11h • Creative Force Dispatch
Creative Force Dispatch
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?
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Generative AI Has Changed Mathematics Forever. Where to From Here?
Read it here • The Conversation — opinion essay, August 10, 2026
The occasion for this essay was OpenAI's announcement of ten mathematical and computer science advances produced using its unreleased Astra model, spanning geometry, cryptography, and coding theory. But the authors are after something larger than a scorecard. OpenAI paired the announcement with a statement acknowledging unresolved questions about attribution —who is accountable for the correctness of an AI-assisted result —and about how mathematical discovery itself is changing—and that acknowledgment, the essay argues, is the real story.
What follows is a portrait of a discipline that has not settled on an answer and knows it. University departments are working through the ethics of these tools in both research and teaching. Journal editorial boards are receiving AI-written submissions and deciding how to assess and disclose them. The essay sets two recent collaborations side by side: one deliberately excluded generative AI on ethical grounds, the other treated it as an indispensable partner while preserving the customs of mathematical research. Both produced good mathematics. That non-convergence is the essay's central observation — the question is no longer whether these systems can contribute, but how their use squares with collaboration, transparency, and intellectual integrity. One mathematician quoted describes the moment as a profound spiritual crisis; the Leiden Declaration, signed by thousands, argues that AI should augment rather than replace human mathematical creativity.
CREATIVE FORCE: Notice what the community is actually fighting about. Nobody is seriously disputing that these systems can produce correct results — that argument is over. What is under negotiation is whether mathematics is the theorems or the doing of them, and that is a question about creativity, not capability. The unease says something the field rarely says out loud: mathematicians believe the practice is the point. That should sound familiar to anyone who has defended conceptual teaching against a demand for faster procedures. What mathematicians choose to protect when a machine can do the answer-getting will tell us much about what we should protect for students — in language that comes from inside the discipline rather than from pedagogy alone.
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On AI Policy, Students Have Plenty to Say
Read it here • EdSurge — news feature by David Weldon, August 13, 2026
At America's Youth AI Festival in Boston, student leaders from across the country spent three days drafting what became the STUDENTS FIRST Act — a first-of-its-kind national AI policy for K-12 classrooms, written by the students themselves. The event was hosted by Day of AI, MIT RAISE, AASA (The School Superintendents Association), and the Edward M. Kennedy Institute, whose replica Senate chamber gave the proceedings their shape: subcommittees, amendments, floor debate, and a closing roll-call vote. The resulting bill goes to AASA's 10,000 member districts for further discussion.
The provisions are more careful than the premise might suggest. Students would be barred from using AI to produce written or artistic assignments, while older students could use it — with teacher permission and disclosure — for brainstorming, studying, and editing their own work. Independent use would begin in ninth grade; AI literacy instruction would begin in grades K-5. The senators pressed hard on equity, backing proportional funding with a baseline minimum so under-resourced districts could actually meet the bill's requirements. And on academic integrity, they drew a line that adults have often blurred: schools should not rely solely on AI detection software, and a student accused of misuse is entitled to a human review and an appeals process. Day of AI's Dan Rae notes the team hopes the act serves as a practical starting point rather than finished legislation to be adopted word for word.
CREATIVE FORCE: Read the bill as a piece of student work, and it becomes a striking artifact. These young people were handed a genuinely open problem — no worked example, no answer key, competing values that cannot all be maximized — and they did what mathematicians do: named the constraints, argued about which to relax, and built something that holds together while admitting where it does not. A majority said outright that the bill is imperfect; that is not a weakness but the mark of people who understand what they built. We often justify ill-structured problems on the grounds that students will need them someday. Here is someday — and the students who could reason about tradeoffs were the ones with something useful to say about their own schooling.
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