结论,再强行把数据往结论上做.
…
你今天制了个样,准备烘干打红外. 结果 1700 的羰基峰很漂亮,但样品没烘干净,3000 以上有水包!好不容易做出来的样品,重做是不可能重做的. 怎么办?用基线把水峰P掉咯,反正不影响我的核心结论. 你对材料进行了 modification,理论上能降低表面粗糙度,于是你约了 AFM. 结果样品还是很粗糙!好不容易做出来的样品,重做是不可能重做的. 怎么办?当然是精心挑一个光滑的地方拍AFM咯,我的理论不可能出错. 你改进了一种反应物,理论上能把表面的 Nodule 结构变成 Sphere 结构,你兴奋地送了SEM. 结果发现只找到了 3 个 Sphere. 好不容易做出来的样品,重做是不可能重做的. 那当然是强行拍一个 Sphere 宣布改进成功咯.
更大的问题是整个自然科学的问题:说到底人类还没有能力把世界解释清楚. 我初高中学习知识时是非常愉快的,我至今记得自己初二学习物理刚学会受力分析,刚知道牛顿力学三大定律时的快感. 我在那之前从来不知道宇宙是如何运作的,苹果为什么会落在地上,虽然看过科普书,但还是不明就里. 就在那个秋天的下午,外面阴着天,教室开着灯,物理老师让我们往笔记本上抄写着笔记但还没详细解释的那一瞬间,我就那样似懂非懂地理解了一切. 真正的理解是在[后来老师进行了详细解释,做过大量习题,把之前的想法中错误的地方慢慢修正]后才形成的,但理解的快感是那一瞬间的事. 那一瞬间,我感觉到的是世界不再神秘,我初中就已经可以学习并理解清楚这个问题,那么等我高中、大学,我会更加理解这个世界,我未来会为人类理解这个世界作出自己的贡献. 那时的我不会想到现在的自己对这一切是如此悲观.
实际上,对这个问题的悲观从很早就开始了. 初中的化学课就让我觉得很不爽,化学反应没有一个像牛顿力学三大定律的理论,总结出一些规律却还总是有一些反例,课本上给出的模型到底还是没那么令人信服. 老师说,这是因为我们才上初中,以后学习了更多的东西就会更好理解了. 可到了高中,化学给我的感觉依然是理论模型解释力有限,同时还出现了另一个让我更加厌恶的学科——生物. 这两门学科给我的感觉都是那样的支离破碎. 我渐渐认清了一个事实,就是做科研不像是牛顿发现三大定律,而更像是在细节上缝缝补补. 慢慢地,就连物理学也变得支离破碎起来,我开始意识到,我的理想世界还是好几百年前的人认识世界的方式,而现代科学展示给我的,就是没有那样的理想世界,这个世界看上去没有真理,或者说,这个世界不像是我曾经以为的那样精巧、美丽,它是在实实在在地运作着,但好像人类终究没法说清它是如何运作的,这让我十分不安.
这当然不会妨碍技术的进步,技术的进步从来不建立在完美的科学之上,人们如此务实,只要能用,便不必在乎是否已经研究清楚,更何况可能永远都研究不清楚. 人们连看似简单的自行车如何保持平衡⧉都说不清,但不妨碍人们骑自行车骑了 200 年. 让我不安的是世界没有真理、人类永远说不清世界如何运作这件事本身,甚至人们也没法证明“人类是说不清世界是如何运作的”. “怕什么真理无穷,进一寸有一寸的欢喜”,对我来说没有“进一步”,更没有“欢喜”.
虽然我对自然科学可能有一些误解,毕竟我没有选择自然科学,但这个感觉就是这样了——自然科学没有解释世界的潜力,虽然这是世界的问题而不是自然科学的错;再加上自然科学的科研本身——那些日复一日、没那么光鲜亮丽的科研活动本身是那样不够严谨,我的完美主义情节终于让我选择了数学.
后记:写完后过了几天决定再读一遍然后就发到博客里时,觉得这几段写得有点不清不楚的,普通读者可能很难理解我对自然科学的悲观到底是什么,它为什么不能解释世界等. 这一定是我的问题,我有时间了读一读科学哲学再单独写一篇详细的吧.
数学当然不是在[我对自然科学的美好幻想破灭]的一刻才登场,我从很小开始就对数学有着很强的兴趣.
最开始的兴趣源于一本书:《小学生提高学习成绩的 500 个数学故事》⧉,这不是什么出名的书,只是我二年级时我爸爸带我去超市给我买的,是一本超市书. 我不记得当时买书的情景了,可能是我在超市偶然拿起这本书在看,我爸爸就想给我买回家看;更有可能的是我爸爸就是想给我买一本书,看到封面上写着“小学生提高学习成绩”就直接买下来了. 书里有很多很多数学家的故事,也有很多很多数学的知识,我一直对这本书爱不释手,一遍一遍地看,我在小学就知道阿贝尔,还能给朋友们讲伽罗华的故事,这完全是拜这本书所赐,尽管我直到大学才真正去学习伽罗华的理论.
由于我小学起就喜欢数学,数学成绩也好,小区的一位老教师奶奶送了我很多奥数的书. 在那些没有手机、没有计算机、没有互联网的日子,我真的总是在看书,能独立解决一个又一个问题,那感觉真的非常快乐.
初中的数学也让人陶醉,我主要是沉浸在了初等平面几何的证明之中了,我发觉到数学就像是一片汪洋大海,我可以自由自在地遨游. 初中时的年级组长是我初三[进到的一个[全年级前 30 名同学组成的]班级]的数学老师,她对我影响很大,跟她一起学习数学是很美好的一件事,那时真的是觉得数学的美无处不在.
高中的第一天直接被班主任老师任命为数学课代表,一当就是三年——我至今不知道这样合我心意的职位是如何恰好落在我头上的,因为我中考数学成绩应该并不是高中班级中的第一名,我也说不清楚我最后选择数学的道路和当数学课代表有没有什么必然的联系. 唯一能说清的是,当上数学课代表后[我和高中数学老师关系]可能比[别的同学和她的关系]更亲密一点,以及我可以利用数学课代表的身份公开地说我非常喜欢数学——毕竟如果我要不是数学课代表的话,公开说我喜欢数学总有点和真正数学课代表“抢戏”的感觉,如果那个真正的数学课代表万一又没那么喜欢数学,难道我还要“篡位”么——这样的公开应该无形中还是给了我学习更多数学的动力,数学课代表这个身份成为了一个对我的监督:尽管大可不必,但有一个“数学课代表应该数学最厉害,应该能解出班级中其他同学解不出的问题”这样一种责任,我甚至说不清这个责任是公认的,还是我自己加给我自己的,但无论如何,它还是帮助了我.
但反过来说,它也没有帮助我多少,它让我沉浸于高中的数学知识,让我满足于“数学课代表”,让我对数学没能尽早形成一个更大的大局观. 我虽然也参加了数学联赛,但到底没有认真学习过,纯粹是去打了酱油;我虽然高二也买了本《高等数学》来看,但最终只是把极限语言学会了,各种什么 L’hospital 的定理学了一遍,而那些定理的证明都没有好好看过;我满足于高中的数学考试大纲,超纲的东西从未主动好好练习,三角函数只会三个最基本的 sin、cos、tan,和差化积、积化和差只是知道却从没有背过——这些东西我还是大学重新自己再学习的. 我嘴里口口声声说着喜欢数学、爱数学,却不知道数学是什么,不知道数学精神是什么,一边不重视证明只会解题,一边又幻想着自己会读数学系,未来会做数学研究,这在今天的我看来是十分令人痛心的. 不过也许怪不得我,我高中还在积极探索自己的路,我还对自然科学的科研抱有幻想,我真正决定读数学系已经是在高三,甚至高考之后,甚至是在填报志愿时. 我不想搞政治;经济、管理没意思;人文科学没意思;我不喜欢实验科学;我是数学课代表,我喜欢数学,我憧憬那些数学家的故事.
我是真的喜欢数学么?是. 我是因为自己是数学课代表才喜欢数学的么?不是,我很小就喜欢数学了. 好,那我可以报数学系了.
最后来到了一所综合性大学,大学的数学系也还可以. 尽管没有特别好,但我知道这也就是我的水平,我高考发挥很正常,也许还有些超常,比一模的成绩高了 10 多分. 大学的诱惑就太多了,我参加了一些学生活动,尤其需要拿出来说一说的是我学习了编程. 上大学以前我没接触过编程,高中的同学当中也没人编程,那时还觉得编程是很厉害很了不起的事;可是到了大学就发现很多人都会编程,还有高中参加信息竞赛的同学,我的一位室友也是我的好朋友编程就很有一套,有一些瞬间就觉得落差有点大. 正好有一个很不错的学校级的学生组织有技术的岗位,他们纳新的时候说零基础也没关系,会教的. 于是我和那位有基础的室友就一起报名了技术部的后端开发. 我从零基础开始,直接上来就是做网站的后端,我投入了很多很多,我的好室友也帮了我很多很多. 大一的寒假独立做了三个不太需要后端的简单的页面;大一结束后的暑假参加了 20 多天的集训,真真正正从头到尾做了一个项目;大二陆陆续续接了几个给学校学工部做的项目:在这个学生组织每做一个项目都有工资可拿,虽然不多,也让我知道,我学习的编程很有价值.
大二上学期和几个大三的同学参加了一个企业举办的单片机大赛,我为那个项目开发了一整套后台管理系统,那个系统帮助我们在答辩时非常好地给评委演示了我们的核心功能,轻轻松松拿到了一等奖. 一个学长代表我们去那个企业参观,并直接给企业老总演示我们的项目,企业老总奖励给我们 1000 块钱,说可以让我们直接毕业后去他那个企业工作,还特意对我的工作表达了赞赏. 我们四个人分了那 1000 块钱,我已经知道,我的技术让我在社会上靠编程已经不至于饿死了,我会的编程技术至少可以为我谋得一份工作. 接下来我想到的马上就是,这家企业好像不是很厉害,以及,真让我以编程为生我好像并不喜欢.
编程当然是比自然科学的科研严谨得多的,因为计算机就在那里,你写出的代码得按你想的去运行才行,这在一定程度上和数学很像,容不得一点马虎的. 然而它却是那样的枯燥,这从“码农”这个称呼中便能窥视一二,本质上和我高中时自然科学的科研那段经历中体验到的“实验民工”如出一辙. 编程看似语言很多,博大精深,但实际上同类型的语言设计的思想基本都是一致的,不一样的只有细节,会了一个语言,入门了编程,其他的语言真的就一点都不难了. 真正困难的而且有趣的应该是算法,应该是设计语言、编写新操作系统这些东西——然而这些东西有计算机专业的同学去做,我又去凑什么热闹呢?如果向这个方向进军,我还会花费更多的精力.
那段时间,全国高校开设了一些电竞专业,我一直对电竞专业持贬低的态度,我就在思考我为什么觉得电竞专业不是一个专业. 我最后得到结论,因为电竞专业的学习研究对象是人为创造出来的. 无论是哪一款游戏,都是有一个公司或团体或个人在经营,电竞专业的学生无论如何研究、练习一款游戏,这款游戏都有可能会发生变化,添加删除新英雄、修改英雄属性,甚至可能到最后这家公司倒闭,这个游戏不再存在. 如果一个专业的研究对象是被别人掌控的,是可能会变化的,那我就觉得这个专业没有任何意义. 我接下来把这个结论进行推广,就会发现,计算机这个专业又何尝不是这样?计算机是人类创造的,虽然有一个标准在这里确保了计算机的架构不会有太大的变化,但放在人类历史的长河中,这个学科终将没有意义,我们哪怕把目光拉进一点点,有了量子计算机呢,会不会有一些理论就和目前的理论不兼容了?
注记:今天在读到阮一峰,为什么世界上没有安全的工作?⧉时发现 Flash 工程师和塞班工程师的例子能更好地说清楚我在这里想说的问题,要知道 Flash 开发和塞班开发是比电竞更像是一门值得研究的学科,然而这些技术如今已经没落了,遑论电竞呢?再往外延伸,就是我想说的计算机这门学科也可能不具有永恒性. 而最有永恒性的学科当然是数学. 补充于2020.2.8.
意识到这些,我越发觉得,对计算机、编程领域的探索,到这个程度就可以停止了吧,我学到一点点技术,帮助我能更好地生活,这就足够了吧,我真正的人生职业规划,那就真的只有数学——基础数学,让我非常满意了:数学它严谨、优美,它揭示永恒的真理,它是人类创造的游戏;数学它和生活完全无关,它亘古长存. 也就是在这时我意识到,我的大学前两年已经过去了,我在数学上没有什么长进. 大一上学期的数学基础课比较简单,数学分析和高等代数最前面的内容我在高中都知道个大概,我以为我已经会了,对证明没太在意. 结果大一下学期数学分析(二)就直接挂了科. 我糊弄着自己把前两年学完,靠着考试前极限突击,虽然没再挂科,到最后却什么也没学到. 大三分专业,我惊险地成功进到了数学和应用数学专业,我真不知道自己如果没能进到这个专业,被分到信息与计算数学专业,我现在会是什么样子. 大三我退出了那个学生组织,开始专心学习数学,但前期没养成很好的学习习惯,大三的课程也学习得不扎实. 转眼就大四了,我考研、失败、降级、再考研、再失败,然后就是现在.
我觉得自己就像是一个渣男,我明明很早就认识数学了,却看不出数学的好;面对花花世界,我喜新厌旧,什么都想试一试,什么方向都想走一走. 我兴趣爱好极其广泛,交朋友对我来说总是容易,因为我和任何人都能很快找到共同话题. 我这个也学那个也学,没接触过的都想好好学一学. 岁月就那么匆匆而过,当我终于知道自己的心头所爱是数学时,数学已经不爱我了. 在数学系,有一些大佬,他们兴趣爱好没我丰富,除了数学懂的也不如我多,可是他们一心扑在数学上,在和我相同的年纪,他们已经迈进了现代数学的大门. 他们有的人从小就学数学竞赛,一路和数学为伴,如今已经在解决一些数学开放问题了;有的也和我一样大学才接触数学,有的甚至高考没有考到数院,但是发现自己爱数学后通过转专业,更加刻苦更加废寝忘食地学习,也有保持绩点第一、保研北大清华、出国留学的同学. 只有我,已经进了数院却不好好学习,还去学习编程,什么都试了一遍才确信自己最爱的是数学,等那些真的不喜欢数学、觉得自己没能力做数学的同学转行了计算机、转了金融、经济,我回过头来想做纯数. 我只知道自己起步晚了,学数学学晚了,还没努力试一试,对自己有没有能力做数学根本一无所知.
我有时在想所谓“素质教育”真的重要么?人生的宽度真的比人生的深度重要么?我如果能带着我目前的期待重新过一遍的话,我肯定选择从小就更加刻苦地学习数学,至少到了大学刻苦学习数学. 然而,刚上大学的我对一切都那么不确定. 也许人生就是充满了后悔和遗憾,也许即便我好好学习了数学我还会后悔、遗憾别的东西,也许人在每一个岔道口颤颤巍巍迈出的每一步都会被后来的自己否定.
“悟已往之不谏,知来者之可追”,21 世纪 10 年代过去,我 23 岁了,我再次站在了人生的岔道口上,又该颤颤巍巍地迈出新的一步了.
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