摘要：哈维穆德学院2024年的毕业典礼演讲，到现在都过去一年了，还在持续发酵中，社交媒体上很多推荐这个演讲的，这个演讲也被誉为青年学生最值得听的演讲之一。这样的毕业典礼演讲的影响力，实在是太难得了。

哈维穆德学院2024年的毕业典礼演讲，到现在都过去一年了，还在持续发酵中，社交媒体上很多推荐这个演讲的，这个演讲也被誉为青年学生最值得听的演讲之一。这样的毕业典礼演讲的影响力，实在是太难得了。

2024年的毕业典礼，哈维穆德请了一位网红数学老师做演讲嘉宾，他叫 Grant Sanderson，在油管有一个有700多万订阅者的数学教学频道，名叫3blue1brown，是油管上最受欢迎的数学可视化教学频道之一。

Grant Sanderson曾在斯坦福大学学习数学和计算机科学，随后于 2015 年加入可汗学院的内容团队，协助创建多变量微积分课程。2017 年，他开始全职投入自己的项目3Blue1Brown。他曾在2023年访问过哈维穆德学院的数学系，并发表了演讲《数学与物理的交汇》。他在演讲中探讨了运动学、光学与量子计算之间意想不到的联系，深受哈维穆德学生的喜爱。在2024年哈维穆德毕业生投票“希望担任毕业典礼演讲嘉宾的人选”时，Grant Sanderson以压倒性优势胜出。

“大家喜欢他，是因为他能够将数学和物理中许多艰深概念进行深入浅出的拆解与可视化，这帮助了很多哈维穆德学院的学生更好地理解课堂上所学的内容，学生们认为Grant Sanderson体现了哈维穆德学院的核心价值观：不仅能够理解复杂的课题，还能将其有效传达，并以此影响他人和整个社会。”

下面我们来看看他到底讲了什么，为什么都过去一年了，他的演讲还时时被人提起？

演讲的题目叫：追随梦想忽略了什么？

感谢 Nimpard 校长的热情介绍和邀请，也感谢 2024 届的毕业生让我参与这个特别的日子。

对于现场不认识我的人，我是一个专注于制作数学视频的人，尤其注重可视化。

这是一个有点奇怪的职业，但我非常热爱它，说它是梦想中的工作一点也不夸张。

人们常说，一个幸运地实现了梦想职业的人，会自信满满地站在刚毕业的学生面前，告诉他们：“要追随你的梦想。”

坦率地说，这种说法本身并不是很好的建议。

当然，这个陈词滥调背后是有一定道理的：

确实，最有影响力的人往往是那些被激情驱动的人；

确实，如果你能从事自己热爱的事情，生活会更有乐趣；

而且，也确实你不应该被社会的条条框框束缚住。

但问题在于，不是每个人都早早就有一个已经“烘焙完成”的梦想，等着自己去追随。

即使你是那个幸运的人，有一个想转化为职业的激情，我也认为，想要真正实现梦想，还需要一些现实的考量，而这些往往无法很好地融入励志演讲中。

现在我知道在座的是一个非常“理工”的听众群体，所以我很想用更数学化的方式来解释我的观点：

在“所有可能的建议”的向量空间里，如果“追随你的梦想”是一个向量，我想探索的是它的正交子空间。

不过，也许我还是先讲一个故事更好。

我刚上大学的时候，就是那种已经知道自己想学什么的人。

我喜欢数学。

我在高中喜欢数学，在大学也一样喜欢。

但我也热爱小提琴。

让我们花点时间想象一下两位音乐系的学生，我叫他们 Paganini 和 Taylor。

他们都很有天赋，非常有天赋。

Paganini 追求技术上的完美，练习那些炫技的高难度曲子；

Taylor 则致力于创作能够打动人心、引起共鸣的音乐。

在音乐学院里，Paganini 每次都会拿到更高的成绩，也总是拿到更好的位置。

但在追求音乐事业的路上，Taylor 却明显更有优势。

所以，我的第一个建议，也是我希望能回到过去告诉自己、告诉现在坐在你们位置上的我的建议：

如果你有一份热情，并希望将它融入职业生活，那么请退一步，认识到“追随梦想”这个陈词滥调忽视了一个关键点——你梦想的内容必须不仅仅关于你自己。

在第一份工作中脱颖而出的，是那些即使要做自己不喜欢的事也能让团队更轻松的人；

在博士项目中脱颖而出的，是那些理解自己工作如何融入更广泛研究领域的人，而不是只把它当作学业下一章的人；

成功的创业者，是那些始终关注“自己要卖的东西是否正是别人想买的东西”的人，而不仅仅是想做一些“了不起”的人。

而对于某些人来说，“追随你的梦想”这句话会显得空洞，因为你并没有一个特别明确的激情。

就像我之前说的，这完全没问题。

我认为，如果你从“寻找那些能用你在这里学到的技能为他人创造价值的机会”开始，那你一样会取得成功，甚至比别人更好。

从那里开始，我保证，激情会随之而来。

我记得多年前，一位朋友给我说过一句最好的建议之一：“行动先于动机。”

这句话在很多日常的小事上都很实用。

激情当然也很重要。

我已经提到过最重要的一点：成功取决于你为他人带来的价值。

如果一项追求只是你喜欢，但不能帮助或娱乐到任何人，那它几乎没有成功的机会。

但还有一个关键因素：我在时间点上的运气也非常好。

如果我早生十年，那时候的互联网还处在婴儿期，几乎没有足够的基础设施来支持这样一份工作，我可能无法接触到这么多观众。

如果我晚生十年，这个领域可能已经非常饱和。

所以我想给出的另一个建议，也是一种让你“追随梦想”更有可能成功的方式是：问问自己，现在能做哪些事，是十年前无法做到的？而这些事情在未来十年可能会变得更难？

在一个尚未被拥挤填满的领域里机会更多；

如果你能参与一个正在兴起的浪潮中，你的成长机会也会更多。

但这通常也意味着你要面对那些“不走前人路”的不适感。

接下来，我想说说：你该关注谁的梦想？因为，这不仅仅是你自己的梦想。

我去年访问 Harvey Mudd 时，有幸与数学系的瑰宝Talithia Williams 聊天。我问她：“嘿，你当初为什么决定学数学？”

她的回答很明确。她说，她以前从没认真想过这个问题，直到某天高中微积分课上，老师 Mr. Dorman把她叫到一边说：“Talithia，你真的很擅长这个。你应该考虑主修数学。”

显然，她以前从未这样想过，但就是这句话推倒了第一张多米诺骨牌，最终引导她走向一条非常成功的数学之路。

多年来，我问过很多数学家同样的问题，而你会惊讶地发现，有多少人给出了几乎一模一样的回答：“是某位老师说了那么一句简单的话，开启了后面长达几十年的鼓励与成长。”

千万不要低估你对他人的影响力，尤其是那些比你年幼的人。

随着你年岁渐长，周围比你年轻的人所占的比例会不可避免地不断上升。随着这种变化发生，你对后辈梦想的影响，可能比你对自己梦想的追逐更加深远。

最后一点，我想说，“追随梦想”这个说法最大的风险，是它暗示着梦想是一个固定的终点。但在接下来的 10 年、20 年、30 年里，世界将发生巨大变化，而这些变化往往难以预测。

其实，我根本不用强调这个观点：你们是经历了疫情、在高中和大学过渡期中成长的一届人。

但不仅仅是外部世界会变，你们自己也会变。

今晚在庆祝毕业的同时（也别忘了今天是母亲节），请花点时间问问比你年长的人：

“他们是怎么变化的？”

“他们的性格和价值观，和学生时代相比，有了什么变化？”

如果你们在走入人生下一章时，始终关注如何为他人创造价值，你更有可能成为引领者。

如果你们知道“行动先于动机”，你更有可能成为引领者。

如果你们常常问自己“现在可以做什么是十年前做不到的”，你更有可能成为引领者。

如果你们意识到自己可以多么深远地影响下一代人的生活，你更有可能成为引领者。

如果你们能适应一个不断变化的世界，把“激情”当作燃料而非终点，把“梦想”当作“机遇”，你们更有可能成为引领者。

影响力并非平均分配给每一个人。

而我，宁愿是你们来掌舵，带领我们这艘疯狂的船驶向未来。

Thank you, President Nimpard, for that very warm introduction and for inviting me.And thank you to the Class of 2024 for including me in such a special day.

For those in the audience who don't know who I am, I focus on making videos about mathematics with an emphasis on visualizations.It's a weird job.I do love it though, and it's no exaggeration to describe it as a dream job.

A common cliché is for someone who was lucky enough to land in a dream job to stand confidently in front of a group of fledgling graduates and to compel them to follow their dreams.Frankly, on its own, I don't think this is very good advice.

To be clear, there is truth behind the cliché.It is true that those who make the biggest ripples are the ones who are fueled by passion.It is true that the life you live is much more enjoyable if you can find something doing what you love.And it's also true that you shouldn't feel shackled by societal constraints.

But for one thing, not everyone has a pre-baked dream sitting there waiting to be followed.That's completely okay.And even if you are one of the lucky ones who has a passion that you want to roll into a career, I think there are a few pragmatic concerns that don't always fit very neatly into an inspirational speech that are required to make this actually work.

Now I know I'm talking to a very nerdy audience, so I'm tempted to describe my aims here a little bit more mathematically precisely.In the vector space of all possible advice, if you consider the "follow your dreams" vector, I want to explore its orthogonal subspace.

Maybe, though, it's better if I just start with a story.

Before I entered college, I was one of those who knew what I wanted to major in.I loved math.I loved it in high school, and I loved it in college.But I also loved the violin.And let's take a moment to imagine two distinct music students.I'm going to name them Paganini and Taylor.Both of them are talented, very talented, but Paganini pushes for technical excellence.He tries to perfect virtuosically challenging pieces.Taylor strives to write music that speaks to people, that resonates with them emotionally.Now in a music school, Paganini is going to get the better grades every time.He's always going to get the better position.But pursuing music careers, Taylor's at the clear advantage.

My first piece of advice, something I would have told myself if I could go back in time and be in the seat where you are now, is that if you have a passion that you want to incorporate into a career, take a step back and recognize the fact that the cliché to follow your dreams overlooks how critical it is that the dreams you have are about something more than just yourself.

Those who excel in their first jobs are the ones who make life easier for everyone around them, even when it involves doing things they don't love.Those who excel in PhD programs are the ones who recognize how their work fits into a broader research community, not just the ones who view it as the next chapter in school.The successful entrepreneurs are the ones who have a relentless focus on making sure that what they have to sell is what people want to buy, not just those who are looking to make something impressive.

Now, for some people, when you hear the words "follow your dreams," it falls flat because you don't have a defining passion.Like I said earlier, that's completely OK.I think you'll do just as well if you start by seeking out opportunities where the skills that you've developed here intersect with adding value to others, and from there, I promise the passion will follow.

One of the best pieces of advice I remember receiving from a friend many years ago is that action precedes motivation.This is often useful on a much smaller scale.

Passion plays into it.I already brought up the biggest one: success is a function of the value you bring to others, so a pursuit equally fueled by love, but which did nothing to help or to entertain people, just wouldn't have had a chance to work.But another factor I want to focus on is how I was very lucky with the timing.If I had been born ten years earlier, I don't think I could have reached the same number of people posting lessons on a much more infant version of the internet, where there was less infrastructure that could have existed to help form a career doing so.If I had started ten years later, the space would have been a lot more saturated.So another piece of advice that I'd like to offer, another little ingredient that makes following your dreams a little more likely to work out, is to ask yourself what's possible now that wasn't possible ten years ago and which might get harder ten years from now?

There are more opportunities in a less crowded landscape; there are more chances to grow if you're part of a rising tide, but this requires pushing past the inevitable discomfort that comes from following a path that has little to no precedent.

Now, next, I want to take a moment to talk about whose dreams you should be thinking about because it's not just your own.When I was visiting Harvey Mudd last year, I had the pleasure of talking to one of the gems in your math department, Talithia Williams, and I asked her, "Hey, what made you pursue math in the first place?"She had a very clear story.She told me she hadn't thought about it very much until one distinct day in her high school calculus class, her teacher Mr. Dorman pulled her aside and said, "Talithia, you're really good at this.You should consider majoring in math."Evidently, she had never thought about it before, but that one comment was enough to knock over the first in a series of dominoes that led to a very flourishing career in the topic.Over the years, I've asked a lot of mathematicians the same question, and you would be shocked how often I hear a very similar answer: there was this one particular teacher, and one seemingly simple thing that they did that was the beginning in a long series of encouragements.

Never underestimate just how much influence you can have on others, especially the ones who are younger than you are.Growing older is a process of slowly seeing the proportion of people around you who are younger than you are rise inexorably closer to 100%.As this happens, you stand to have as much influence by shaping the dreams of those behind you as you do by following those of your own.

And as a very last point, the biggest risk in the "follow your dreams" cliché is the implication that there's one static target point at all.In the next 10, 20, 30 years, the world around you is going to change a lot, and those changes are going to be unpredictable.I hardly need to emphasize this point: you are the class who spent your formative transition from high school to college under a pandemic.But it's not just the world around you.Tonight when you're celebrating your graduation and hopefully remembering to celebrate Mother's Day as well, take a few moments to ask the people who are older than you how they've changed, how their personalities, how their value systems have changed since they were a student.

If you step into the next chapter of life with an implacable focus on adding value to others, you're more likely to be the ones at the helm.If you recognize that action precedes motivation, you're more likely to be at the helm.And if you ask what's possible now that wasn't 10 years ago, you're more likely to be at the helm.If you appreciate just how much power you have to shape the lives of the generation that follows you, you're more likely to be at the helm.And if you remain adaptable to a changing world, treating passion not as a destination but as a fuel, following not dreams but opportunities, you're more likely to be at the helm.

Influence is not distributed uniformly in the population and I for one would feel a lot more comfortable if it was you who were at the helm guiding this crazy ship that we're all riding.

来源：米高视角