For years, Microsoft and OpenAI have fought to keep certain information out of the public eye in their fight with news organizations that have accused the AI firms of teaming up to violate copyright laws by stealing tons of news content to train AI.

However, now the details that should never have been marked confidential are starting to leak. In a motion for summary judgment that was unsealed Thursday from news plaintiffs led by The New York Times, internal documents are exposed that news groups alleged show exactly how Microsoft and OpenAI viewed the threat to news before unleashing new AI products like ChatGPT and Copilot.

Perhaps most explosively, Microsoft Director of Applied Science Brent Hecht repeatedly warned in documents that scraping news for AI training was “an astonishing theft of unprecedented proportions,” calling it perhaps the “largest theft of labor in human history,” news orgs said. In another document, Hecht contradicted Microsoft and OpenAI’s argument that training AI on news content is fair use, suggesting that the plan to widely scrape news made “a complete mockery of the idea of ‘fair use.’”

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Screens for School

One of the biggest challenges facing parents (and schools) today is that the 1:1 devices (usually Chromebooks or iPads) given out by the district are entirely reliant on the internet to operate. A Chromebook is an internet browser, not a digital tool— if it cannot connect to the internet, it is virtually useless. Many parents have spent years limiting their child’s access to the internet before they enter traditional school— only to find out that their kindergartener now has the ability to access numerous websites and apps that parents never would have approved at home.

A parent recently reached out to me to share her own struggle with her district. She told me that in spite of selecting the district’s option that stated she as a parent “withholds consent for Internet use at school” on their own “Information Release” and “Student Acceptable Use Policy,” the district was refusing to comply. She found it odd that while the district had already denied her intention to opt out of the Chromebook entirely, they still provided an “internet opt out” option during their registration process. This was confusing— the Chromebook wouldn’t function without the internet, so why was there an option to refuse the internet, but not the Chromebook?

I actually experienced this myself in Seattle Public Schools. When I first prepared to refuse the 1:1 Chromebook for my daughter several years ago, I found a form on the district website titled “Internet Opt Out.” At first I thought, “Great! This makes it super easy!” and filled it out, though I did notice that the form had not been updated since 2011.1 However, it was still available on the district website. But as soon as I submitted the form, I was told by the district that “this option is no longer available” and the form disappeared from the website.

More recently, in a similar scenario, parents in Lower Merion County in Pennsylvania filed a lawsuit alleging that when parents attempted to decline student devices via a district policy that permitted device opt-outs, the District contrived to repeal and replace the policy to prevent parents from doing so.

It’s The Internet, Not Just the Devices

In many ways, the issue around EdTech is not just the platforms, apps, digital curricula, or mandated screentime (though those are indeed still problematic). More broadly, the bigger issue is the fact that all these products rely on the internet to function. This is in part why I provided public comment urging the FCC to reevaluate eRate funding for schools— not because I want to restrict schools from having internet access, but because the high-speed and premium levels that are required to run EdTech products and apps is costly and puts money in the pockets of EdTech executives, while exposing children to harms.2

I actually wrote about this in an essay a over a year ago:

The same is true for internet-connected 1:1 school-issued devices. If there is an academic benefit to providing children computers in school (and that is a debate for a different essay), then is that not possible to provide without internet access? A Chromebook isn’t a computer; it’s an internet browser. None of its features work without internet connectivity or a child having a Google account.

If (and again, a lot of heavy lifting on the “if”) there is a pedagogical benefit to providing a child a computer in or for school, why have schools only contracted with companies whose curricula or software functions only when these devices are internet-connected? Why can’t a curriculum be downloaded onto a device or tools [placed on an “allow-list”] (meaning any digital platforms or tools used go through a vigorous vetting process first vs. the digital whac-a-mole approach taken today to attempt to block sites) and built into the hardware?

(And for those who wonder about updating materials, the internet can be accessible to the adults whose job it is to update or improve the materials; the children themselves do not need access.) If you noticed in my Four Norms of EdTech, I differentiate between “internet-connected devices” and computers for these reasons explicitly (remember, EdTech is not the same thing as Tech Ed.)

Remove the ability for children to access the internet on school-issued devices and you return the computer as a tool that children do need to learn about in this highly digital world.

There are now many excellent resources available to parents about how to refuse 1:1 devices and EdTech products (including my Unplug EdTech Toolkit, which has seen thousands of downloads), which is an excellent sign that momentum is only building. The tide is turning.

We’re Not Asking; We’re Declining

The parent who reached out to me said I was welcome to share both the letter she sent to her school district (Midland Public Schools in Michigan) and their response (personal information has been redacted).

For parents interested in opting out of EdTech products and platforms or district-issued devices, it is helpful to see a great example of a parent declaring their intent to refuse (subtly different from asking permission to opt out). Similarly, it’s also helpful to see how districts reply, even in conflict with some of their own policies and values.

This parent wanted me to note that in drafting her letter, she drew heavily from sample letter language in my resources and those from Distraction-Free Schools. Other parents are welcome to do the same. I’ve highlighted key points in the letters.

Letter to Midland Public Schools from Parent

August 15, 2026

Hello teachers & admin team,

We’re excited and looking forward to a great 8th grade year! Thank you for all the work that’s already been happening in classrooms and behind the scenes! As a public school teacher myself, I know there’s a lot that happens in these last August weeks!

I’m writing to alert everyone to a change we’re making for ——’s 8th grade year - we’re opting-out of Chromebooks this year, and we’d like to have a conversation with involved parties about how that will look for the academic calendar and for specific classes. We’ve been discouraged by the overuse, distractive nature, and lack of evidence for EdTech products and digital curriculums over the last 4 years as part of MPS, and decided a change is necessary. While we applaud the district for identifying current problems with technology use within MPS, the new technology use guidelines (August 2026) do not provide enough meaningful changes at the middle or high school level, thus this notice.

Screens are too frequently being put before skills. We’ve heard the tired argument “kids need tech to be future ready”; however, we know that other critical skills are far more valuable and needed first, including executive function, critical thinking, in-person communication among others. Declining test scores domestically and globally over the past 20+ years have been directly linked to school technology use, and research is very clear in showing that children learn better when they write on paper and read from physical books/printed text.

Our concerns include, but not limited to:

1. Cognitive impact. 1:1 devices do not improve learning outcomes, rather they hinder learning. Distracting, and poorly structured screen time poses documented harms to children’s development, capacity to pay attention, and well-being.

2. Efficacy: EdTech products do not improve learning outcomes. We’ve yet to find any independent, peer-reviewed evidence that the EdTech products currently in use show improved learning outcomes relative to non-digital instruction, while at the same time there is ample evidence that reading and writing on paper improve retention and comprehension.

3. Distraction. A report in Science Direct found that when students use a device in class, 38 minutes of every 60 minutes are spent off task. Expecting children to stay “on task” when provided an internet-connected device with access to YouTube and video games is absurd from a brain development perspective.

4. Skill Displacement. In short, time spent on screens is time not spent doing other more worthwhile learning endeavors. Too much screen time is damaging to cognitive health, mental health and physical health.

5. Engagement mistaken for learning. Many EdTech games and apps are embedded with manipulative design techniques, “persuasive design,” which sole goal is to keep users engaged as long as possible which is fundamentally at odds with best healthy learning and development. Engagement becomes confused for learning within gamified apps, again with no evidence for learning outcomes, drowning students in dopamine and crippling attention spans.

6. Data privacy. MPS does not provide a list of specific EdTech apps that are being used by students, nor have we seen any clear documentation of what student data is collected by these platforms, how it’s stored, whether it’s shared and/or sold with third parties, or how long it’s retained. Under the 1974 federal law FERPA (Family Education Rights and Privacy Act) schools are required to provide this information to parents.

7. Lack of safeguards. Neither GoGuardian, nor any content filter, is failsafe. MPS does not currently use a whitelist model, and therefore any student internet-connected device is not safe for student use - which I can confirm as my child’s Chromebook was tested to this end and disastrous findings were shared with BoE in May 2026.

8. Student use of generative AI products. We have particular concerns about AI student use on school-issued devices which research increasingly shows significant risk to children’s cognitive development.

9. Digital curriculua. While digital curriculua may be a cheaper alternative to books, there is no data to support these curriculums outperform analog courses.

In lieu of a Chromebook, we ask that —— receive meaningful and reasonable analog alternatives for assignments, assessments, homework and classroom work throughout the 2026-2027 year. As a teacher myself, I want to be immensely sensitive to the potential burden our request may place on ——’s individual teachers and wish this were not ultimately their responsibility. I wish there were better alternatives already in place for the many students who struggle with online learning products.

We look forward to partnering with the academic teams in finding solutions to providing —— with necessary materials he’ll need to participate in his learning experiences without a device. We’re happy to purchase textbooks, workbooks, additional paper, and other analog materials teachers may require. I’d welcome the opportunity to volunteer in classrooms, and provide support in any way that would be most helpful.

Nothing in this email should be interpreted as declining our child’s responsibility to comply with all school rules, academic integrity standards, respectful conduct expectations, or other district policies. —— will continue to abide by all behavioral expectations while participating in school.

Other considerations:

School culture: We know that the district desires to promote school culture that is inclusive, kind, respectful, curious, helpful, grateful, responsible and safe. To that end, we’re instructing —— to respond with “I learn better without screens” to inevitable student inquiries about the absence of his device. It is our hope that teachers and staff can continue building classroom cultures where all learning needs can be honored without stigma, bullying, or unkindness just as other students learn better with glasses, hearing devices, certain seating, or other learning tools.

Standardized Testing: Whenever possible, we request —— participate in mandated testing in paper/pencil format rather than digital testing formats. We request —— take the spring 2027 MSTEP assessments in paper/pencil format which needs to be requested to the state before November 6, 2026. As I understand, there is no paper/pencil format for NWEA nor PSAT in which case we are open to having —— take the assessment 1 or 2 times maximum per academic year in digital format until a paper/pencil version becomes available.

We greatly appreciate the understanding and flexibility of MPS staff to support ——’s learning in the way that will best support his growth. If you can please,

1. confirm a time that is best to meet in person and discuss, and

2. place this letter in ——’s educational file, and

3. provide written confirmation describing how MPS intends to accommodate these requests.

If additional forms or procedures are required, please provide instructions.

Many thanks,

Parents of ——

This letter is clear, communicates goals and values, emphasizes collaboration, seeks to reduce impact on teachers, and expresses gratitude.

Unfortunately, the district’s response left much to be desired, including opening by using the wrong name for the student in question.

Letter from Midland Public Schools to Parents

August 20, 2026

Dear Parents,

Thank you for your message regarding your request to opt —— [note: they used the wrong student name] out of school-provided digital devices and online learning platforms for the upcoming school year. I apologize for the delay in the district’s response. It has been a busy week preparing for the kids next week.

After careful review by our administrative team, we cannot approve this request. Our district aligns its curriculum with state educational standards that utilize digital literacy and technology integration (MITEC) across core subjects. In addition, MPS teachers integrate online platforms and devices into daily instruction, assignments, and assessments. Last, we are unable to provide an entirely non-digital alternative curriculum that meets these learning objectives. Therefore, individual opt-outs from general technology are not available.

As you know from your participation in our committee, the district is addressing some of your concerns by implementing our new technology guidelines and wireless communication device policy. Both of these district initiatives actively pursue reducing overall screen time across our schools, ensuring devices complement hands-on learning rather than replace it. This is especially true at the K-5 level, where we value research showing that younger students benefit from increased engagement through human-to-human interaction and from fine motor development through handwriting. While neither guideline may be completely to your liking, I would remind you that these guidelines are a first step in our journey as we address this complex topic.

Regarding artificial intelligence, our only student-facing AI product for grades 6-12 is SchoolAI. While teachers may use other AI software for their own personal use, MPS educators are not to use these products with K-12 students. Use of SchoolAI is optional for teachers and students. In addition, the district has instructed teachers to send a note home to parents informing them that the teacher has elected to use SchoolAI. At that point, parents can contact the teacher to inform them that they would like to opt out of using SchoolAI. The teacher will then work around this limitation by producing paper versions of what is being accomplished within SchoolAI with no negative consequences.

In addition, I would like to update you on Securly, our new classroom management software that helps teachers manage student devices. Teachers can see, monitor, and direct students’ online activities on their district devices, all from the teacher’s computer. With these capabilities, teachers can minimize distractions and keep students on task during class. Securly will also be used as the district’s network filter. Our testing has shown that this product yields better results for filtering and monitoring student use of district devices than the previously used GoGuardian software. In addition, Securly has a parent portal that allows parents to monitor student device use and limit student device interactions during after-school hours. This feature will be introduced to parents as soon as it is configured, which should be within a few weeks.

We take student privacy and device management very seriously. All school-issued technology complies with federal guidelines, including the Children’s Internet Protection Act (CIPA), Children’s Online Privacy Protection (COPPA), and the Family Educational Rights and Privacy Act (FERPA). If you have specific concerns regarding screen time, digital citizenship, or security settings on your child’s device, our IT team is available to discuss how we manage these safeguards.

As for required state testing, the Office of Educational Assessment and Accountability made it clear that schools are expected to administer the assessment online. They also stated that we can request a limited number of students to be opted out of the digital form of the M-STEP assessment. Due to a low number of requests at this time, we will be able to accommodate your request for —— to be tested with a paper-and-pencil version of the M-STEP assessment. However, the state requires all 8th-grade students to take the College Board PSAT in ELA and math. As stated in your email, you are correct that there are no paper-and-pencil versions of the PSAT. In addition, the district requires students in grades K-8 to be screened using NWEA, and there is no paper-and-pencil version of the NWEA test. These required assessments must be given digitally.

While we value our partnership with parents and welcome their input, we are unable to accommodate your request. As such, BOBS will be assigned a device to use with the MPS curriculum. School administrators and teachers remain committed to working directly with families to address specific concerns and ensure every student is supported.

Sincerely,

Associate Superintendent of Curriculum, Instruction, and Assessment

MPS District Vision: Lead with respect, trust and courage. Ensure an equitable, collaborative and inclusive culture. Enable all to achieve success.

MPS Mission: Midland Public Schools is committed to creating a safe, innovative, and student-centered learning community where every learner is challenged, supported, and inspired to reach their full potential.

MPS Vision: Our Graduates are prepared with the essential knowledge, skills, and character to achieve personal success and positively impact their communities.

Final Thoughts by Emily

A few things of note in the district’s response:

1. The district says they “cannot approve the request” to opt out—it is not a request, it is a declaration;

2. The only AI use is for a platform called SchoolAI, which is “optional” for use by students and teachers, but which students are allowed to opt out of and and can do paper versions of with “no negative consequences” (so they are able to provide paper-based options for certain things);

3. Like many districts, MPS relies on problematic “secondary EdTech” or “surveillance” tech products to “monitor” student usage, which yet again burdens teachers to manage how students spend time on devices (not their job);

4. The district intends to force this child to accept a device, in spite of what the parents expressed: “While we value our partnership with parents and welcome their input, we are unable to accommodate your request. As such, —— will be assigned a device to use with the MPS curriculum.” Appalling. Will the district shoulder the responsibility when students encounter unsafe content through their ability to access the internet?

5. The MPS “Mission” under the administrator’s signature states the district is committed to creating a “…student-centered” learning community where students are “…supported…” in reaching their full potential— but apparently this is only true if children use an internet-connected device.

I don’t know how a district can quite literally force a Chromebook on a child, but it appears they are willing to try. Because this parent already opted out of the internet per the district’s own policy, however, it would seem that a non-internet connected Chromebook would be quite useless. I applaud this parent for her continuing persistence to do right by children.

Fish friends, we are making progress, but we have a long way to swim in turning this school in a different direction. Courageous parents like this gives me so much hope. Keep asking curious, non-judgmental questions. Continue to be clear about your values and unwillingness to compromise children’s safety. Be persistent in your quest— do not accept “We cannot accommodate” as an ending; rather, it is an opening salvo.

Keep swimming.

I’m not a fan of improv. I’ve even walked out of a class before—being told to pretend to give birth just wasn’t for me. But its popularity was once never in doubt: people were all too willing to shell out hard‑earned cash to watch performers fumble through impromptu sketches. Nowadays, the form has lost its shine, and Dennis M. Hogan traces whether it still has a place in today’s culture. The inspired title alone means this is a read you should say “yes” to.

During the boom years of the late 2000s and 2010s, improv persuaded many people that it was not just a wacky gimmick but, as I believed, an art in itself. The rise of stars like the improv-trained Steve Carell, Tina Fey, and Amy Poehler convinced casting directors and network executives that improvisers had graduated from sideshows to being bankable talents in their own rights. Performances were packed with newbies and aficionados alike. Major theaters added classes and facilities to meet growing demand, allowing many improvisers who never made it big to eke out livings as teachers and theater staff. The gospel of improv spread to those far outside the comedy world, from self-improvement seekers hoping to level up their interpersonal abilities to corporate suits eager to take advantage of the latest team-building and soft skill-optimization fad.

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

A sentiment echoing throughout the mathematics community right now is that solving problems and generating proofs have always served as proxies for the true goal of mathematicians, which is to further human understanding. When proofs can be generated without that understanding, it undermines their value as a proxy.

This immediately raises a question: What other proxies should we use instead?

I want to propose that we more firmly define a notion of a “motivated explanation” and that we give novel and compelling motivated explanations academic credit similar to what generating new proofs of open problems has had historically.

Further, I believe this is an important step to help those outside of math better understand what it is that mathematicians contribute. If outsiders believe that proof-generating machines render mathematicians obsolete, while insiders see that as a misconception of what researchers add, it’s incumbent on this community to better project its true values through the kind of work that it rewards. Outsiders can be forgiven for this misunderstanding if the work most celebrated skews heavily toward generating proofs, while clarification and exposition are treated as second-class.

I should acknowledge up front an obvious personal bias. I have a non-traditional career in math, focused on producing videos about the topic. This shares the goal of “furthering human understanding”, but my focus has been on explanations and intuitions that resonate with the public, not on solving outstanding problems. A cynic could easily read this proposal as shamelessly self-elevating.

As a practical matter, though, my own career and funding exist outside academia, and I have no skin in the game for what this community assigns credit to. Moreover, in proposing that we elevate the status of motivated explanations, I don’t mean popularization. I mean any work which primarily aims to answer the question “how would you think of that?”, even if the subject matter requires deep expertise to appreciate.

The examples I highlight below show this is nothing new. Practicing mathematicians already devote a meaningful amount of mindshare to work like this. The proposal here is mainly to 1) more clearly define this work, and 2) elevate its status.

What defines a motivated explanation?

Although it might be clear what this phrase “motivated explanation” is intended to mean, it’s worth briefly contrasting it with proof.

In a proof, definitions sit at the start. It is common and expected to begin with a new construction and proceed by analyzing its properties.

In a motivated explanation, definitions sit in the middle. New constructions are only allowed to enter the vocabulary if the problem they are addressing has been clearly established.

In a proof, all statements must be correct, each claim following as a necessary implication from what comes before.

In a motivated explanation, it is okay and often desirable to start with an idea that is not quite right and requires correction, but whose origins are relatable.

A genre of motivated explanation I’m fond of is “discovery fiction”, a term coined by Michael Nielsen. You develop an idea with a narrative that starts with a simple-but-wrong solution to a problem, see where it breaks down, fix that problem, discover a new problem, and so on.

The scope of a proof is to explain why a particular theorem is true.

The scope of a motivated explanation is not only to clarify why a theorem is true, but why the theorem is the right one to pose in the first place, and how it is used in the surrounding context.

One clear shortcoming of a motivated explanation is that its validity is not binary the way a proof’s is. This is a big reason proof is so useful a way to measure progress: You can clearly define what does and does not have a proof yet. There will never be Lean for motivated explanations.

If we’re serious about the goal of advancing human understanding, there’s no way around the fact that this aim is intrinsically squishier than that of finding proofs, because defining human understanding itself is squishier. To shy away from metrics which are more subjective is to shy away from the more human aspects of the field.

The reason I’m leaning on the word “motivated”, as opposed to other potential choices like “lucid” or “demystifying”, is that this is a more verifiable property. It’s not quite as rigidly verifiable as a proof; almost nothing is. But it’s enough to be a practical measure. In my own work, I often repeat the phrase “I want this to feel like you could have discovered it yourself”. I say this not just to placate a viewer, but because it’s an actionable guideline for myself to assess whether an explanation feels complete or not. For each new idea introduced, you can ask whether it’s clear where that idea comes from. The answer is not quite a binary yes or no, but it’s close enough for practical purposes.

Exemplars of motivated explanations

One of the best repositories I can think of for motivated explanations is Part IV of the Princeton Companion to Mathematics. It covers over two dozen active fields of research, each one introduced by an expert with a talent for clear communication.

Whether it’s Andrew Granville explaining analytic number theory, or David Ben-Zvi introducing moduli spaces, these articles offer a level of intuition and motivation more typically found in one-on-one conversation at a blackboard.

The background on this book is noteworthy for the present discussion. It was edited by Timothy Gowers, who discusses it in his interview on the Numberphile Podcast with Brady Haran. Having been asked what impact the Fields Medal had on his life, here’s what he had to say:

People who’ve got Fields Medal feel freer to do slightly different things…for example I took on editing a book called the Princeton Companion to Mathematics, which was an absolutely massive task. It took I would estimate half my working time for about five years or something like that…It was a project I believed in and possibly wouldn’t I probably wouldn’t have actually been offered the chance to do it if I hadn’t been a Fields Medalist.

He was right to believe in it; this work adds tremendous value to the field of math, but it seems a shame to me that one requires a Fields Medal to feel justified in spending time on it.

Another example of someone exceptionally talented at writing proofs, but whose contributions extended far beyond proof, is Bill Thurston. His deservedly famous essay On Proof and Progress in Mathematics, though written three decades before LLMs, opens by suggesting that the right framing of the question “What is it that mathematicians accomplish?” is to ask “How do mathematicians advance human understanding of mathematics?”

Here’s one section with uncanny resonance with today:

The rapid advance of computers has helped dramatize this point, because computers and people are very different. For instance, when Appel and Haken completed a proof of the 4-color map theorem using a massive automatic computation, it evoked much controversy. I interpret the controversy as having little to do with doubt people had as to the veracity of the theorem or the correctness of the proof. Rather, it reflected a continuing desire for human understanding of a proof, in addition to knowledge that the theorem is true.

On a more everyday level, it is common for people first starting to grapple with computers to make large-scale computations of things they might have done on a smaller scale by hand. They might print out a table of the first 10,000 primes, only to find that their printout isn’t something they really wanted after all. They discover by this kind of experience that what they really want is usually not some collection of “answers”—what they want is understanding.

The essay itself offers a beautiful articulation of what the practice of doing math is beyond generating proofs. I want to draw your attention to what he writes at the end.

I have put a lot of effort into non-credit-producing activities that I value just as I value proving theorems: mathematical politics, revision of my notes into a book with a high standard of communication, exploration of computing in mathematics, mathematical education, development of new forms for communication of mathematics through the Geometry Center (such as our first experiment, the “Not Knot” video), directing MSRI, etc.

Again, why should these “non-credit-producing activities” follow a Fields Medal, and not contribute to it?

On a personal note, one product from the Geometry Center he referenced had an especially meaningful impact on me when I was younger. It was a short film called Outside In, perhaps the earliest example of a viral video about substantive math, visualizing the key idea of Thurston’s own construction for sphere eversion.

An original proof that showed an eversion must exist, say Smale’s, advances human understanding in the sense of going from 0 to 1. A video like this which gets millions of people to engage with the underlying idea, advances it in the sense of going from 1 to N. I’m grateful that Thurston spent so much time on this “non-credit-producing” activity.

Another relevant paper is Timothy Chow’s A beginner’s guide to forcing. Not only does the paper itself offer a prime example of a motivated explanation, but its introduction offers helpful vocabulary around it.

All mathematicians are familiar with the concept of an open research problem. I propose the less familiar concept of an open exposition problem. Solving an open exposition problem means explaining a mathematical subject in a way that renders it totally perspicuous. Every step should be motivated and clear; ideally, students should feel that they could have arrived at the results themselves.

What would it look like for these open exposition problems to be treated similarly to open research problems? As an extreme case, we might imagine what it could look like to have an analog of the Millennium Prize Problems for open exposition problems. An institution or group of researchers would formally define mathematical results they see as important, and which are not yet well understood despite technically having proofs. At the moment, every AI-generated proof is born an unsolved exposition problem. As such, it seems likely the next few years will see a flood of them, and it will be valuable for leaders to clarify which ones deserve focus.

A rubric would have to be agreed upon for what constitutes a resolution to an important unsolved exposition problem. Again, this is intrinsically more subjective than verifying a proof, but any serious engagement with the more human aspects of math necessarily wades into this kind of subjectivity. And again, I’ll emphasize that checking whether key ideas are motivated is not unlike checking whether the steps of a proof follow logically.

If the world outside of math sees its leading figures treat open exposition problems with the same seriousness as they treat open research problems, it could go a long way to correcting misconceptions about the role of mathematicians.

The last example I’ll highlight is one that may better foreshadow things to come.

In April of this year, Liam Price submitted a solution to Erdős Problem 1196, sometimes called the asymptotic primitive sets conjecture. The solution came from Price’s interaction with GPT-5.4 Pro. Unlike many earlier Erdős problems which had been resolved with help from AI, this is one that those in the field had found both important and elusive. Stories like this are increasingly familiar these days, but at this point in the story, despite a proof technically existing, human understanding had not yet been advanced all that much.

The proof made its way to Nat Sothanaphan and Jared Lichtman, who were able to interpret what the AI’s approach was and clean up the proof into a human-readable form. In May, Boris Alexeev, Kevin Barreto, Yanyang Li, Jared Duker Lichtman, Liam Price, Jibran Iqbal Shah, Quanyu Tang, and Terence Tao put out a paper which expanded on the key idea underlying the proof. The authors explained how that key idea clarified not only the original problem, but many around it, for instance offering a cleaner proof of the Erdős Primitive Set Conjecture.

The value here is not that one more Erdős problem could be ticked off as solved. The value lies in the fact that our understanding of primitive sets is notably cleaner and more satisfying now than it was at the start of 2026. The original problem solution played some role in this, but arguably the work that deserves more celebration is this paper expanding, clarifying, and contextualizing its key idea.

Practical calls to action

At a pragmatic level, what would it look like for us to elevate the status of a motivated explanation? Here are a small handful of suggestions.

• A PhD advisor can still assign a small problem from their field for a new student to cut their teeth on, but the deliverable would not be to write up a solution; it would be to present that solution to peers and faculty as a talk. It could be an already-solved problem which lacks clarity, or perhaps it’s a problem that lacks a solution, and the student uses AI to help find it. In either case, the student knows that on a certain date they have to understand it well enough to explain it, and that the desired output is for others to understand it as well. In short, even small problems could be treated like small PhD defenses.
• A leading figure (cough, Terry, cough) could enumerate a modern analog of Hilbert’s problems, instead focusing specifically on unsolved exposition problems. What areas are both important and lacking in the deeper understanding we desire?
• Written standards could clarify what constitutes a motivated explanation, aiming to make it nearly as verifiable as proof, so that the resolution of unsolved exposition problems can be recognized and celebrated in the same way proofs of open problems can be.
• Journals can be established which focus more explicitly on making results understood more widely throughout the mathematics community. Mathematical Discourse offers an interesting new example in this direction.
• Hiring and tenure decisions could place a higher value on writing great textbooks and similar work. Think of the AMS Steele Prize for Exposition, but at a more granular scale with an emphasis on early-career contributions in this vein.

The value of visible cultural shifts

I’d like to close with a broader pitch that visible culture shifts in math carry an intrinsic benefit right now with respect to the external image of mathematics as a career.

Many young students who are otherwise passionate about the field are afraid to pursue it now due to the uncertainty of what happens in an age of proof-generating machines. However, framed correctly, this is one of the most exciting times to go into the field, because there is nothing more exciting than entering a field when it is malleable and you have a chance to actively shape what it will look like in the future. Even if we completely set aside any potential benefits from AI to help with our understanding, young prospective mathematicians should feel energized knowing that they are entering at a unique point in history when they might play a real role in determining what the field as a whole looks like.

However, change like this is only exciting when it feels deliberate, whereas it feels terrifying if it seems driven by forces outside your control. As such, tangible action from the field’s leaders now to help define and clarify what the field is will reassure young entrants about who is in the driver’s seat, and that the status of the career does not depend on what entities produce the proofs.

Similarly, I also believe this is one of the best times to fund math. If the next chapter of math is ushered in by the drumbeat of two words “human understanding”, whatever changes are about to happen seem likely to amplify math’s value as a public good.

"Turns out, Silicon Valley isn't especially altruistic," writes the nonprofit education news site The 74. They're reading a new book promising "the inside story of how Big Tech catalyzed, co-opted, and ultimately came to capture computer science and AI education in America". Written by New York Times business reporter Natasha Singer, Coding Kids: Big Tech's Battle to Remake Public Schools tells "the story of the nonprofit Code.org and its charismatic, Harvard-educated leader, Hadi Partovi," according to their review: Thirteen years ago, Partovi... delivered a worrying message: Kids who didn't learn to write code would be left behind. And the long-term success of the United States economy depended on training these students to fill a million open tech jobs.... Fast-forward to 2026, and now we're dealing with AI, and tech is reading from a similar playbook. Asked by The74's Greg Toppo, "Does this moment seem different to you?", Singer replies, "This moment is different, but also similar. "We are in a moment in society where a lot of people have increased distrust of these huge tech companies, and we see a wave of parents pushing back against tech in schools. But we also see waves of people pushing back against Flock cameras, against data centers, that there's this feeling that tech has taken so much, and that people feel like they have lost control — that tech is being enacted on them... And parents are worried about the effects of unfettered tech access and kids' compulsive use of social media and phones, and so there's a different climate. And yet there seems to be a disconnect in some ways with AI because you see that Microsoft and OpenAI and Anthropic and Google are all competing to get their AI tools into schools, and you see school districts across the country say "We've partnered with OpenAI." "We are a ChatGPT Pioneer School," or "We've partnered with Microsoft, and we're going to use 10,000 licenses of CoPilot." It's amazing to me. We have had these cycles of tech in schools where there are all these promises about the latest tech, laptops, learning apps, massive open online courses, virtual reality, big data's going to revolutionize schools and like democratize access to education for kids and get them these great career skills, and we keep having these cycles. My concern is that we don't learn anything. One of the reasons I wrote this book is because it feels like we have collective amnesia. Now we're in the sixth or eighth cycle of this — and shouldn't we be asking questions about the push for AI in schools, based on what we've learned about the push for all the other things that came before? Two Slashdot posts are cited in the book, both submitted by long-time Slashdot reader theodp (Slashdot UID #442,580), who even gets a shout-out in the book's "Acknowledgements" section (along with consumer advocate Ralph Nader). Ironically, one member of Amazon's "Vine" program received a free copy of the book in exchange for a review — and apparently misunderstood its topic, writing that it made coding "feel approachable and even fun... [T]his is exactly the kind of book that could help a child become interested in technology without feeling overwhelmed by it. I particularly liked the way it encourages kids to be curious, experiment, and solve problems on their own. I would definitely recommend Coding Kids to parents, grandparents, or teachers looking for a good introduction to coding..."

Read more of this story at Slashdot.

While at work today, debugging a weird edge-case where some emails to Outlook have some unexpected padding, I learned something weird: Microsoft Outlook still (kinda) supports WordArt.

If you’re too young to remember: when Microsoft Office ’97 came out, it shipped with a feature called WordArt. Basically, these were a somewhat-customisable set of on-demand clip-art-esque text styles that you could apply to your own text.

The ease with which you could make use of these wacky designs meant that, for a while during the late 1990s, you wouldn’t see a poster advertising a school disco nor the front page of a GCSE essay that didn’t feature at least one¹ of these colourful eccentricities.

They gradually got phased-out and replaced with more-tasteful tools, but if you used them back in the day then images like the one above are sure to evoke a feeling of nostalgia.

Even as Microsoft adopted the Web as a platform, they were half-hearted about it. While HTML rapidly became used for things like styling emails as well as Web pages, Microsoft resisted the change, instead favouring two of their own standards in their own email clients. Outlook Express preferred to do “formatted” email using RTF, the format underpinning Microsoft Write, while fully-fledged Outlook effectively used Microsoft Word as its formatting engine².

You can still use RTF in some modern versions of Outlook (but you shouldn’t). But nowadays if you’re typing formatted text in Outlook, you’re almost-certainly creating HTML (albeit probably still using Microsoft Word³).

But this introduced a problem with backwards-compatibility. If Outlook switched to HTML as its default rendering format, what would happen to all the old WordArt? I’m confident that somebody asked this in a meeting at Microsoft in around 2007.

It turns out that Microsoft implemented a whole stack of custom CSS directives, just to support WordArt in Outlook⁴. For real! You can use CSS like mso-effects-shadow-angledirection: 5400000;⁵ to put a text-shadow directly below your text or mso-style-textoutline-outlinestyle-dash: longdashdotdotgel; to outline it with a mixture of dots and dashes. And it only works in Outlook. These form part of a translation layer for converting WordArt to and from a HTML-like format⁶.

So yeah: you can send an email containing classic WordArt to a modern Outlook installation and it still looks as horrible as it always did:

But you know what I find myself wondering? How do Microsoft’s new, Web-based Office Suite apps handle this?

I assume that if you send them “classic” WordArt from e.g. Outlook ’97, then they render it correctly. But to do that, they’re presumably…

1. Receiving the original WordArt in whatever proprietary format Word ’97+ used to put these graphics into emails.
2. Converting the WordArt to mso-prefixed CSS directives that Outlook 365 can understand.
3. Converting those custom CSS directives into standards-compliant modern CSS directives that your browser can understand.
4. Rendering that to the page you see the WordArt in all its… “glory”.

That seems like an insane amount of work, but it might not be far from reality. The (horrifying) alternative would be that Microsoft maintain a cluster of virtual machines running old versions of Windows, Office, and Internet Explorer, used just to convert WordArt into static images!

Or maybe Outlook 365 for Web finally killed off WordArt for email? I haven’t tested. But if it did… then it was probably about time!

In any case, this was a fun and unanticipated discovery of some long-maintained backwards-compatibility. It brought a smile to my face during the otherwise-tedious task of regression-testing blind-coded changes against a variety of versions of Microsoft Outlook!

🥰 RSS is great, and I'm glad you're using your feed reader... but you're missing out on some WordArt-like font magic that you can only see if you visit the original post. Maybe give it a look? 👀