Daniel Gohl

When math seems simple — like calculating a tip — that’s often only because notation has made it so. “We have these notational technologies that allow us to not see this as significant math, but it is,” said math historian David Dunning. quantamagazine.org/how-writing-ch…

All meaning needs footnotes. An insightful, literary review of a world classic poem. Best part is translator’s poetic equivalence of the human, contemporary impact of the words, rather than matching word meaning, What Dante Is Trying to Tell Us apple.news/AUeXYWIDRTBmHW…

Florida educators working in math, science or STEM are welcome to apply or please nominate a deserving teacher.

Improve the quality of edu & governmental operations through transparency of utilization, active AI intervention, & higher user satisfaction. Join me on March 19, 1 pm ET @HP @HPEDU @govtechnews A Platform Approach to Smarter Device Fleet Management webinars.govtech.com/A-Platform-App…

If global learning has been on your “someday” list, this is a practical first step. Global Ed Lab Virtual Exchange Meet-Up Register: globalcities.org/contact Let your classroom be a place where global dialogue begins.

@ChrisLaubAI Vygotsky’s Zone of Proximal Development for the teacher-student dyad. Learning as method of discovery within constraints of dyad’s capacities. And it scales across model sizes, important for SLMs running locally.

MIT just published a paper that quietly explains why LLM reasoning hits a wall and how to push past it. The usual story is that models fail on hard problems because they lack scale, data, or intelligence. This paper argues something much more structural: models stop improving because the learning signal disappears. Once a task becomes too difficult, success rates collapse toward zero, reinforcement learning has nothing to optimize, and reasoning stagnates. The failure isn’t cognitive, it’s pedagogical. The authors propose a simple but radical reframing. Instead of asking how to make models solve harder problems, they ask how models can generate problems that teach them. Their system, SOAR, splits a single pretrained model into two roles: a student that attempts extremely hard target tasks, and a teacher that generates new training problems. The catch is that the teacher is not rewarded for producing clever or realistic questions. It is rewarded only if the student’s performance improves on a fixed set of real evaluation problems. No improvement means zero reward. That incentive reshapes everything. The teacher learns to generate intermediate, stepping-stone problems that sit just inside the student’s current capability boundary. These problems are not simplified versions of the target task, and strikingly, they do not even require correct solutions. What matters is that their structure forces the student to practice the right kind of reasoning, allowing gradient signal to emerge even when direct supervision fails. The experimental results make the point painfully clear. On benchmarks where models start with zero success and standard reinforcement learning completely flatlines, SOAR breaks the deadlock and steadily improves performance. The model escapes the edge of learnability not by thinking harder, but by constructing a better learning environment for itself. The deeper implication is uncomfortable. Many supposed “reasoning limits” may not be limits of intelligence at all. They are artifacts of training setups that assume the world provides learnable problems for free. This paper suggests that if models can shape their own curriculum, reasoning plateaus become engineering problems, not fundamental barriers. No new architectures, no extra human data, no larger models. Just a shift in what we reward: learning progress instead of answers.

Best stargazing of 2026: Top events not to miss earthsky.org/tonight/best-s…

🚀 Launching the AI Innovator Challenge 2026! Join us 1/9/26 at 10 AM for a session on turning early ideas into meaningful AI projects. Hear design-thinking tips, see examples from past standout teams, and get your questions answered. 🔗 Register now: hubs.li/Q03Y5z1q0

ＡＩ ａｎｄ Ｅｄｕｃａｔｉｏｎ Human-centered co-design of AI tools is essential. #InnovatingLearning | bit.ly/LSIedtech @FloridaState | @FSUResearch | @FSUGlobal | @UNESCOIICBA | @fdremoe | @WBG_Education

Looking for some light reading over the winter break? Our final article on the Work Cycle is here, a good piece to start on if you haven't been following our Work Cycle series this year. Check it out: algebra.org/2025/12/22/wor…

Here are the biggest breakthroughs that happened in mathematics this year. quantamagazine.org/the-year-in-ma…

Always a great end of year review.

🌍 Ready to make global learning part of everyday instruction? Join a global community of teachers turning big ideas into real classroom impact. 📏 Measure Global Competency: Designing Classroom Assessments 🗓️ Nov. 18, 8PM ET or Nov. 20, 10AM ET 👉 tinyurl.com/GlobalLearning…

Super proud Dad moment! Thank you to all staff at @browardschools @myPBHS @SunriseFalcons @VSYMontessori for cultivating environments of intellectual curiosity, holistic development, and playful growth. Full credit to @eringohl for the home front nourishment! Congrats Patrick!

With recent discussion of updating the “Turing Test” for #AI to quantize gravity & explain how it did so, find an explanation of the @cpepphysics Gravitation Chart for consideration. youtu.be/ICEbWQSkSGI?si… via @YouTube @OpenAI, start arxiv.org/html/2505.0485… #CausalSetTheory

The latest issue of @LIGOMagazine is out now and free to read 🎉 Celebrate 10 years of gravitational-wave astronomy with us 🎉 ligo.org/wp-content/upl… #GW10Years

Government, #HigherEducation , & #K12 colleagues: Please join me on July 8 at 1 ET with @HP & @AMD as we discuss building the infrastructure for exceptional service to the #PublicSector. Localizing AI: Powerful Compute for Real-World Impact webinars.govtech.com/Localizing-AI%…

Teaching quantum physics to everyone: pictures offer a new way of understanding – Physics World physicsworld.com/a/teaching-qua…

It’s a complicated world, but teaching global skills doesn’t have to be. We’ve spent more than a decade helping classroom teachers spot, teach, and assess global learning outcomes. See what's in it for your students: globalcities.org

How we teach & learn is always adapting in response to knowledge, culture, & technology. Some districts lead. How AI is Transforming Learning at #HP #AI Spotlight School, Ypsilanti Community HS. youtu.be/S3z6ilYNhoM?si… via @YouTube @HP @DigitalPromise @HPEDU @ycschools_us