"If you want to go into mathematics, doing the mathematics itself has to be the thing that’s the reward"
True. In other words mathematics is the biggest 'Nerd Sniping' source ever existed on Earth. Math was my hobby when I was younger, and every minute of learning and thinking about theoretical math had a huge opportunity cost of not learning something more useful. Fortunately math is no longer a hobby of mine, so my knowledge is becoming more rounded/practical nowadays. I have became an expert of detecting any nerd-sniping, which at a younger age I was prone to. Surely I still teach math to my children when they need help, but otherwise I use math only when needed, not l'art pour l'art.
Coincidentally I comment much less on public forums too. (Another non-useful activity.)
Your post is written with a positive atmosphere, but I can't help feeling like you've lost something you once found rewarding. And... while it's tempting to think about your own life in terms of opportunity cost, I would caution that it risks giving rise to constant discontent if you focus too much on that. Bertrand Russell has a good quote in "In Praise of Ideleness":
> There was formerly a capacity for light-heartedness and play which has been to some extent inhibited by the cult of efficiency. The modern man thinks that everything ought to be done for the sake of something else, and never for its own sake.
I try to find joy in creating stuff that some other people find useful or enjoy. Creating something just so that I enjoy the process but society do not value at all is something I have a very bad feeling about nowadays. Like I am wasting my time/life. As an engineer it is more rewarding for me to create a videogame that people enjoy than creating a nice optimal algorithm or solving a hard math problem.
I understand that feeling, but recognize you yourself wouldn't play your own game (because it wastes time) but get satisfaction from others wasting their time with your creation?
Maybe you just want to be more efficient about increasing the fun experiences beyond yourself. But don't discount fun for fun's sake either!
What ends up being useful is hard to predict, so it's better just to do what you enjoy. Lots of useful math started out as just an idle curiosity, though mostly it ends up being useless. Probably most engineering projects are the same though (most end up in the dustbin sooner or later).
Solving hard math problems is a prerequisite for those video games.
While we are in a good spot right now. I'm convinced that we need a lot more progress to really make the synthesized simulations / games that I see in my imagination.
Hardware, algorithms, and architecture all have huge room for improvement.
I don’t fundamentally disagree with your attitude, but then, number theory ended up being pretty useful after about a couple of thousand years of art for art’s sake.
> Creating something just so that I enjoy the process but society do not value at all is something I have a very bad feeling about nowadays. Like I am wasting my time/life.
This is very understandable, especially in a professional setting. But - assuming one has not reached a state of total zen - one cannot live a life in complete selflessness. I am guessing there are things that you do for the sheer enjoyment: watch movies, read books, go for walks? Can the reading and practising of pure mathematics not fall under such a use of time?
You are right: it could still work as something I enjoy. It is just that I am in a state of my life where I do not want to put too much time into such an activity: I have a greater desire to create things that people want. But I still watch interesting movies and occasionally it could be joyful to solve a math problem. But as I do not watch movies dozens of hours weekly, I also do not want to solve math problems dozens of hours weekly. This has probably to do where I am in life currently. This may change later in life (I am middle aged.)
Funny contrast to me. I finished getting my kids up into college using my "useful enough to others to be paid for it" software skills and immediately went back to grad school for math precisely because it is such a joyous activity. Why would one eliminate a consistent source of transcendent pleasure from your life in this hard hard universe full of suffering and death?
And I have to say my training in low dimensional topology and mathematical techniques as a youngster was extremely useful for developing software and software systems.
Practical knowledge has a tendency to overfit and overfit in a society where change of technologies and techniques is as high as it's ever been.
Reminds me of one of my Maths professors in college, Ben Freedman. He was a writer and an engineer until his son Michael started asking math questions that dad couldn't answer. So he went back for his PhD in his 40s. Michael ultimately won a Fields Medal.
That enlightened activity is funded in part because it frequently yields massive military benefits/massive benefits to other exploitive technologies. There's currently no way to control that as a Mathematician, unless you're publishing in an anti establishment mathematical activism cell, in which case you public mathematical career is halted.
Very few mathematians want to become political enemies of the state, but that's what they're forced to do if they want to rise to this principle. I guarantee that takes away some of the enlightened wonder, and adds back a lot of genuine terror and boring bullshit.
These activities are "non-useful" in the sense that they generally don't bring direct financial rewards to the individual people who spend time on them (beyond modest salaries for teaching/research for those who work full time on it). However, from a societal perspective, such activities in aggregate often compound and have very high leverage and therefore disproportionately large benefit, especially compared to purely consumptive hobbies. The rewards are not carefully accounted and are reaped by miscellaneous strangers, sometimes far in the future.
As the OC mentioned in a sibling comment, it's actually the societal aspect that leads people to abandon pursuing things like mathematics.
When I was in grad school, I was surrounded by people who had these interests. I could work on a cool math problem, and people would be interested. I could have a conversation with them about it.
Fast forward to the "work" world, and there's not a single person I know in my city with whom I can have these discussions. And trust me, I looked.
As the OC said, it becomes an incredibly lonely life. If I want to study a typical grad level math course after work hours, it can easily consume all my free time (trying to solve a given problem could take hours).[1] After a few years of trying, I had to abandon it for the sake of my mental health.
In retrospect, there probably is a middle ground, and if I return to it, I'll aim for that middle ground. Intentionally choose topics I can do in bite sized amounts, and topics that I can share online that have a higher chance of engagement.
[1] And this was when I was single without kids. Imagine how much less time you have with kids.
It is not just about the financials. It can be a very lonely activity to create something that other people do not care about, or just very very few people care about. (As it is described in the article.) Besides financial reward, social reward is important too.
I think this is basically true but I don’t know if it is good advice for most people. In the sense that the math that most people are exposed to up until the first couple years of college is the practical stuff. (Maybe I’m showing my age here, are there, like, Math Influencers now that are sending the bright kids into the really abstract stuff?)
In most cases a kid that aces all their math classes will make a great engineer or physicist, which is a good outcome for everybody involved.
And, besides, all the math I use was invented by the 1950’s. At the time, I’m sure they thought some of it was useless. Somebody has to cook up the stuff for the engineers of 2100.
What’s the problem with nerd sniping? It’s fun, and something useful may come out of it. I’d like to say that I’m at a stage in my life where I don’t need to “forcefully progress” anymore, but truthfully that was never actually the case. I came to be where I am because I was following a passion, so it was all nerd sniping with useful side effects, I guess.
The problem with nerd sniping is that it is instant gratification in a way. Always focusing on tech and math problems because you like solving them can lead to neglecting other areas. But maybe learning more about those other areas could lead to better success in life. At least this is my experience. It solved itself in my case. My interest just shifted to be more end-product focused gradually.
Though I feel that I can usually tell whether some product's internals and engineering, and not just what it's meant to represent from the outside, have been a "labor of love" as well, or whether it's been cobbled together to just fit some particular outcome. The former is usually more robust, thought through, stable, and generally better to work with.
I don't know how much that applies to games. I guess it depends on the genre. I can imagine that for some games, playtesting and bugfixing gets you to a good state. But for some roguelikes for example, especially ones where there is a large amount of things to combine (so where playtesting just cannot test every combination), I can imagine that "artful engineering" are beneficial for the games' stability and polish. Those are games that are meant to be played over, and over, and over again, in different ways.
Joy with creating something other people enjoy or find useful. For example creating a videogame. But formerly I enjoyed creating the underlying technology (engine programming, which is a nerd sniping too), nowadays I am more interested in the game as a whole (more game-design focus and less game-tech focus.)
In my experience, you can do both. I recently made a tool where I had great fun making the internals as “elegant” as possible. What other people perceive though is only the usefulness of the tool.
I would have had significantly less fun with a more pragmatic approach, and maybe the tool would not be as polished as a result.
But someone had to create the underlying technology for you to be able to focus on more high-level tasks. Seems it's easier for you to share these new tasks than your old tasks, but not that one is intrinsically more valuable than the other.
I have somewhat similar feelings on my side. I really enjoy mathematics, but at university, I realized how vast the field is and how it can be fairly easy to dedicate your life to learning something that no one around you cares about. As such, if I ever get back into these disciplines again, I'll probably focus primarily on the math necessary to solve physics problems. Not because I think that's inherently more useful or valuable, but merely as a heuristic to limit the scope, so I don't go insane with the vastness of mathematics.
Can I ask if other people care about the game you’re making? As someone with a fair amount of indie experience it seems easier to create a proof people care about than a (even reasonably) popular video game.
It is too early to tell for my current project. I know that it is very hard to create a successful game. Certain genres are more crowded than others though. Creating a successful 2D platformer is almost impossible nowadays for example. I am creating a grand strategy game. It is a niche where the supply and demand dynamics is reasonable, but it is still hard to create something successful.
How theoretical is the math in a game engine? (I’m asking because I have no idea but I assumed it’d all be really applied linear algebra stuff, that sort of thing).
Not very theoretical. But with 'nerd sniping' focus I tended to create my own tech unnecessarily, and wasting too much effort to optimize things that do not necessarily need to be that much optimized. Nowadays I try to reuse other people's code as what I really enjoy is to create the end-product.
If you use an existing game engine all you need really is some decent Google-fu...
I've been commissioned to create some non-public VR experiences for a couple of people and all I needed during development was some basic high-school vector math (like literally addition, multiplication, very occasionally a cross prodcut or a dot product which I googled by their purpose [e.g. "how to find a tangent to two vectors" or "how to check if a vector is aligned with other vector"]).
You do use that math constantly especially in shader tricks which do some visual magic based on angles between stuff but the difficulty is not in the math itself at all.
If you're not applying math to whatever endeavor is more valuable than math, how do you expect to build and wield power in that endeavor?
On the backs of more technical people, I suppose?
I reject that approach.
About half of the successful business moves I do depends on developing better mathematical tooling than my competition.
Consider adopting category theory as your lingua franca for modeling real world processes. It's universal and it's everywhere, from software engineering to business strategy and communications.
There's no such thing as nerd sniping when every piece of math you do can be transported to every other endeavor you do. That's the job of Categories, and if you don't use them, then your mathematical education cannot really empower you.
I think this idea is true of all human endeavors. You have to enjoy the process as the appreciation of an individual achievement will fade very quickly and you're just left with doing the process again.
So in a way, nerd sniping is great, it hooks you into a process you enjoy.
IMO the magazine article was a much more accessible read, and a different story about the author himself and the essay.
Replacing the story feels disrespectful to both the journalist, for his work that certainly only amplified the reach of the essay, as well as the author for denying him the spotlight.
I agree, the essay was a perfectly fine personal reflection, but the quanta article was way better - the reporter was a skilled interviewer, and helped bring out far more of the essence of what the author was trying to say in his essay, and relate it to the overall state of mathematics today.
Pretty sure that's what he means. It's one of the more competitive academic positions.
Anecdote, but: I knew several math and physics PhD students. About half of the physics ones eventually obtained tenure track faculty positions in the US. Not a single math one did.
This gels with my experience (purdue physics/math grad 2011). It also reflected in the composition of staff for the departments. I think to field a robust math department you don't need the staff levels that you do to field a dual theoretical/experimental program in something like physics or chemistry.
e.g. at MIT the ratio of grad students in physics/math is 2.4 even though the undergraduate programs in Math (especially if you include Math+CompSci) are much greater
For the other departments, generally the university does not provide that funding anyway. The faculty members are expected to fund it themselves via grants. Although often for new faculty members, the university may promise one or two years of funding for labs. But again, since they get a cut of every grant that's coming in, they can afford to do so.
Again, epistemology and the recommended book "NEW DIRECTIONS IN THE PHILOSOPHY OF MATHEMATICS"[1].
It is always interesting how the people who were in the epistwemology of math could easily predict this. I personally participated in Gregory Chaitin [2] conferences.
I haven't read the article yet but the moment I saw the writer is "Jordana Cepelewicz" I knew it is going to be great! I have read few of her past articles and they were excellent think pieces.
And yet being able to practice that failure while in the classroom is all but outright disincentivized. I completely agree with the interview... but educational currents do not have the space for the type of failure that helps one become a good mathematician. In fact, failing can remove a lot of prospects.
the biggest disappointment is the absolute contempt with which the society treats high end knowledge work. Math, theoretical physics, theoretical computer science, these are the highest form of art and sophistication created with human brain, but people who love these subjects have to forgive financial independence, endure poverty, have less than 1% job prospect in academia, social snubbing & ridicule, for what, inner joy? Screw that.
These days, my main advice is the same as what Scott Galloway gives to avoid long term disappointment. Follow the bucks, once you have enough of it, you can then think of satisfying your inner curiosity.
> Some students talk about turning to a different career later on, after they’ve made enough money. “Nowadays, English concentrators often say they’re going into finance or management consulting for a couple of years before writing their novel,” said James Wood, a Harvard professor of the practice of literary criticism.
> Mr. Desai said all of this logic goes, “‘Make the bag so you can do good in the world, make the bag so you can go into retirement, make the bag so you can then go do what you really want to do.’”
> But this “really underestimates how important work is to people’s lives,” he said. “What it gets wrong is, you spend 15 years at the hedge fund, you’re going to be a different person. You don’t just go work and make a lot of money, you go work and you become a different person.”
Danny Calegari seems like that rare combination of humility, insight, and empathy. Some really good quotes in this interview:
> If you want to go into mathematics, doing the mathematics itself has to be the thing that’s the reward, because no one cares, and what’s considered important doesn’t always make sense. ... I think 100% of mathematicians think that no one cares, that no one even knows anything about their best work.
> G.H. Hardy was once asked what distinguished Ramanujan as a mathematician. One of the things he said was that Ramanujan had a remarkable capacity for coming up with hypotheses very quickly, but that he was also very quick to revise his hypotheses. He was nimble: If something didn’t work, he was able to pivot and revise his way of thinking.
> the same kind of psychological pressures that make it difficult for people to deal with failure are at work in making it hard for people to carefully and critically evaluate arguments that they have a huge personal investment in being correct.
> One of the great, tremendously useful and valuable functions of good writing is that it gives you a way of seeing what it’s like to be other people. You can see inside people’s heads. This is one of the great gifts of literature: You get to see that everyone else is weird, too, not just you.
