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Nearby, at 1221 Sixth, property of The Rockefeller Group, which owns and manages some six million square feet of office space in Midtown Manhattan, a sunken plaza — also a POPS — has at times been blocked off on weekends. Due to complaints and advocacy by Phillips and his followers, the Department of Buildings has served Rockefeller with a violation on this issue, but they remain determined to skirt the law when they can. A sign barring the public from the lower plaza that is used on weekends sits nearby. And just two days earlier, security on the same property attempted to remove Phillips for filming on the property, though he was not breaking any of the posted rules about the plaza’s use.

In fact, as we walk from one plaza to another, I remark that Phillips seems scrupulous about following the rules of these plazas. “That’s my whole leverage,” he grins.” That’s my whole thing, is [that] I’m going to document that I’m being completely a normal guy.” The message of all his videos and advocacy is one of following the rules, and in the comments, he often pushes back when his followers urge some kind of civil disobedience. The ethos of his Instagram account and all his interactions with building personnel seems to be that the public should be respectful of these public spaces by observing the rules, and that the owners should do the same. “The issue is when they start to put their own rules into effect” and refuse to abide by their own agreements with the public, he says.

Since Phillips began making these videos, security follows him around when he is in these spaces. The evening of my visit, as we sit in the sunken plaza, a security guard watches us carefully and keeps talking into his phone. Just two days earlier, at the same spot, Phillips was removed by security.

Walking north, Phillips shows me another POPS, this one at 31 West Fifty-Second Street where, until he made videos about it, the handicapped access ramp was blocked off. It’s open, for now. Another offending restaurant on the same property has reduced its outdoor table intrusion to just one, which Phillips thinks is acceptable even if it might technically be out of line. “It’s a give-and-take,” he says, “because obviously nothing is ever perfect,” pointing out that it might be hard for an owner to completely forbid a tenant to use outside space that they’d assumed was part of the deal when they rented the space.

Phillips is not someone who has a hard time seeing the viewpoint of others, especially those in the same industry as him. “As a security guy, I work with a lot of these types of guys,” he says. “They kind of get the ego thing when they work in a building like this.” But they are not actually enforcing the law. Rather, they are enforcing the desires of a corporation uninterested in holding up their end of the bargain to the public.

Phillips says building owners are getting more fines and being issued more violations in response to his complaints. Phillips’s advocacy has engaged city officials, including the Buildings Commissioner Ahmed Tigani, who was appointed by Mayor Zohran Mamdani in January and has met with Phillips and toured the offending sites. Phillips calls Tigani “a great, great asset.” Phillips would like to see the city strengthen enforcement and streamline the process for responding to complaints; at present, it’s hampered by the fact that multiple agencies are involved (exactly the kind of problem Mamdani’s Commission on Government Efficiency [COGE] has been trying to fix). He’d also like to see city council legislation to increase the fines on repeat offenders.

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Phillips also holds dance parties, concerts, and most recently, a well-attended Halloween flash dance party and costume contest in the POPS, spreading the word about the violations but also reclaiming these public spaces for public joy. For the Halloween party, Phillips himself showed up in full king regalia, including a crown and scepter — the Lord of Bench, crowned as such.

While the response to his project is satisfying so far, Phillips would like to see the real estate industry comply more fully, and he thinks Mayor Mamdani’s attention on the issue would help significantly. “This is the one issue I cannot believe he has not said a word on since the moment it started,” Phillips says, noting with some annoyance that many content creators “with far less following, with far less reach” have been in conversation with the mayor. “I’m not one of the crazy guys out here!” says Phillips. “We need his voice on this.”

Phillips’s project — fighting for public control of space against real estate oligarchs who want to take it away — seems closely aligned with Mamdani’s own. Both have been fighting for the working class to quite literally have a place in the city: a bench, an apartment, a park, a soccer field, a night at the opera. Both insist that New York is for everybody.

Phillips, for his part, does not frame his crusade in ideological terms. “This is an issue that transcends everything,” he says. “Doesn’t matter if you’re left, right, green. Everybody’s gonna sit on a bench.”

This article originally appeared in Jacobin, a democratic socialist magazine publishing long-form essays and analysis on politics, economics, and culture. Subscribe to the print edition for $20 a year.

What if, rather than being terrifying or utopian, AI is just a waste of time?

Source

There are no generalized solutions to the three-body problem. Say you have three planets orbiting each other: it’s impossible to calculate how they will move using Newton’s laws of motion and gravity.

Unlike the two-body problem, the three-body problem has no general closed-form analytic solution. The differential equations that govern the motions of three gravitating bodies are not integrable and cannot be solved to give explicit formulas for the positions of the bodies as a function of time. For most initial conditions, the dynamical system for three orbiting bodies is chaotic, and the only way to predict their motions is to estimate them using numerical methods.

But thousands of stable three-body orbits have been found — their paths repeat after a given interval. The Three Body Orbits website is an atlas of some of those orbits: you can watch each three-body system play itself out in a wide variety of different shapes and complexities. There’s this simple figure 8, this slightly less simple one, and this one that looks like a spirograph.

The site even enables you to search for new stable solutions to the problem in your browser. This is what one of my unsuccessful tests looked like — two of the planets locked in a gravity death spiral while the other one peaces out in the other direction:

Tags: infoviz · physics · science

Hilbert's hotel is a thought experiment about a fully occupied hotel with infinitely many rooms. It shows why infinite collections do not behave like finite ones.

Between text, images, audio clips and videos, there are so many elements at your fingertips to tell a story in the digital era. A new expressive tool is now available to make it easy to assemble material online and share your creation widely.

Tapestries is a user interface developed by Bob Stein and Dan Visel (who works on the Wayback team) that allows people to make dynamic, multi-linear presentations with various digital objects. The curation tool lets users gather items from all over the web and put them together into a single space to tell a story. Rather than simply listing links at the end of a document, a tapestry can be designed by dragging photos, video clips or other items onto a digital canvas that viewers can click to open.

The finished product can be kept private or posted publicly – with the option of inviting others to collaborate, comment on the project, or make copies of the tapestry to edit and revise.

The Tapestries platform launched as part of the Internet Archive’s Oct. 21 celebration. Stein, Visel, as well as the project’s new director, Ben Vershbow, were on hand to demonstrate the tool during the Funston Avenue party.

“We’ve made Tapestries open source and have a good foundation for people to start building on it,” said Stein, a digital media pioneer who incubated the project with the Internet Archive. “I love that we’re entering [a time] when the author or producer or designer is not stuck with one medium. They can use any combination of media to tell a particular part of a story.”

A New Canvas for Digital Storytelling

Vershbow, who worked with Stein at the Institute for the Future of the Book, and most recently was with the Wikimedia Foundation, is director of the Tapestries project.

“Over time, I got to know the tool, use it and see the potential,” Vershbow said. “It’s about curating different types of media, arranging them however you’d like and fully embedding the media objects. It’s a novel, free way to assemble and make sense of material in the digital world.”

After a limited early release of the tool in 2025, some educators began to experiment with Tapestries in the classroom.

Dene Grigar, professor and director of creative media and digital culture in the Department of Digital Technology & Culture at Washington State University Vancouver, introduced students to Tapestries to learn about digital storytelling. Along with her own majors who specialize in multimedia content design and development, it allowed her to teach non-majors unfamiliar with digital tools and programming how to create born-digital content.

“The students loved it. It’s an easy drag-and-drop system,” Grigar said. “It’s great for my non-majors and my majors because it’s a way for them to get more experimental, do more interesting things, take some risks. I used it last spring in my Internet Revolutions class, and it was so successful that I’m teaching it again this semester in my Digital Storytelling class as a way to produce digital narratives.”

The application allows students to draw images, add commentary and captions – sometimes diving in after just an hour of introduction. Grigar said she likes that Tapestries is open source, rather than a proprietary product with the risk of becoming outdated.

Stein suggested Grigar have her class use papers and videos of computer pioneer Alan Kay to examine his work through an intergenerational lens and use Tapestries to tell his story. That project in the spring will include student interviews with Kay, now 86, that will culminate with an exhibition of Kay’s work in Tapestries.

“Students are learning the cycle of the importance of holding on to things that are dear to them, expressing themselves about why it’s dear, and then making it available for other people to see what it’s like. That’s the value of what we’re doing here,” Grigar said. “We want people not to be just consumers of media, we want them to be producers of their own knowledge.”

Vershbow said Tapestries opens up a new dimension for teachers in protected digital space and offers a low barrier to entry. Because it doesn’t require specialized technical expertise to use, he said, the application levels the playing field yet challenges students to think creatively.

“At this moment in education where AI has flooded the zone, we’re seeing this crisis of students not developing critical research skills,” Vershbow said. “Doing assignments in Tapestries is a compelling alternative to traditional research papers, which are really vulnerable to AI shortcutting. This tool changes the equation. Students draw from a larger range of media material and they have to show their work. The process becomes the product, which we think opens up a lot in terms of learning outcomes.”

Reimagining How We Create and Connect Online

In addition to schools, the creators of Tapestries see potential use for the tool with historical archives to create digital scrapbooks, exhibits, and presentations.

“Tapestries are meant to be archivable,” Vershbow said. “It is deliberately low-tech and minimal. You can export a whole tapestry as a zip file – and it could be deposited in the Internet Archive as its own cultural media object.”

Acknowledging that digital memory on the web is fragile, Vershbow said, Tapestries can be viewed as a personal digital archiving tool complementary to large institutional preservation. “It allows individuals and small communities to make their own choices about what matters and what they want to pass on to the future,” he said.

After years of linear creations in print, film and TV, Stein said, it will take time to throw people into a world to see the potential of thinking in two or three dimensions. Yet, he believes users will design “breathtakingly new” projects in Tapestries.

Stein, co-founder of The Voyager Company and The Criterion Collection, sees potential for crowdsourcing creative works since authors can grant anyone permission to copy a tapestry and change it in ways that are useful. His “dream project” is to send 50 invitations to artists (filmmakers, composers, photographers) to put something on the center of a tapestry. Then they can extend the invitation to anybody else in the world. “We could look back in five or ten years and they will have evolved into an amazing tableau or mosaic of ideas,” Stein said.

Tapestries gives users a way to find agency online at a time when the web has become dominated by large platforms and algorithmic feeds, said Vershbow. Rather than having information summarized and knowledge processed, users are relating directly with sources for raw material.

“It’s a connection to an earlier era of imagining and working with digital information and invention,” he said. “It’s more on your own terms. You have the freedom to associate with these things and pull them all into one universe that you sculpt.”

The post Weaving ‘Tapestries’: Introducing A New Tool for Digital Storytelling and Archiving first appeared on Internet Archive Blogs.

[This is a guest post by Gireeja Ranade. This blog post was initially written in a different file format and converted using AI. — T.]

The day after the Navier-Stokes result was announced, a student came to my office hours. They said, “Can we please talk about the Navier-Stokes result and what it means? I really need some therapy.” Two days ago another student mentioned, “I used to be really motivated, but now that all the models can do everything with just a prompt, I don’t feel like putting in any effort at all.”

Every time I have such a conversation with students, I appreciate how lucky my generation has been. We didn’t have to grapple with the temptations or threats of AI when we were students. Not being able to quickly look up answers forced us to challenge ourselves, and do it together with our friends. And years of challenging ourselves somehow made us love it [1], and led us to challenging jobs across academia and industry. These jobs are simultaneously wonderful and hard. But I wonder and worry for my students, for the next generation. What do we need to do to make sure these jobs [2] are (1) available for the next generation and (2) that we have enough students who are motivated to train for them?

I’ve been in conversations where people are concerned about whether mathematics will survive. I’m actually not concerned about this — I’m fairly sure it will, so let us set that aside for the moment. But what I want to think about is, what do we need to do to make sure all mathematicians survive? And not just the `great’ mathematicians, but also regular, ordinary mathematicians? Because even if we decide society only really needs the `greats [3],’ we need to train many tens of thousands of students to identify who those greats are. If we want one Steph Curry, we need to make basketball exciting for a whole generation of people, and we need to support college basketball, and after-school basketball, and neighbourhood basketball.

We’ve seen that by treating mathematical problems as a benchmark, humans have been able to train AI models to be very good at solving hard math problems and writing proofs. Soon we will create benchmarks about `asking good questions’ and `giving clear explanations’ and then AI models will be good at those tasks too. They will do the thinking and the meta-thinking. This is the reality we need to plan for.

For this post I will talk about “mathematics,” but I often mean mathematics broadly construed (the sciences, engineering, social sciences, and even many humanities subjects that require complex reasoning and critical thinking).

Background

People are attracted to mathematics and mathematical sciences for a variety of reasons. But importantly, whatever the motivation, mathematics has always been a `safe’ subject to study. Historically, being good at math has led to a solid job and a stable lifestyle. Why? Because along the way, by studying beautiful mathematics (which in itself might not be exactly what leads to employment), the student learns critical thinking and perseverance, and becomes stronger. The transferable skills are helpful for employment.

As a result, society has encouraged students to do math, even when they might not be `great’ at math. For example, as a teenager, I was part of a special program called Gold 2002, [4] which trained students for the International Mathematical Olympiad (IMO). I was not among the `greats’ in this program. I did not make it to the IMO, unlike some of my friends. And today, I have no hope of ever winning a Fields medal. But I still enjoy doing mathematics, and (thanks to some hard work as a teenager) I’m good enough at it to be paid to do it (again broadly construed, I’m a professor in an EECS department [5]). But one of the reasons that my parents let me spend months and years working on crazy math problems was that math was a `good’ thing. And so it was ok to do this, even if I didn’t win any gold medals.

But today people wonder — does mathematics still have the same status? Do we need critical thinking if a prompt can do it for us? My students ask — is it worth their time to get a PhD, in mathematics, or any theoretical field, without an immediate application? Or should they focus on learning to train better deep learning models? When previously I would have many undergraduate researchers from my lab applying for PhD programs, many now prefer to go straight to industry. What do we say to them?

I have heard people say — in this new era, math will become more like the humanities. We will continue to pursue mathematics because it is beautiful and because we love it. While this may be the case, will as many students pursue it if it does not lead to a good job and a steady life [6]?

Which leads to the thought — well, does society really need all these mathematicians? We will have only our strongest, most passionate students do the very hard math, or those who love mathematics enough to do it even as `starving artists’. With AI, if one mathematician can do the job of five or ten, should we shrink our departments and our graduate programs? What jobs do we expect our students to get when they graduate? And if there are no jobs for `thinkers,’ and `intellectual explorers’, then why should students pursue a path towards a PhD in math or a theoretical science?

This brings us to a public goods problem, which I elaborate on further below. I believe it is essential for us, the human society, to maintain our intellectual culture. And for this we need lots of students getting degrees in mathematics, sciences, and the humanities, but we need to find ways to actually motivate the students to want these degrees and the associated training.

What is our culture and why is it important?

As a child, I would see a big splash in the newspaper about the Nobel prizes every year. I didn’t understand the science or why the literature was meaningful. I just understood that this stuff was important, and that humans valued creativity, expression and intellectual and scientific achievement. And until recently, I had never consciously wondered about the cultural importance of Alfred Nobel establishing those prizes. I had always taken for granted that we should strive for excellence… but I see now that this was an impact of our culture, and that there are so many conscious decisions that have led to this culture.

But now, people have begun to worry about `The end of the age of heroes‘. In his blog post, Noah Smith makes multiple interesting points, but I will paraphrase one: even as mathematicians will likely retain their jobs as math-understanders [7] (since mathematicians are relatively cheap), they will lose their status as heroes.

My question is: while it may be ok for the mathematician to lose their hero status, what impact does this have on the next generation? In my younger days, and even now, I know I benefitted from being around, and hearing about, heroes — the brilliant, blazingly quick, hardworking minds, with the humblest of personalities to match. It gave me someone to look up to and goals to aspire to. With heroes gone, how would we orient our cultural compass?

Aspects of our culture are built on respect for facts about the universe. Nvidia CEO Jensen Huang said in an interview with Ezra Klein a few weeks ago that it doesn’t matter if the multiplication table is starting to be forgotten, and that “we’re going to lose some finer intellectual dexterity … I don’t know how valuable it is for most people to learn how to do surface integrals or partial differential equations. I don’t really know how important that is, but it’s important to some people.”

I was bothered reading this, because I was worried about the implications for our culture.

Multiplication tables matter not just for their own sake but for what they represent [8]. Yes, knowing builds fine intellectual dexterity. But they also show young children that there are fundamental, unchanging facts about the world. Invariants. And starting from this, we can build up confidence that allows kids to grow into students who are grounded and questioning because they can both see and understand why there are invariants [9].

Our understanding of partial differential equations allowed us to develop numerical computer programs that can solve them for us. And when the computer does solve them, it is amazing that we (as a human society, not every individual) are able to understand exactly what the computer did. But this is not true when AI does all the work for us; we lose the essential human understanding. I will come back to the value of this soon.

It is important to maintain a culture where we value and respect intellectual dexterity and expertise. And admire the young children who know their multiplication tables, and the older people who win Fields medals and Nobel prizes. And respect those people who care deeply about partial differential equations, and create space for them to develop their expertise, even if not everyone understands them. The goal of expanding and developing human expertise in subjects can and should be independent of the state of AI [10]. So that we can ensure generations of students will continue to want to study and experience the “unreasonable effectiveness” of mathematics.

Education: Canary in the coal mine

Every professor and teacher I know has grappled with AI-based academic dishonesty by students. Students cheat when `doing it the right way’ doesn’t seem worth the time and effort. And because our culture for students (especially in the United States) has focused on achievements/badges (or, as I tell my students, `sticker collection’), instead of building true understanding and intellectual depth, students want to do more and do it faster, even if they are not doing it deeper or better.

We need to realize that this is just the canary in the coal mine. Students are turning in proofs/essays/code they don’t fully understand. But this behavior is not limited to academic settings. It is likely that engineers are checking in code they didn’t fully read. It is only a matter of time before a researcher publishes a result they don’t fully understand, or an administrator signs off on a decision they don’t fully comprehend. And soon enough, AI systems will be making ever more complex decisions that we just sign off on, because we don’t understand the foundation of the system and we gave up questioning.

If we go down the slippery slope, we risk becoming AI-sock puppets [11]. Faced with AI-output, we will take quick looks and “sanity checks” to make sure AI output is reasonable and move on, but it won’t have the same gravitas and deliberation that comes from a human-authored proof/document. We will have no choice but to use AI, because that will be the only way to keep up. Sanity checks themselves may become illusions — because we will be out of practice at true understanding. It is likely that we will have verified Lean proofs that assure us of correctness, but now we have to evaluate the faithfulness of the theorem statements. (And Lean itself has a very steep learning curve. There is a lot of work to be done to make sure such verification tools are universally accessible to all [12].)

The only thing that can protect us against this is culture. A culture where the point of pride is in the understanding of the work and in the exposition of it. A culture where it is ok to say we don’t understand, ask for clarification, or (respectfully) push back. And where such requests are valued (instead of saying, “let us move on, we only have a few minutes”).

A culture that appreciates being slow and steady and careful. A culture where a student can pursue a more theoretical research area for their PhD, but also be assured that this does not destroy their chance to get a stable, enjoyable job.

So how do we cultivate this culture?

Such culture building must start in the classroom. We must teach harder, better, and stronger [13]. We need to train students so that they know what they know and don’t know — students who can identify proof by intimidation and by authority, and have the confidence to push back. We should provide homework problems that let students explore concepts in depth, and force them to confront ideas they do not understand. Students thrive when they are challenged (with support) and then succeed. This needs resources.

We must walk away from classes that teach students the “high-level ideas” but do not expect students to fully grasp the rigorous details “because AI can do this stuff nowadays, [14]” or because “it is too hard for the students [15].” Because these can create a generation of students who don’t know the difference between understanding things deeply versus superficially. And then this can propagate.

This is now a bigger deal than it was a few years ago. It used to be that knowing a solution strategy or the right algorithm to apply was sufficient for students to become productive members of society. But now that this work can be done by AI systems, we have to be able to understand what the AI has generated, process it and question it, which requires not just knowing the names of the algorithms but also the proofs of why they work, what the key assumptions are, and where and how they break down.

A theorem may be correct given its assumptions. But the gap between assumptions and what we actually care about might admit counterexamples. Identifying such counterexamples requires knowing the modeling and the math at multiple levels. Interpretation matters and ambiguity can creep in when identifying if a formal Lean statement is faithful to the natural language. For such tasks mathematical mental muscles are essential.

Amit Sahai, Po-Shen Loh, and others have beautifully argued why we are going to need more (highly trained) mathematicians. I won’t repeat their argument here. But I will add to their point — it is important that we have a large, diverse set of people, with different life paths and trajectories, becoming mathematicians. People who do not all think exactly the same way, who can interpret, debate, disagree and convince one another.

A public goods problem

This brings us to a public goods problem. We need to maintain our culture. For this, we need to engage and excite lots of different students. We know that if we don’t incentivize students to learn, many of them won’t, and our (humankind’s) mental muscles will atrophy. We know that when humans moved from working in the fields to having indoor desk jobs, our bodies suffered. And to compensate, we invented things like the gym to make sure our bodies stayed fit.

But there is a catch. We pay to go to the gym, not the other way around. Entry-level jobs in fact used to train people while also getting useful contributions from them. Entry-level jobs, or PhD programs, are like being paid to go to the gym. If these are taken away by AI, how do we train people? And how do we convince people that they should be trained?

There is a tremendous investment needed in thinking about what future sustainable solutions to this will look like. This is just the beginning of that conversation. But in the short term, it is important culturally to celebrate and reward the work of understanding and communicating mathematical results — and not just by mathematicians but by society at large. We also need to advocate for educational institutions at all levels and for what they represent for our culture. Teachers need more resources, not less, to be able to teach in the AI-age, because we need to be teaching more, not less. There is no silver bullet. AI tools alone cannot solve problems in the education sector — these come with their own set of challenges. We should be able to offer individualized, 1-1 human tutoring to help students at different levels. I hope we can collectively build a positive future, where we use AI-tools effectively to help us in ways that raise everyone up together.

As a concrete first step in this direction, I invite university leaders to declare their commitment to hiring across departments in the sciences, engineering, social sciences and humanities, and announce their unwavering support for human intellectual growth and exploration. Similarly I invite philanthropists and funding agencies to declare their support for open-ended research, theoretical pursuits and rigorous, grounded education in the fundamentals. Students need to know that we have got their back, and that we are working for their future — because they are our future.

I would like to thank Terry Tao and Nestor Guillen for the invitation to write this post, and also Ted Theodosopoulos, whose 1st Relatorium dialogue on Mathematics and AI started part of this conversation. Thanks also to Anant Sahai for many conversations that have helped refine these thoughts, as well as Vinayak Ranade, Sukhada Fadnavis, Shubhangi Saraf and Amit Sahai for their helpful feedback. Thank you also to the organizers and participants of the Renaissance Philanthropy AI for Math Workshop 2026 — conversations there also influenced my thoughts.

Notes

[1] I understand that challenge and struggle does not work for all students, but it does help a good number. In this post, I will focus on that set. There is a longer discussion about education to be had more broadly at another time.

[2] Jobs that are typically held by PhDs that apply mathematical/other critical thinking skills. I understand that there are far more complex questions regarding jobs in the age of AI, and I’m not trying to tackle them. For now I focus on the narrow question of jobs for highly-trained scientists/mathematicians/humanists.

[3] I argue that we need far more than just the `greats,’ but just hypothetically.

[4] I am forever indebted to M. Prakash sir, out of the Bhaskaracharya Pratishthan. He intensively trained 200+ highschoolers across Pune, India, and several from the group went on to win IMO medals (another example of the Steph Curry argument). And the rest of us benefitted on the side. It was a privilege to participate.

[5] I teach courses on the mathematical side of the department, such as optimization, probability, and deep learning.

[6] I also love to dance, it is beautiful. But I am nowhere good enough to earn a living doing this. Luckily the math worked out ;-).

[7] Human understanding can never be developed by an AI, no matter how good AIs get. AI-augmentation of humans cannot generate human understanding.

[8] Perhaps we will find skills that are a suitable substitute for multiplication tables, that do everything that tables do and are `better’ in other ways. I’m ok with teaching those skills instead.

[9] As Picard said “there are four lights.”

[10] And every PhD granted is a new human expert in a subject.

[11] Not quite a meat proxy, but still bad.

[12] Some of our work to make lean accessible is available at leantutor.org

[13] not faster. https://www.youtube.com/watch?v=gAjR4_CbPpQ

[14] There is a space in this system for courses that teach students how to “use” tools (e.g. prompt engineering courses that have recently come up at many community colleges in California), or general AI literacy courses. But we must not confuse the role of these courses. Those may be helpful (in the current climate) for maintaining employment. But they do not replace the role of courses that fundamentally teach critical thinking, and should not take resources away from such courses.

[15] To cater to the fact that students come in at different levels, we need to have scaffolding classes at the lower-division level. A student may take longer to graduate, but should be able to take even the hardest class given enough time and hard work.