Maths Shows Why Your Vote May Not Count the Way You Think It Does Read it here • University of Cambridge — research news, July 31, 2026 Frederik Ravn Klausen of Cambridge and Sebastian Tim Holdum of the University of Copenhagen have proved an impossibility theorem for electoral systems, and the result is unusually easy to state. A fair national election, they argue, would satisfy three conditions at once: regionality, meaning everyone who wins a local seat keeps it; proportionality, meaning national seat totals match national vote shares; and a fixed parliament size. Once enough parties are competing, no system can deliver all three. As Klausen puts it, this is not corruption or conspiracy — it is simply mathematics. The work began with the 2022 Danish election, where for the first time in seventy-five years the seat count stopped tracking the vote count — and the resulting single-seat discrepancy decided the election. The paper traces the same strain elsewhere: Germany's Bundestag swelled from 598 seats to 736 before 2023 reforms capped it, at the cost of guaranteed local representation, and the UK's 2024 general election was its least proportional ever, with Labour taking 63% of the seats on 33.7% of the vote. Crucially, the authors do not stop at the negative result. They propose an algorithm called geographically ranked guaranteed proportionality, which sets national totals before any voting occurs and then allocates seats by ranked local performance. It works — and it pays for itself in regionality, since a candidate can win comfortably and still lose the seat once the party's quota is spent. The paper appears in the Annals of Operations Research. CREATIVE FORCE: This is what a constraint looks like when it is honest. Most of what students meet in school mathematics is a problem with an answer waiting at the end; here the mathematics arrives to tell us that a thing we badly want is not available, and then — this is the creative turn — goes to work on what we can have instead. The impossibility is not the end of the inquiry; it is the beginning of design. For the classroom, it is a rare gift: an accessible impossibility students can hold in their heads all at once and feel the pinch of before anyone writes a proof. And the follow-on question is the better one — given that something must give, which one, and who decides?

What Happens When AI Policy Meets a Real Classroom? PODCAST · THIS WEEK WITH EDSURGE · AUGUST 5, 2026 Read it here Jody Britten spent a year reading the AI policies of more than 100 school districts and sorting them into a five-level framework, running from active promotion at one end to outright prohibition at the other. Her finding: most districts land well toward the cautious end, and their policies are frequently disconnected from the state guidance intended to inform them. The episode pairs her with a second guest who helped write policy from inside a system — someone who knows what gets negotiated, softened, or quietly dropped between a draft and a board vote. The value is in the gap between those two vantage points. Britten sees policy as a corpus that can be coded and compared; her counterpart sees it as a set of compromises. Neither view alone tells a teacher what to do at 8:15 on a Tuesday — and that gap is where most of us are working. CREATIVE FORCE: Every AI policy encodes a theory of what a school subject is, whether its authors intended one or not. A rule written mainly to prevent students from quietly obtaining answers asserts that mathematics is a body of answers worth guarding. But if mathematics is a creative act — conjecture, false start, revision — then the thing worth guarding was never the answer. It was the student's authorship of the reasoning. Districts are drafting this language now; if mathematics educators are not in the room, the definition gets written without us. _____________________________________________ This Startup Just Raised $6M for an AI Tutor That Helps Kids Figure It Out Themselves NEWS ARTICLE · GEEKWIRE · TODD BISHOP · AUGUST 6, 2026 Read it here Seattle-based Wild Zebra has raised $6 million to expand its AI learning platform for math and reading, wagering that a purpose-built educational product can hold its ground against the free general-purpose study tools now shipping from OpenAI, Google, and Anthropic. The funding is modest by edtech standards. The design decision behind it is not. The example in the reporting is worth sitting with. A student who has told the system she is interested in baking gets a fractions problem framed around a cookie. She works out that each section is one-twelfth. The AI confirms that step — and then asks the next question, rather than finishing the problem for her. Restraint, in other words, is the feature. In a market where speed to the answer is the default competitive axis, a company has raised money on the premise that not answering is what parents and schools will pay for.

Fields Medal 2026: Leaked Names Reveal a Century of Math Solved at Once → read it here Four days before the International Congress of Mathematicians opens in Philadelphia — the first U.S. congress in more than four decades — a front-end coding error on the ICM website exposed schedule entries marked “HIDDEN,” revealing the four probable winners of math's most prestigious prize: Yu Deng, John Pardon, Jacob Tsimerman, and Hong Wang. What makes the cohort remarkable is not the leak but the ledger: between them, they resolved the Kakeya conjecture (open since 1917), the kinetic-theory portion of Hilbert's Sixth Problem (posed in 1900), the André-Oort conjecture in arithmetic geometry, and foundational problems in symplectic topology — several of mathematics' longest-running open chapters, all closed within a single four-year window. If the list is confirmed at Thursday's ceremony, Wang becomes just the third woman to win the medal, and she and Deng become the first Chinese-born mathematicians ever to receive it. CREATIVE FORCE: It's tempting to read four once-in-a-generation results as four lone geniuses striking at once. The truer story is more interesting: this is a generation that grew up on each other's preprints, built on each other's tools, and closed problems the previous generation left open — creativity as a relay, not a lightning strike. That's a powerful reframe for our classrooms and research groups alike. The mathematics our students inherit is not a finished cathedral but an active construction site, and the drama of this week — leaks, prediction markets, a boycott, a ceremony — is a reminder that mathematics has stakes, personalities, and stories worth telling out loud. _______________________ Mathematicians Are Closing In on the Hidden Order Inside Chaos → read it here

Faster Solutions, Lower Test Scores: How AI Is Eroding Math Skills RESEARCH-DRIVEN ARTICLE | THE HECHINGER REPORT · JILL BARSHAY | JULY 6, 2026 Read it here A doctoral student at UC Irvine teamed up with researchers at McGraw-Hill and did something clever: rather than asking students whether they use AI, they let the data answer. Analyzing millions of interactions with ALEKS — an online math platform used by more than four million students a year, from fifth grade through college — they compared two problem types. Word problems can be pasted straight into a chatbot. Graphing problems can't, not easily. After ChatGPT arrived, the two diverged. Time spent on word problems fell sharply — down 31 percent among high schoolers — while time on graphing problems held steady. And accuracy on supervised placement tests dropped from roughly 80 percent to about 60 percent, a decline that appeared only on the AI-outsourceable problems and vanished under proctoring. The researchers call the pattern "cognitive surrender." Notably, they don't argue for banning AI; carefully designed AI tutors have improved achievement in controlled experiments precisely because they ask questions and withhold answers, increasing the time a student spends thinking. The ALEKS data show the opposite happening in the wild. CREATIVE FORCE: If mathematics is a creative force, then the unit of creative work is the interval between encountering a problem and understanding it. That interval is where representation gets built, where a student decides what the words mean before deciding what to do with them. This study is essentially a measurement of that interval collapsing — four minutes to under three, and for some students, to seconds. The finding that should reshape our practice is not "AI is bad." It's that speed and learning came apart, and that the most vulnerable tasks were those requiring translation from language into mathematics, the most creative act in the whole sequence. For anyone designing tasks: the question is no longer whether a problem is hard, but whether it is outsourceable. Graphing problems weren't protected because they were harder. They were protected because they were inconvenient to hand off.

Reading and Math Scores Rise for Younger Kids, Stall for Teens Research Report Education Week / NPR · June 10, 2026 The latest release of NAEP's Long-Term Trend data offers tentative signs of recovery after years of decline — but only for some students. Nine-year-olds improved in both reading and math compared with three years ago, with the lowest-performing students in that group making especially large strides. For 13-year-olds, the story is different: their scores in both subjects have stagnated, showing no statistically significant change since the last administration in 2023. The middle-school numbers carry a sting of history. Between 1978 and 2012, the average LTT math score for 13-year-olds climbed 21 points — a rare bright spot across five decades of data. This report shows most of those gains have now been erased, with the lowest-performing students showing no improvement over the 1978 results. "As a nation, we have to bring more focus to the middle school years," the National Assessment Governing Board's executive director told reporters. CREATIVE FORCE: The divergence between age groups reframes the recovery debate. The 9-year-olds tested were four when the pandemic hit and largely started school after in-person instruction resumed; today's 13-year-olds spent critical early-literacy and numeracy years amid closures. For math educators, the data sharpens a question the shortlist keeps circling — whether our measurements are capturing real learning, and where in the K–12 arc intervention actually moves the needle. ___________________________ Are Universities Returning to In-Person Exams to Combat AI Cheating? Feature Times Higher Education · Late June 2026 Faced with students submitting polished written work they can't explain when questioned, universities are reaching back to a method as old as Socrates: the oral exam. Alongside a revival of invigilated, closed-book sittings, institutions are experimenting with Socratic-style questioning and a broader philosophical shift from assessing a student's output to assessing their process — how they arrived at an answer, not just what the answer was.