The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

The 1’s add no information. And so it’s more convenient to exclude 1 from the list of prime numbers. That’s what allows us to say that each number has a unique prime factorization.

It seemed as though he’d lived the entirety of his childhood and adolescence on autopilot, so busy living out the life expected of him that he never questioned whether he actually wanted it. ​ In his own mind, he was worth caring about only because of his achievements. ​ The burnt-out case of today belongs to a culture without an off switch. ​ She would fantasise in our sessions about going home and sleeping, waking only for stretches of blissfully catatonic inactivity over uninterrupted, featureless weeks. ​ This belief, she had come to realise, had taken a suffocating hold on her life: “the longer I live in wait for this magical event, the more I’m not living this life,

So by the time you hear the news that I’ve died, the full story—the book of my life—will be ready to read.

and pay more attention to consolidation, exposition and preservation of the knowledge we already have. more room for quiet study and reflection.

The city streaked past, the bridge cables flickering like a delay, or a glitch.

It’s become a place where we count the good things and experience the bad things.

It was as if the news of his cancer’s progression opened something inside of him so that he could clearly see into another world, another place he was on his way to. Whatever it was he saw endowed him with an overwhelming generosity of spirit and the most intense humanity I had ever witnessed. I don’t mean he wandered around performing good deeds; it was something more internal. He was overtaken by something like joy. Not a giggling and hysterical one, but a calming joy that infected every room he entered. ​ When you know somebody with less than six months to live and that person agrees to spend any moment of it with you at all, the immensity of that generosity does change you, undeniably. ​ —or, as my coworker, Jeff, used to say before he left the job and moved to California to be a social worker: Khalil is crackers, an arrival straight from the cracker factory. Why would the world endow this young boy with such wackiness, with the young Johnny Cash’s lopsided gait and pool-ball eyes, with the right amount of kindness to soothe the youngest children in the room and the right amount of self-assurance not to be intimidated by the presence of the older children, if he were not meant to live? I know that Khalil will be famous one day—a rock star, a basketball hero, a politician who will become the first Arab American President of the United States because he is so beautiful, and he knows suffering, and he will be cured, and I know for sure: he will live long enough to enter a presidential election, he will live long past thirty-five. ​ Some kids arrive in class sailing down the hallway on their IV poles ​ He never laughs anymore, and I thought I’d never hear him laughing again,” she said, and she was crying. ​ We enjoy ourselves in Writers’. ​ I helped him write—a loose hug that lasted at least the length of a single poem, but often, towards the end of his life, a hug that lasted the entire class.

But really I work not because it's super-happy-fun-time each and every time I turn on my computer, but because if I do a bit of work first, then I have the freedom to not work later.

And so here we are: leaning on an open, beautifully staid, inert protocol. SMTP as our savior. ​ Mr. Chimero almost never writes but when he does makes the day a good day. ​ These newsletters are the most backed up pieces of writing in history, copies in millions of inboxes, on millions of hard drives and servers, far more than any blog post.

but they are different from social privacy. Social privacy is the expectation that we shouldn’t want to pry into each others’ lives. ​ Defining social privacy in an online context is difficult because it’s not clear what our “public face” really is. Unlike our physical environment, our online world contains layers of our past, present, and future selves, all occupying the same timespace. We are all time travelers, navigating multiple realities at any given moment.

And close reading is intimately tied to the kind of “close thinking” that math requires, especially the more advanced, theoretical kind of math. You need to be able to pass back and forth flexibly between the micro and the macro. You need to see both the big picture and the minutiae, both the forest and the trees.

I’d put something on my weekly to-do list, and it’d roll over, one week to the next, haunting me for months. ​ In a marked shift from the generations before, millennials needed to optimize ourselves to be the very best workers possible. ​ I took piano lessons for fun, not for my future. ​ We didn’t think our first job was important; it was just a job and would eventually, meanderingly lead to The Job. But these students were convinced that their first job out of college would not only determine their career trajectory, but also their intrinsic value for the rest of their lives. ​ Things that should’ve felt good (leisure, not working) felt bad because I felt guilty for not working; things that should’ve felt “bad” (working all the time) felt good because I was doing what I thought I should and needed to be doing in order to succeed. ​ And when we don’t feel the satisfaction that we’ve been told we should receive from a good job that’s “fulfilling,” balanced with a personal life that’s equally so, the best way to convince yourself you’re feeling it is to illustrate it for others. ​ Josh Cohen, a psychoanalyst specializing in burnout, writes. “You feel burnout when you’ve exhausted all your internal resources, yet cannot free yourself of the nervous compulsion to go on regardless.” ​ One of the ways to think through the mechanics of millennial burnout is by looking closely at the various objects and industries our generation has supposedly “killed.” ​ At least in its contemporary, commodified iteration, self-care isn’t a solution; it’s exhausting. ​ That’s one of the most ineffable and frustrating expressions of burnout: It takes things that should be enjoyable and flattens them into a list of tasks, intermingled with other obligations that should either be easily or dutifully completed. The end result is that everything, from wedding celebrations to registering to vote, becomes tinged with resentment and anxiety and avoidance. Maybe my inability to get the knives sharpened is less about being lazy and more about being too good, for too long, at being a millennial. ​ or take refuge in avoidance as a way to get off the treadmill of our to-do list. ​ It’s not a problem I can solve, but it’s a reality I can acknowledge, a paradigm through which I can understand my actions.

It is as though we’re only starting to learn what the supposed pleasures of this new level of monitoring are supposed to be. But our conditioning in consumerism is such that many are willing to take it on faith that the pleasures will emerge ​ The ubiquity of a product begins to convey a pleasure in its own right — just as the sheer demonstrable popularity of a song can make it seem “good,” can make participation in it feel inevitable and joyful, a consubstantiation of the zeitgeist.

and throughout the process instilling ownership, confidence, and competence among the students. ​ Under my approach, a student taking an exam is handed a sheaf of all the reading-summaries she’s written, class by class. It’s an open-book exam where each student has written her own book, if she���s availed herself of the opportunity. If the student knows this ahead of time, there’s a big incentive for writing that book, which requires that she keep up with the reading during the weeks preceding the exam. ​ One thing my students tell me is that they often end up not consulting the summaries at all during an exam, but that they’re still glad they wrote them. My students will spend much of their time after graduation solving problems for which no solution-sheet exists and trying to convince others that their solutions will work. To do that well, they need to acquire communication skills, which I can help them cultivate now by having them present solutions to their peers and get feedback on those presentations.

relaxing a notion of “sameness” gives us extra currency with which to explore new phenomena

Stay loose. Let go. There are other bananas.

“Physical fitness and brain performance are tied together, and it shouldn't be a surprise that grandmasters are out there trying to look like soccer players,” Ashley says.

Haskell is a purely functional programming language: by default, Haskell functions do not cause side effects such as system I/O, nondeterminism, or exception handling. As such, Haskell programs are generally expressed in terms of monad transformers, which provide the facility to compose different side effects into a single interface powerful enough to express the programmer's needs. The monad transformer library, mtl, is mature and powerful, but complicates and in some cases constrains the construction and generalization of user-specified monads. A class of libraries known as 'effect systems' have emerged in an attempt to solve the problems associated with monad transformers. Effect systems provide a compositional approach to program construction, generally using a single monadic type specialzed with a programmer-provided list of capabilities. Effect systems are more powerful and flexible than monad transformers, but their adoption in industry has been minimal, due both to their incompatiblity with mtl and their historically poor performance. The new fused-effects library changes the status quo: it provides an extensible and flexible vocabulary for program construction, yielding a more expressive interface than mtl without sacrificing any performance characteristics. I'll describe the history of effect systems, outline the tradeoffs associated with programming with effects, and demonstrate the use of fused-effects in practice. Patrick Thomson GitHub, Inc. @importantshock Patrick is a senior engineer on GitHub's Semantic Code team, building systems to understand and analyze the corpus of code on GitHub. He enjoys peaceful countryside walks and loud rap shows.

With Instagram, self-defining and self-worth-measuring spilled over into the rest of the day, eventually becoming my default mode. I would keep scrolling as though the cure for how I felt was at the bottom of my feed. The landscapes I once Photoshopped my way into were materializing around me. There were a million versions of all of us running around in one another’s heads.

The Swift Programming Language. Contribute to apple/swift development by creating an account on GitHub.

1) the full moon can be glorious, but it's really the moon phasing in and out that is the most interesting to me 2) morning moons sometimes beat evening moons, especially when they hang big and low by the horizon and startle you when you turn a corner or come out from under the shade

You will have the opportunity for unparalleled focus on whatever your research question is. ​ Those who have recently obtained a PhD can outwork virtually any of their peers in terms of duration and efficiency ​ To undertake this vow of poverty voluntarily, while doing work that is more intellectually challenging than most of your peers that are earning average salaries shows superhuman commitment to seeing something through to completion ​ This criticism will either get to you, and you’ll bail out of the program, or you’ll learn to separate the valid criticism from the invalid criticism, a skill that will serve you well in any profession, in any discipline ​ If you work on your degree alone, you’re doing it wrong. Have a side job. ​ Stick to your schedule. Be humble. Don’t expect to get more than 3 hours of high-order intellectual work done per day

How you act — as a manager, as a co-worker, as a partner, as a parent — has ripple effects that extend far past the immediate relationship. ​ Are you willing to have slightly less so that others can have significantly more? Or, as I like to think about it, do you actually care about other people? ​ But we’re removed from the conditions that produce it, the living conditions that result from it, and the realities of the waste it produces. All we see is a deal.