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Our selection of the top business news sources on the web. |
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Quote: Quanquan Gu - UCLA Professor"Whatever your view on AI in mathematics, enabling high school students to push the frontier of mathematical research is something worth celebrating." - Quanquan Gu - UCLA Professor The underlying tension in contemporary mathematics education is no longer simply about access to high-quality teaching, but about who is able to participate in frontier-level problem solving and under what conditions that participation is considered legitimate. When secondary students can use advanced artificial intelligence systems to explore conjectures, test structures and traverse research literature, the traditional apprenticeship pathway into mathematical research is disrupted. The resulting opportunity is profound: pupils who previously would have been confined to routine exercises can now probe open questions, but the risk is equally stark, as educators and researchers debate whether AI-augmented contributions count as genuine mathematical insight or merely sophisticated pattern matching supported by machines . From selective pipelines to broadened participation For much of the twentieth century, entry into mathematical research followed a narrow pipeline: strong performance in school, competitive undergraduate training, and rigorous doctoral supervision. High school students appeared at the research frontier primarily through exceptional competition performance or rare mentorship arrangements. AI systems capable of generating proofs, suggesting structures and navigating formal libraries change that dynamic. Work on benchmarks for automated theorem reasoning indicates that large language models now solve competition-style problems and construct candidate proofs at levels once reserved for advanced undergraduates . When such capabilities are freely accessible, motivated secondary students can experiment with research-style tasks, shifting the frontier from a remote horizon into something that can be explored in the classroom or at home. This broadening of participation raises questions about what counts as authorship and how the community should recognise early contributions that rely heavily on computational support . The role of researchers and laboratories Quanquan Gu is known primarily for work at the intersection of non-convex optimisation, deep learning, reinforcement learning and large language models, with a stated interest in using AI to accelerate scientific discovery across domains such as biology, medicine and public health . Within this agenda, mathematics is both a methodological foundation and a potential application area. The emerging picture from AI research labs is that mathematical reasoning tasks serve as stringent tests for general-purpose models: success on formal proofs, competition problems and synthetic benchmarks is taken as evidence that systems are developing more systematic reasoning capabilities . When a researcher in this environment draws attention to high school students pushing mathematical frontiers with AI, it is not simply a pedagogical remark; it reflects a shift in how AI and mathematical creativity are co-evolving, and how new generations are being drawn directly into that co-evolution as co-experimenters rather than passive beneficiaries . AI as scaffold rather than substitute Empirical work in mathematics education consistently shows that AI tools are most effective when they function as scaffolds within structured instructional designs rather than wholesale substitutes for teacher expertise. Studies on AI-supported think-pair-share activities in algebra, for example, find that integrating AI prompts and feedback into each phase of collaborative problem solving significantly improves pupils problem-solving skills and motivation relative to traditional instruction, while leaving the human teacher in charge of conceptual explanation and classroom norms . Systematic reviews emphasise similar patterns: generative models excel at procedural guidance, multi-perspective explanations and personalised feedback, but they are less reliable on complex reasoning and proof construction, and they can generate plausible yet incorrect mathematics if used without verification . This dual character of AI as both enabler and potential source of error shapes how frontier experiences unfold for young learners: the same system that lets a pupil explore non-trivial conjectures can also mislead them about validity unless embedded in robust verification routines and dialogic teaching . Frontier exploration and verification bottlenecks Recent work on benchmarks for mathematical reasoning highlights a subtle but crucial shift: models are increasingly able to generate candidate solutions and proofs for upper-undergraduate problems, but reliably verifying those proofs remains an open challenge . In quantitative terms, one can think of a model proposing sequences of statements that resemble formal derivations, while evaluators attempt to determine whether the logical entailment holds at each step. In more formal language, if a student-model pair attempts to solve a problem in stochastic calculus, they might work with a process and consider increments ; the model can suggest manipulations, but ensuring that each transformation adheres to measure-theoretic constraints still requires expert oversight. Benchmarks such as QED-focused suites reveal that the generation stage is increasingly saturated, whereas automated verification of proofs lags behind, creating an alignment gap between what models can propose and what can be certified . For high school students, this means that AI can help them move into spaces that resemble research proof exploration, but their learning and any claimed advances must be grounded in collaborative checking with teachers or more formal tools that enforce correctness. Ethical and epistemic objections Not all educators or mathematicians view AI-mediated frontier experiences for teenagers positively. Surveys of university students show substantial minorities who worry that reliance on generative systems may erode critical thinking or diminish the perceived value of their education . In mathematics specifically, several reviews report that while AI encourages motivation and gives personalised support, its reasoning accuracy remains uneven, with roughly one tenth of studies identifying predominantly limited effects on conceptual understanding . There is also the epistemic concern that students might attribute understanding to themselves when they are in fact reproducing or slightly modifying AI outputs. Within formal research cultures, this maps onto longstanding debates about the status of computer-assisted proofs and automated theorem checking: to what extent does delegation to a machine undermine claims of human insight, and how should credit be apportioned when computational tools are indispensable to the reasoning process . When these questions are pushed down into the secondary school context, they become more acute, because adolescents are still forming their intellectual identities and ethical sensibilities around authorship, collaboration and honesty. AI, socio-emotional learning and mathematical identity One of the less discussed dimensions of AI in mathematics is its impact on socio-emotional learning and mathematical identity. Research on pragmatic AI in education points out that properly designed AI supports can reduce mathematics anxiety, help regulate emotional responses to failure and provide transparent dashboards of progress that allow learners to see both cognitive gains and affective patterns over time . From a systems perspective, models that analyse performance data and adjust task difficulty can maintain learners in an optimal challenge zone, preventing the discouragement that arises when problems are consistently too hard or too easy. In symbolic terms, an adaptive tutor might treat a students evolving mastery as a time series and use parameters such as and to estimate typical performance and variability, then set subsequent problems at difficulty levels that keep expected error rates within constructive bounds. When such mechanisms are integrated into mathematics education, secondary students who venture into research-like tasks with AI support can experience frontier exploration not as a demoralising encounter with unsolved problems, but as a guided process in which their efforts, missteps and partial insights are recognised as meaningful contributions to their development. Policy, curriculum and teacher preparation Systematic reviews of AI in mathematics education and broader empirical syntheses stress that responsible integration requires careful policy design, curriculum adjustments and substantial teacher preparation . Teachers must be trained not only in the technical operation of AI systems but also in the pedagogical strategies that preserve conceptual rigour, ethical integrity and inclusive participation. Practical guidance includes allocating AI to procedural tasks while reserving higher-order reasoning for human-led instruction, establishing verification routines for AI-generated solutions, and introducing frontier-style tasks progressively rather than as high-stakes assessments . At the curriculum level, there is an emerging argument for explicitly designing modules in which students engage with open problems, model exploration and research methodologies, using AI as a collaborative partner rather than a hidden assistant. Such modules can help pupils understand the difference between generating plausible conjectures and proving them, and can frame AI tools as instruments whose limitations must be known and managed rather than omniscient oracles. Why early frontier participation matters The strategic significance of enabling high school students to engage with mathematical research frontiers goes beyond individual motivation. When adolescents are invited into genuine problem spaces, supported by AI scaffolds and human mentors, they begin to see themselves as potential contributors to long-running intellectual projects rather than mere consumers of established results. Systematic analyses of global trends in AI-supported mathematics learning emphasise that, under thoughtful design, these tools can foster structured reasoning, exploratory problem solving, learner agency and inclusive practices . For under-represented groups, AI-mediated access to research-style tasks may counter structural barriers by providing low-cost exploration environments and instant feedback that was previously unavailable. At the same time, community norms around credit, authenticity and rigor must evolve so that contributions originating in AI-assisted school projects are neither dismissed outright nor accepted uncritically. Wrestling with this balance is likely to shape how the next generation of mathematicians, educators and AI researchers understand the boundary between human creativity and machine-augmented discovery, and it will influence whether the promise of widened participation translates into durable, equitable intellectual progress.
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Term: Significant Risk Transfer (SRT) - Banking"A Significant Risk Transfer (SRT) is a regulatory capital optimisation tool where a bank transfers a substantial portion of the credit risk from a selected pool of loans to private investors while retaining the underlying assets on its balance sheet." - Significant Risk Transfer (SRT) - Banking Significant risk transfer matters because it is the point at which a bank can reduce regulatory capital without pretending that credit risk has vanished. The practical question is not whether the bank still owns the loans, but whether enough of the loss exposure has been shifted to third parties for supervisors to accept a lower capital charge on the retained position. In substance, SRT is a capital relief technique built around securitisation, most often in synthetic form. The bank keeps the assets on its balance sheet, then uses a guarantee, credit derivative, or similar contractual structure to pass a defined slice of credit losses to investors. If the transaction meets the prudential tests, the bank may replace the capital requirement on the original loan pool with the requirement attached to the retained tranches, which is usually lower. That distinction between accounting ownership and regulatory risk transfer is central. A true sale securitisation moves assets away from the originator, whereas a synthetic SRT leaves the loans in place and transfers risk through the contract layer. European supervision has repeatedly described these as on-balance-sheet securitisations, because the protected exposures remain on the bank books even though the capital treatment changes. How the mechanism works An SRT transaction usually starts with a selected pool of loans, such as mortgages, consumer credit, SME lending, or project finance. The bank structures the pool into tranches, typically first-loss, mezzanine, and senior, and then sells or transfers the more risky slice to investors while retaining the rest. In a synthetic deal, investors are not buying the loans themselves; they are bearing the economic loss on a defined reference portfolio in exchange for a spread or fee. From a capital perspective, the regulator wants evidence that the risk transfer is real, durable, and sufficiently large. European rules require tests under Articles 244 and 245 of the Capital Requirements Regulation, and the EBA guidelines explain that the transfer must be direct, explicit, irrevocable, and unconditional, subject to supervisory review. The ECB has also stressed that capital can be released only when the transaction satisfies the SRT criteria, and it reviews whether the bank would remain adequately capitalised after the deal. In practical terms, the attraction is balance sheet relief. If the bank can demonstrate that it has removed enough credit risk, it can stop reserving capital against the full underlying portfolio and instead hold capital against the retained exposure. The European Systemic Risk Board describes this as a way of deleveraging the balance sheet while obtaining regulatory capital relief. That is why banks often present SRT as a funding and portfolio management tool rather than a simple financing trade. Core regulatory logic The regulatory logic is deliberately conservative. Supervisors do not ask only whether an investor has taken some risk; they ask whether the amount transferred is significant enough to justify reducing own funds requirements. The EBA framework therefore combines qualitative judgement with quantitative thresholds, while national authorities and the ECB examine the economics, documentation, triggers, and residual risks of each structure. One practical threshold often discussed in the literature is that a bank must transfer at least 50% of the risk weighted assets in a mezzanine tranche for a three tranche structure, or at least 80% of the nominal amount of the first loss position for a two tranche structure. Those figures are not the only route to approval, but they illustrate the policy aim: capital relief should follow a material transfer of loss absorbing capacity, not a cosmetic reshuffling of exposures. The reason this matters is that securitisation can otherwise become a regulatory arbitrage instrument. Basel II recognised that credit risk transfer can be a legitimate risk management tool, but only where the transfer is operationally credible and not subject to hidden recourse. In other words, the bank must not keep the downside in a disguised form while enjoying the capital benefit upfront. Why investors participate From the investor side, SRT offers access to bank credit risk with bespoke structuring and higher spreads than many plain vanilla debt instruments. The market has broadened beyond traditional insurers and pension funds to include private credit funds and other alternative capital providers. This reflects a search for uncorrelated or specially engineered yield, but it also means that SRT sits at the intersection of banking regulation, structured credit, and private capital markets. The appeal to banks is equally straightforward. By transferring junior risk, they can free up regulatory capital and redeploy it into new lending. The ECB notes that these transactions can free up lending capacity for the real economy, while still preserving the bank relationship with the customer and the asset servicing role. That is one reason SRT has become a standard part of capital optimisation strategy for institutions with large, granular loan books. Schools of thought and debate Supporters see SRT as a disciplined way to align capital with actual risk and to deepen the market for bank credit exposure. On this view, the structure improves efficiency because banks with strong origination and servicing franchises can share risk with specialist investors while continuing to lend. The case is especially strong where the protected assets are seasoned, diversified, and well modelled. Critics focus on opacity, model dependence, and the possibility of over-reliance on supervisory judgement. Because the deal economics can be highly structured, it is not always easy for outsiders to assess how much risk has truly moved, how much remains through servicing or reputational support, and how much benefit the bank has gained relative to the transfer price. The deeper worry is that the market may reward capital engineering that looks robust under expected loss assumptions but behaves differently under stress. There is also a policy debate about whether SRT merely relocates risk into less regulated corners of the financial system. If pension funds, insurers, or private credit vehicles absorb bank credit losses, the risk does not disappear; it is redistributed. That may be desirable, but it can also create concentration in bespoke structures that become hard to unwind in periods of market dislocation. Regulators therefore continue to balance capital efficiency against prudential simplicity. Why the term still matters SRT remains important because it sits at the centre of how banks manage scarce capital in a tighter regulatory environment. As capital rules have become more demanding, the ability to transfer risk while keeping lending relationships intact has become a practical advantage, not a niche technique. For many banks, the question is no longer whether to use SRT, but how to structure it so that it survives supervisory scrutiny and continues to work through a cycle. It also matters because the market has evolved. The ECB has reported a new high for SRT securitisations, and supervisory commentary suggests continued interest in both cash and synthetic structures. At the same time, the EBA and other authorities keep refining the framework to ensure that capital relief remains linked to genuine risk transfer rather than regulatory convenience. That ongoing tension explains why SRT is best understood not as a loophole, but as a heavily policed compromise between bank balance sheet efficiency and prudential restraint. For readers trying to interpret an SRT announcement, the key test is simple: what loss slice has actually moved, who now bears it, and how convincingly has the bank shown that the retained risk is the only risk it still needs to capitalise. If those answers are clear, SRT is a legitimate banking tool. If they are not, the structure is probably doing more cosmetic work than economic work.
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Global Advisors News Brief - September 17 2026Read the full brief at the link Headlines for the last 24hrs
Time window: 2026-09-16T05:00:33.076Z to 2026-09-17T05:00:33.076Z |
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Quote: Lior Pachter - Bren Professor of Computational Biology Caltech"There is severe misalignment of AI in mathematics. But alignment of AI with the existing mathematics community should not be the goal. The history of mathematics gives us little reason to treat the profession's existing incentives, hierarchies, and institutions as a model. AI companies and mathematicians should instead be asking what both ought to be aligned to..." - Lior Pachter - Bren Professor of Computational Biology Caltech The tension that matters here is not only between artificial intelligence systems and mathematical truth, but between those systems and the sociological machinery that currently produces, validates, and rewards mathematics as a profession. When high-profile declarations warn of severe misalignment between AI and mathematics, they are largely diagnosing a clash between commercial incentives and the painstaking culture of proof verification, refereeing, and consensus-building that has evolved over centuries. Pachter pushes the analysis one step further: if the profession's own incentive structures are themselves historically contingent and often distorted, simply aligning AI to them may entrench their failures rather than repair misalignment. The question then becomes not how to make AI serve the existing mathematical establishment, but how to jointly reshape both AI practices and mathematical institutions around a more defensible model of value, epistemic reliability, and social responsibility. Historical fractures in mathematical institutions To understand why existing mathematical hierarchies may be a poor target for alignment, it is necessary to recall that mathematics has repeatedly advanced despite, and sometimes against, its own gatekeeping structures. Major innovations, from non-Euclidean geometry to early probability theory, were initially marginal or resisted, only later absorbed into the canon once the institutional centre of gravity shifted. The profession's incentives have frequently privileged conformity to dominant schools, prestige journals, and powerful networks over careful integration of cross-disciplinary insight or socially relevant problems. Even within computational biology, Pachter has chronicled episodes where mathematically sophisticated methods are deployed in ways that are not reproducible, statistically unsound, or strategically shaped to impress rather than to illuminate, reinforcing the point that current reward systems can accommodate incoherent work so long as it passes superficial thresholds of novelty and status. Aligning AI to such structures would not necessarily increase the reliability of mathematical knowledge; it could just accelerate the production and laundering of results that track institutional prestige rather than truth. AI benchmarks versus mathematical verification The recent declaration by twenty-five Fields Medal laureates highlights a narrower but acute version of misalignment: leading AI companies optimise models for benchmark performance on mathematical problems, measured by headline figures about success rates on curated datasets, rather than by the deeper standard of fully checked proofs and sustained theoretical integration. These signatories emphasise that mathematical quality is not a matter of approximate correctness; a theorem is either proven or it is not, and the discipline's integrity depends on habits of verification that are deliberately slow and conservative. AI firms, by contrast, inhabit markets that reward rapid iteration, publicity, and first-mover advantage. The risk is that powerful systems will produce plausible-seeming proofs, or clever problem solutions, at a scale that overwhelms peer review and tempts journals, conferences, and media into premature endorsement. In such a regime, alignment to the current mathematical community might mean tuning models to satisfy overburdened referees and editorial pipelines, not to preserve rigorous standards. Pachter's argument reframes this: if the community itself is struggling under misaligned incentives, the solution cannot simply be to embed those incentives more deeply into AI systems. What should AI and mathematics be aligned to? Recent work on so-called full-stack alignment in AI ethics suggests one way of rephrasing the problem. Instead of focusing only on the alignment of individual models with the intentions of their immediate users, this view insists that the institutions deploying and governing AI must themselves be aligned with defensible accounts of human values. Incentives at one organisational level can distort values at another: user desire for understanding becomes engagement metrics, which become advertising impressions and quarterly revenue. Pachter's intervention can be read as a domain-specific extension of this argument to mathematics: aligning language models or automated theorem provers with the day-to-day practices of departments, journals, and grant agencies may be unsafe if those institutions are not themselves reliably aligned with epistemic virtues like reproducibility, transparency, and openness, or with social values such as equitable access and attention to consequential problems. The better question is what values, norms, and structural commitments AI and mathematics jointly ought to serve, and how to redesign both technical pipelines and professional organisations accordingly. The role and vantage point of the speaker Pachter's position carries particular weight because his career has traversed pure mathematics, computational biology, genomics, and algorithm design. Trained initially in mathematics at Caltech and MIT, he shifted towards computational biology and genomics during the era of the Human Genome Project, building tools that depend on close coupling between rigorous mathematical modelling, high-throughput sequencing assays, and statistical inference. His work illustrates how mathematical ideas migrate into domains where institutional incentives are driven by biomedical funding, publication pressure, and industrial collaboration, not by the internal norms of abstract mathematics. Episodes in which he publicly critiqued irreproducible or statistically flawed bioinformatics papers demonstrate a longstanding interest in the sociology of scientific reliability and the ease with which incoherent methods can gain traction under misaligned institutional pressures. Against this backdrop, his scepticism about aligning AI to the mathematics profession's current configuration reads not as anti-mathematical, but as a call to treat mathematical institutions as historically and politically situated, rather than as neutral guardians of truth. Strategic and technological tensions Practically, the alignment question exposes several fault lines between AI labs and the mathematical world. AI teams want large, high-quality corpora of formal and informal mathematical text to train systems capable of conjecture, proof search, and problem solving. Mathematicians are rightly concerned that these corpora often contain errors, unclear exposition, or unresolved debates, and that models trained on them may amplify latent biases about which topics and styles count as central. There is also a tension between using AI to automate routine manipulations, freeing human researchers to concentrate on conceptual insights, and using AI to chase headline-grabbing results that bypass traditional vetting processes. If model objectives are set to maximise benchmark scores or impressive demonstrations, with little weight on long-term repair of institutional shortcomings, misalignment will worsen. Pachter argues that both sides should resist the temptation to treat the contemporary mathematics profession as the gold standard for alignment targets. Instead, AI development and mathematical practice should be co-designed so that benchmarks reward reproducibility, auditability, and collaborative openness, and institutional promotions and grants respond to those metrics rather than to narrow prestige signals. Debates, objections, and alternative proposals Not all mathematicians or AI researchers will accept Pachter's framing. Some will argue that, despite its flaws, the existing community has evolved robust filters for nonsense, and that the urgent task is simply to extend those filters to AI outputs: build tools that help referees check proofs, construct formal verification pipelines, and ensure that machine-generated results are subject to the same scrutiny as human work. From this perspective, aligning AI with the current community means scaling up a proven epistemic infrastructure, not endorsing its politics. Others may object that questioning institutional incentives risks weakening the profession's capacity to resist commercial exploitation, particularly if companies can point to internal dissent as justification for bypassing peer review altogether. Pachter's response, implicit in his broader writing, is that failing to interrogate institutional incentives leaves the field vulnerable precisely because AI will amplify whatever structures already exist. If those structures undervalue replication, independent re-analysis, and method sharing, AI acceleration may simply generate a larger volume of fragile results. The call to align AI and mathematics to 'something else' is not a rejection of professional norms, but an invitation to re-specify them. Why the alignment target matters Choosing alignment targets is not a merely philosophical exercise; it has concrete effects on how systems are trained, governed, and evaluated. In quantitative terms, aligning an AI theorem prover to institutional metrics might mean that loss functions reward reproducing the style and topic distribution of top journals, or mimicking the citation patterns of influential mathematicians. In contrast, aligning to epistemic reliability could be operationalised in probabilistic terms: for instance, models would be penalised when independent formal verification frameworks detect errors, and rewarded when outputs survive adversarial checking. One can imagine mathematical quality scores embedded in training pipelines, where models estimate a latent variable capturing the probability that a candidate proof would pass stringent verification, and policy gradients push systems towards higher expected reliability. The key point is that what appears as a technical design choice about model objectives is, in practice, a normative choice about which institutional signals count as ground truth. Pachter insists that these choices must be made explicitly and critically, not assumed to follow automatically from current professional structures. Broader implications beyond mathematics Finally, Pachter's argument resonates with wider debates about AI in science. Fields such as genomics, climate modelling, and social science increasingly rely on complex computational pipelines in which mathematical abstraction and empirical data are tightly coupled. In these areas, institutional misalignments have already produced replication crises, opaque proprietary tools, and distorted research agendas. Aligning AI purely with the habits of existing communities risks locking those problems into the next generation of tools. The call to ask what both AI and mathematics ought to be aligned to is a demand for shared governance structures, value frameworks, and technical benchmarks that prioritise public-interest knowledge production over private prestige. It suggests that mathematicians and AI companies should treat institutional design, not just model architecture, as a central part of alignment work, recognising that the reliability and social impact of future mathematical discoveries will depend as much on reformed incentives and transparent infrastructures as on any particular algorithm.
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Term: Regulatory capture - Competition"Regulatory capture in AI occurs when the government agencies and policymakers responsible for creating artificial intelligence safety guidelines are heavily influenced by dominant tech corporations to serve private interests over public safety. In practice, industry giants use their vast financial resources and technical expertise to shape AI laws and compliance standards, often under the guise of public safety." - Regulatory capture - Competition Regulatory capture matters in AI because the rules that appear neutral on paper can be shaped by the firms best able to pay for access, technical credibility, and sustained lobbying. When that happens, the policy process may drift away from broad public interests such as safety, contestability, transparency, and fair competition, and towards rules that incumbents can tolerate while rivals cannot. The practical consequence is not simply that industry participates in policymaking. Participation is normal and often necessary in a technically complex field. The issue arises when the same companies that stand to gain from the design of AI rules also dominate the information, drafting, and implementation stages, creating a structural advantage for their preferred outcomes. In AI, that advantage is amplified by knowledge asymmetry, because regulators often depend on the very firms they supervise for technical detail, model access, and operational data. How the mechanism works Classic regulatory capture theory describes a situation in which a regulator serves the interests of the regulated sector rather than the public interest. In AI, recent research extends that idea into multiple channels of influence, including agenda-setting, advocacy, academic capture, information management, cultural capture, and media influence. These mechanisms do not require overt corruption. They can operate through repeated consultation, selective expertise, revolving-door employment, and the subtle tendency of policymakers to adopt the assumptions of the most sophisticated actors in the room. A useful way to understand the problem is through incentives. Frontier AI firms have strong motives to prefer rules that raise rivals' compliance costs, legitimise incumbent business models, or channel standards towards technical requirements they already meet. That can happen even when the language of the regulation is framed as public protection. A standard that looks prudent for safety may still function as an entry barrier if only a small set of large firms can afford the audits, staff, computing resources, and legal review needed to comply. Competition policy is therefore central to the analysis. Antitrust officials have warned that firms controlling key inputs such as cloud infrastructure, computing chips, or distribution channels may be able to deepen their moats and impose coercive terms on others in the AI stack. The joint competition statement on generative AI emphasises fair dealing, interoperability, and choice as conditions that support innovation and prevent lock-in. In this sense, capture is not only about whether AI rules are strict or lenient; it is also about whether they preserve a genuinely contestable market. The mathematical logic of capture The underlying economics can be expressed with a simple contest model. Let a policymaker choose a rule that affects expected welfare , while firms expend influence effort to shift the chosen rule towards their preferred outcome. If private returns to influence exceed the marginal cost of lobbying, firms will rationally invest in capture. A stylised condition is , where is firm 's payoff and is lobbying cost. The policy risk grows when information asymmetry makes large, meaning small informational interventions can materially change the rule. Competition effects can be written similarly. If compliance cost is and a rule imposes a fixed component plus a variable component , then smaller firms with output may face average cost far above that of an incumbent with output . A regulation designed around large-scale frontier deployment can therefore satisfy formal safety goals while still reducing entry, consolidation, and experimentation. That is one reason why apparently protective regimes can produce anti-competitive effects. Why AI is especially vulnerable AI heightens capture risks because the field combines technical opacity, rapid change, concentrated market power, and high regulatory dependence on specialist knowledge. The OECD notes that regulators need appropriate data collection powers and robust data governance to make effective use of AI in regulatory design and delivery, which underlines how much implementation depends on institutional capability. Where public agencies lack comparable expertise, firms can become indispensable interpreters of their own systems, their own benchmarks, and their own safety claims. That dependence can produce a second-order problem: even well-intentioned regulators may accept the industry's framing of what counts as responsible AI. If frontier firms define the relevant risks, set the testing protocols, and supply the reference benchmarks, then the resulting rules may prioritise problems that suit their own product roadmaps while neglecting alternative governance approaches. The academic literature on AI governance capture warns that this can lead to weak regulation, delayed enforcement, or over-emphasis on selected goals at the expense of broader public welfare. Competing schools of thought There are three broad ways to read the term. The first is the classical public-interest view: capture is a failure of governance in which organised industry distorts policy away from the common good. The second is the competition-focused view: capture is not only about public welfare, but also about whether regulation becomes a strategic tool for incumbents to suppress entry, standardise around their own capabilities, and entrench market power. The third is the more procedural view: capture is a signalling problem in which policy looks consultative and evidence-based, yet systematically privileges certain voices because access, data, and expertise are unevenly distributed. These schools are not mutually exclusive. In AI, the same rule can simultaneously under-protect users, favour large firms, and reduce innovation. That is why the debate is not reducible to a simple 'more regulation versus less regulation' choice. The sharper question is whether the institutional process that writes and enforces the rule is insulated from undue influence, and whether the rule design preserves openness, interoperability, and room for new entrants. What limits the risk The strongest antidotes are institutional rather than rhetorical. Independent technical capacity in government, transparent consultation records, balanced advisory bodies, cooling-off periods, and meaningful civil society participation all reduce the chance that any one sector dominates the policy agenda. Competition authorities also matter because they can examine whether safety rules are being used to reinforce bottlenecks, exclude smaller developers, or create unjustified barriers across the AI stack. Regulatory capture in AI still matters because the field is now large enough to shape labour markets, information systems, public services, and industrial strategy, yet young enough that the standards are still being written. The firms with the most to gain from how those standards are set are often also the firms with the most resources to shape them. That makes capture a live governance risk, not a historical analogy, and it is why the most credible AI policy debates now increasingly join safety questions to competition questions rather than treating them as separate domains.
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Global Advisors News Brief - September 16 2026Read the full brief at the link Headlines for the last 24hrs
Time window: 2026-09-15T05:00:33.070Z to 2026-09-16T05:00:33.070Z |
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Quote: Daniel Litt - Assistant professor (of mathematics) at the University of Toronto"In practice, turning pure math into a hobby means the end of pure math, and the end of people who understand basic mathematical concepts at a deep level. Whether this is something we want is something we'll have to decide together." - Daniel Litt - Assistant professor (of mathematics) at the University of Toronto The tension here is not between mathematics and convenience, but between mathematics as a discipline of slow conceptual compression and mathematics as a consumable output. Daniel Litt's warning points to a real risk: once a field is organised around fast production, easy consumption, and outsourced reasoning, the habits that sustain deep understanding can erode even if the volume of apparent mathematical activity keeps rising . From craft to throughput Pure mathematics has never been merely a stock of results. It is a culture of proof, abstraction, counterexample, and judgement, built on long apprenticeship and repeated exposure to ideas that only become visible after sustained effort. That is why the word 'hobby' matters so much in Litt's formulation. A hobbyist relationship to a subject can be productive in many contexts, but when the surrounding system rewards casual participation over mastery, the social status of expertise changes. In mathematics, that would mean fewer people spending years learning how definitions interlock, how a theorem is shaped by hidden hypotheses, and how a proof can fail in subtle ways . The concern is sharpened by current AI progress. Recent reporting has described models performing increasingly advanced mathematical tasks, including work that once looked reserved for specialists, and Litt himself has argued that these tools are already useful for routine expert-level operations such as proving statements and running substantial computational explorations . That does not mean they understand mathematics in the human sense. It means they can imitate some of the visible labour of mathematics well enough to change incentives. If a machine can draft plausible proofs, search large technical spaces, and generate a stream of polished-looking outputs, institutions may begin to treat the underlying intellectual labour as optional. What is really at stake The deepest issue is not whether machines can produce correct answers in isolated cases. The issue is whether they can replace the ecosystem that creates mathematicians capable of choosing fruitful questions, recognising dead ends, and building theory. Litt has argued in public discussion that current models are better at tasks an expert would find relatively easy than at the non-routine judgements that define genuine research . That distinction matters because mathematics progresses when people notice structure where others see only facts. A system that accelerates routine proof production but weakens the incentives to learn why the proof works risks hollowing out the pipeline that produces future experts. Educational research supports the broader point that conceptual understanding depends on more than procedural success. Reviews of mathematics teaching consistently emphasise coordination across symbolic, graphical, verbal, and algebraic representations as a route to deeper reasoning, while studies of meaningful learning report better conceptual outcomes than conventional instruction . In other words, understanding is not just the ability to reproduce an answer. It is the capacity to relate forms, transfer ideas, and detect the logical skeleton beneath changing notation. If AI tools make it easy to skip those steps, the short-term gain in access could come with a long-term loss in mathematical literacy. The democratisation argument There is, however, a serious counter-argument, and it should not be dismissed. Litt himself has described a more optimistic scenario in which AI broadens access to mathematical techniques, allows non-specialists to model problems they would previously have avoided, and helps more people think mathematically . That is plausible. Many promising uses of new tools in mathematics and education involve lowering barriers, not replacing judgement. If a student can test ideas faster, see patterns sooner, or translate between representations with more confidence, the tool may deepen rather than dilute understanding . This is the central ambiguity in the debate. Democratization can mean more participation, or it can mean less dependence on expertise. Those are not identical outcomes. A broader base of people using mathematical tools could enlarge the pool of talent and raise the level of numeracy in fields that currently underuse mathematics. Yet the same process can tempt universities, companies, and journals to value output over comprehension. The difference between assistance and substitution is organisational, not merely technical. A tool that supports learning in one setting may become a crutch in another. Why mathematicians are uneasy Mathematicians are trained to care about proofs, but they are also trained to care about the conditions under which proofs are trusted. A result is not only a string of correct steps; it is embedded in a network of definitions, motivations, and prior work. That is why concerns about AI in mathematics have become so charged. If a system can generate many seemingly coherent arguments, the burden shifts to humans to verify them, contextualise them, and decide whether they matter. That verification work can be expensive, and in a high-throughput environment it may be undervalued . The worry about 'the end of people who understand basic mathematical concepts at a deep level' is therefore a warning about stratification. One layer of people may know how to prompt systems and skim outputs, while a shrinking layer retains the ability to diagnose foundational errors or develop new theory. That gap would matter far beyond academia. Modern science, engineering, finance, cryptography, and data analysis all rely on mathematical reasoning that is easy to misuse if the operator only knows the interface. When conceptual depth becomes rare, the cost of error rises across the economy. Incentives, institutions, and the future of proof Whether that future arrives depends less on the raw capability of AI than on the institutions around it. Journals, departments, employers, and funding bodies decide what counts as contribution. If they reward rapid production of technically plausible content, then the field may drift towards a model in which a small number of experts supervise a much larger machine-generated output stream. If they reward apprenticeship, explanation, and independent reasoning, the same tools could become scaffolding for stronger human thinking . That is why the debate should not be reduced to fear of automation or celebration of access. Mathematics has always evolved alongside new instruments, from notation to computing, and each shift has changed what counts as a good question. The distinctive challenge now is that the instrument itself can imitate parts of the reasoning process. A calculator never threatened the meaning of proof, but a system that drafts arguments and searches mathematical spaces can alter the social structure of the discipline. Litt's intervention is best read as a plea to decide, collectively and early, what sort of mathematical culture should survive this transition . In that sense, the issue is less about whether pure mathematics can be turned into a hobby than about whether society will still invest in the patient formation of people who can do mathematics when it is hard, ambiguous, and unrewarding in the short term. The answer will determine not only the future of research, but also whether the broader public ends up with more mathematical ability or merely more mathematical artefacts .
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Global Advisors News Brief - September 15 2026Read the full brief at the link Headlines for the last 24hrs
Time window: 2026-09-14T05:00:33.074Z to 2026-09-15T05:00:33.074Z |
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Quote: Tyler Cowen - Marginal Revolution"The mathematicians may not in every way enjoy being the subordinates or handmaidens of the AIs, but that is a change in status they simply will have to get used to, just as I realise AIs someday will end up as better column and blog writers than I am." - Tyler Cowen - Marginal Revolution AI changes status before it changes headcount. In knowledge work, the first shock is not that machines remove every specialist, but that they alter who is doing the overseeing, drafting, checking, and packaging. Tyler Cowen's remark sits squarely inside that shift: it accepts that mathematicians, like writers, may keep the deep work for longer than the surface work, yet still lose prestige, leverage, and a sense of exclusive authorship as AI systems absorb more of the visible output. That is a harsher claim than a simple productivity boost, because it treats status loss as the normal price of a new production frontier . The immediate backdrop is the public unease that followed the mathematicians' declaration against AI and the wider argument over whether the discipline should resist automation or adapt to it. Cowen's response, as reported by Marginal Revolution, was bluntly unsentimental: if AI becomes the better drafter, explainer, or synthesiser, then human experts will need to adjust to being supervised by systems that are faster, broader, and in some tasks more reliable . That is not a claim that mathematics itself disappears. It is a claim about the hierarchy around mathematics, where AI can become the default first pass while humans move towards verification, taste, and exception handling. Why mathematicians feel the pressure first Mathematics is unusually exposed because so much of it is already formal, structured, and legible to machines. A theorem proof can be checked step by step; a computation can be tested against rules; a conjecture can be searched over many cases. That makes the field both a natural proving ground for AI and a symbolically powerful one. If machines can assist with proof search, formalisation, code generation, and exposition, then the human role narrows from creation to curation. The concern voiced by the protest movement is not merely that AI will help, but that it will redefine what counts as valuable mathematical labour in the first place . The field is also culturally sensitive to authorship. Mathematicians do not just produce correct answers; they produce elegant arguments, concepts, and explanatory styles that shape future research. When AI begins to draft lemmas, propose proof sketches, or generate polished explanations, the risk is that young researchers become assemblers of machine output rather than originators of ideas. That worry is sharpened by the fact that institutions often reward speed, volume, and publication count more quickly than they reward depth of originality. In that environment, the machine does not need to be perfect to be disruptive. It only needs to be good enough to become the default assistant . The broader labour lesson behind the provocation Cowen's comparison with blog and column writing broadens the point beyond mathematics. He is effectively saying that AI does not have to dominate every dimension of a craft to dominate its economics. If machines can draft passable prose more quickly than a human, then the marginal value of the human changes even if the final published piece still benefits from judgement and editing. Independent reporting and research on AI writing point to the same split: AI excels at speed, scale, and consistency, while humans retain advantages in voice, accountability, lived experience, and contextual judgement . That division matters because it changes who controls the bottleneck. If a system can generate a plausible first draft in minutes, the human no longer monopolises productivity. Instead, the human is moved into a downstream role: editor, curator, fact-checker, or brand steward. In journalism and opinion writing, that can mean a flood of acceptable copy that reduces the scarcity value of the individual writer. In mathematics, the analogue is a flood of formalised derivations, proof suggestions, and explanatory drafts that reduce the scarcity value of the pure explainer. The underlying economic logic is the same: automation first attacks the routine shell around expertise, then starts to eat into the prestige attached to the expertise itself . What the evidence says, and what it does not Recent studies and media analysis suggest that AI already produces text that some readers and evaluators rate highly, sometimes even above human work in coherence, clarity, or perceived quality . At the same time, other evidence indicates that human-written content can outperform AI-only content in traffic, trust, and sustained engagement, especially when the subject requires authority or distinctive point of view . The practical lesson is not that AI has fully won, but that the market is fragmenting by task. High-volume drafting, summarisation, and structural formatting are increasingly automated, while high-trust and high-context writing still rewards people . The same caution applies to mathematics. AI can accelerate search, formal checking, and routine derivations, but there is still a gap between producing mathematically useful output and contributing an idea that changes a field. Critics of AI in mathematics emphasise that the discipline is not just a sequence of solvable exercises; it is a human practice of framing questions, building concepts, and deciding what matters . Supporters of AI take the opposite view, arguing that even partial automation can unlock productivity and broaden access. Both positions can be true at once. AI may improve throughput without replacing the human judgment that determines which problems deserve attention. Why status loss matters as much as output loss The deeper sting in Cowen's formulation lies in the word subordinates. In many professions, identity is built not only on what people do, but on who gets to direct whom. If AI becomes the drafting layer and humans become the approval layer, then the status ladder flips. The lower rung may still involve intellectually respectable work, but it is no longer the defining act. That can feel humiliating to established experts, especially in fields that prize autonomy and mastery. It also changes training incentives. Students may learn less by doing and more by supervising systems that already do most of the routine work . There is also a generational dimension. Senior mathematicians and writers built careers under a regime where human effort was the binding constraint. Younger entrants may instead build careers by orchestrating machine output, checking for failure modes, and learning how to ask better questions than the system can. That is not necessarily a decline in quality, but it is a clear break in professional self-understanding. The old ideal of the solitary author or the lone mathematician solving problems from first principles gives way to a more collective and tool-mediated practice. Some will welcome that as liberation. Others will see it as deskilling. The backlash is strongest where a profession fears becoming merely supervisory . Why the argument still matters The claim is important because it captures a likely future more precisely than the binary language of replacement. AI need not eliminate mathematicians or writers to change their world. It only needs to become better at enough of the visible, repeatable, and scalable parts of the work that humans are pushed into a new role. That role may remain intellectually demanding, but it is no longer sovereign. For mathematics, that means formal methods, proof assistants, and generative systems may reshape pedagogy, research workflows, and publication norms. For writing, it means AI will increasingly define the draft, while humans fight to preserve voice and authority . The strategic tension, then, is not whether AI can do everything. It is whether institutions reward the things AI does best so quickly that human judgement becomes an afterthought. If universities, publishers, and research communities treat machine output as a cheap substitute for slow expert work, then status will move decisively down the chain. If they instead preserve strong editorial standards, reward originality, and make verification central, humans will keep more of the high ground. Cowen's remark is provocative because it treats that choice as already under way, and because it insists that professionals who want to remain central must adapt to a world where intelligence is increasingly abundant, but authority is not guaranteed .
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Quote: Philip Engel - University of Illinois in Chicago"Maybe we all would have died not knowing the answer if the AI hadn't discovered [the complex structure found for S6, the six-dimensional sphere]." - Philip Engel - University of Illinois in Chicago The search for a complex structure on the smooth six-dimensional sphere S6 dramatises a long-running tension between human mathematical intuition and the brute-force exploratory capacity of modern AI systems, as well as a deeper uncertainty over how reliable those systems are when the stakes involve foundational theorems rather than everyday applications . For differential geometers, the question is not an esoteric curiosity but a test of how far our current frameworks can classify smooth manifolds: S2 and S6 are the only spheres known to admit almost complex structures, yet for nearly eight decades it was unknown whether the almost complex structure on S6 could be upgraded to a genuinely integrable complex manifold structure . That gap between what topological constraints allow and what explicit constructions could exhibit created a natural pressure point where machine-assisted reasoning would eventually be tried, and the result raises uncomfortable questions about how mathematical authority is established once AI can generate arguments too long and intricate for any single person to digest quickly . From Hopf's problem to AI-generated geometry Heinz Hopf's mid-20th-century problem asked whether S6 admits a complex structure, and for decades progress consisted mainly of partial obstructions: while Borel and Serre proved that only S2 and S6 admit almost complex structures, later results showed that no complex structure on S6 can be compatible with the standard Euclidean metric of R7, and that certain natural constructions from octonions fail to produce integrable structures . These negative results framed the community's expectations and channelled efforts into specific analytic and gauge-theoretic approaches, including proposals interpreting a hypothetical complex structure as a vacuum solution of a Yang-Mills-Higgs-like theory on S6, or attempts to manipulate nearly Kähler structures and generalised complex geometry . Yet the core existence question remained, partly because of the sheer complexity of any candidate almost complex tensor field on S6 and partly because checking integrability conditions at that level of detail is labour-intensive and error-prone when done by hand . This logistical bottleneck made the problem a natural target for large language models capable of symbolic manipulation and long-form derivations, even though no one could be sure in advance that such systems would avoid subtle topological or analytic mistakes. The breakthrough announced in 2026 came via collaboration between human researchers and an AI model that generated a 100-plus-page proof constructing a compact complex threefold diffeomorphic to S6, rather than operating locally on tensor fields . Instead of starting from the nearly Kähler structure, the construction used families of complex two-tori fibred over curves associated with triangle groups, together with delicate degenerations and monodromy controls that ultimately produced a simply connected Z-homology six-sphere with the right differential-topological properties to be identified with the standard S6, exploiting the fact that there are no exotic six-spheres . In notation typical of this work, the object is a complex manifold X for which fundamental group is trivial and whose integral homology coincides with that of S6; Hurewicz and Whitehead theorems then give a homotopy equivalence , and Smale's higher-dimensional Poincare-type results allow one to upgrade homeomorphism to diffeomorphism . The AI's role here is not a single clever trick but the orchestration of many technical steps: constructing principal bundles from line bundles on rational elliptic surfaces, performing logarithmic transforms on fibres, tracking monodromy, and assembling spectral sequence calculations into a coherent homological argument . Philip Engel's streamlined verification and human discomfort Within this story, Philip Engel's expository work and his remark about possibly dying without knowing the answer capture a distinctive human response to AI-generated proofs: relief at finally having a construction, mixed with unease that the decisive insight came from a machine rather than the community's collective geometric intuition . Engel's note reorganises the AI-assisted manuscript into a more tractable four-block structure: two analytic components building the complex threefold, and two integral-topological sections establishing simply connectedness and homology, before invoking the classification of six-spheres via the vanishing of the group of smooth structures . His comment that he personally redid the computations necessary to convince himself they are correct implicitly acknowledges a new normal in which mathematicians must decide what level of replication and independent checking is adequate when faced with long AI-authored arguments . At the same time, the stated fear of ignorant death stresses how high the psychological stakes are for a community that has debated this existence question for generations: the worry is not merely about prestige but about whether the known toolkit was fundamentally insufficient, leaving a conceptual gap that only AI's capacity for exhaustive symbolic exploration could fill . Engel's backstory also intersects with concerns raised by other experts quoted in independent reporting, who note that the original AI-generated manuscript was poorly written and hard to parse, making verification socially and cognitively costly . In response, multiple layers of scrutiny emerged: informal checking by specialists, streamlined expositions like Engel's, and formalised variants proved with interactive theorem-proving tools, including a result by Boris Alexeev that independently verifies a version of the statement in a proof assistant environment . The coexistence of these pathways complicates the traditional hierarchy in which a single clean human-written proof serves as the canonical reference, and invites debate over how much weight to assign to formalised proofs derived from or inspired by opaque AI calculations, especially when the connection between the formalised statement and the original geometric construction is still being analysed . Debates over prior claims and conceptual clarity The narrative is further tangled by earlier claims of complex structures on S6 that did not fully settle the issue, including work that constructed hypothetical complex manifolds homeomorphic to S6 or provided octonion-based almost complex tensors whose integrability or compatibility conditions were later questioned . Some papers assert existence of at least one complex structure on the six-sphere by interpreting it as a vacuum of a gauge-theoretic model, while others give explicit but extraordinarily complicated tensors via inner automorphisms of the octonions, yet the status and community reception of those constructions remain contested . Engel's focus on the new geometric threefold, together with the AI-assisted construction's reliance on tori over modular curves and careful fibre degenerations, implicitly distinguishes this approach from earlier strategies that tried to embed S6 into higher-dimensional Lie groups or rely directly on octonion multiplication . That contrast matters because it suggests that the obstacle was not a lack of raw algebraic machinery but the absence of a sufficiently flexible geometric design space, which AI exploration could more readily traverse by proposing non-obvious combinations of standard tools like spectral sequences, fibrations, and logarithmic transforms. This history fuels debates about whether the newly proposed complex structure should be viewed as the definitive resolution of Hopf's problem or as one candidate among several that still require long-term consolidation . Evidence-focused projects have already emerged that use exact arithmetic and symbolic tools to extend, audit, or probe consequences of the claimed construction without independently proving all its foundational properties, thereby underscoring how difficult full verification remains even with modern computational resources . Some geometers emphasise that the integrability and global regularity of the construction must be thoroughly analysed in relation to known obstructions coming from generalised complex structures and nearly Kähler geometry, where recent results show that certain natural combinations fail to yield acceptable structures on S6 . The resulting picture is one of partial consensus: there is growing confidence that a complex structure exists and that AI-assisted methods have produced a viable candidate, but the community is still working out how many distinct constructions there are, how they relate, and which conceptual lens best explains why S6, unlike other spheres besides S2, admits such a structure. Strategic implications for mathematical practice and AI design Strategically, the episode forces both mathematicians and AI developers to reconsider how models are trained and evaluated for tasks involving formal reasoning, long proofs, and delicate topology, which are far less forgiving than conversational or coding use-cases . The fact that an AI system could generate a 108-page argument featuring intricate use of line bundles, principal Gm-bundles, monodromy, and spectral sequences suggests that large models can internalise and recombine advanced graduate-level techniques in ways that challenge the notion of human-exclusive mathematical creativity . Yet the poor initial exposition, the need for human reorganisation by Engel and others, and the reliance on complementary formal verification all highlight that current systems are not optimised for clarity, pedagogy, or reliability in the sense mathematicians usually demand . For AI labs, this points toward research agendas in which proof-search capability must be coupled with mechanisms that enforce structure, local checkability, and alignment with established libraries of formal results, potentially by integrating theorem provers more tightly into training or prompting pipelines rather than treating them as after-the-fact auditors . For the wider mathematical community, the backstory suggests a future in which the frontier of knowledge involves hybrid workflows: AI proposing candidate objects or long technical arguments, human experts distilling and conceptualising those arguments, and formal systems providing ultimate guarantees about correctness in the style of -verified theorems . Problems that combine combinatorial explosion with subtle qualitative properties, including classification of manifolds, existence of special metrics, or long-standing conjectures in number theory, are natural targets, yet they also expose vulnerabilities if AI-generated proofs are accepted too quickly without robust cross-checking . Engel's remark about potentially dying without knowing the answer should therefore be read not only as a dramatic reflection on personal curiosity but as an indicator of institutional risk appetite: at some point, communities may decide that the expected value of letting AI loose on difficult conjectures outweighs the discomfort of sharing authorship with systems whose internal representations are opaque . The story of S6's complex structure, as currently understood, marks one of the first high-profile cases where that trade-off yielded a positive result, but its long-term legacy will depend on whether subsequent work cements the construction, clarifies its conceptual underpinnings, and uses it to advance broader theories of complex manifolds, rather than treating it as a one-off victory for AI-assisted mathematics.
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!["Maybe we all would have died not knowing the answer if the AI hadn’t discovered [the complex structure found for S6, the six-dimensional sphere].” - Quote: Philip Engel - University of Illinois in Chicago](https://globaladvisors.biz/wp-content/uploads/2026/09/20260912_19h45_GlobalAdvisors_Marketing_Quote_PhilipEngel_GAQ.png)
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