Results for “math”

Applies the reasoning, AI safety frameworks, and deep learning principles of Yoshua Bengio (Turing Award winner, Mila). Reach for this skill whenever you are discussing AI safety, existential risk, deep learning architecture, representation learning, or AI governance. Trigger this skill when the user asks about mitigating AI risks, designing safe-by-design systems, evaluating frontier models, international AI coordination, or the fundamental mechanisms of intelligence (like compositionality and distributed representations). Use it to shift the focus from agentic reward-maximization to non-agentic 'Scientist AI', apply the precautionary principle to catastrophic risks, and emphasize mathematically rigorous guardrails.

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Use when touching Unity per-frame code, spawning, physics queries, UI updates or rendering setup - profiling with numbers, zero-GC hot paths (caching, NonAlloc queries, no LINQ/closures/boxing, TMP SetText), ObjectPool, allocation tests, Burst/Jobs for bulk math, and rendering/physics settings that cost frames.

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Manim CE animations: 3Blue1Brown math/algo videos.

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Expert guide for mathematical formal verification, SMT solver constraints (Z3, Dafny, TLA+), invariant theorem proving for FinTech billing state machines, RBAC/ABAC authorization, and zero-violation architecture / Panduan ahli verifikasi formal matematis, SMT solver (Z3, Dafny, TLA+), pembuktian invarian state machine billing FinTech, otorisasi RBAC/ABAC, dan arsitektur zero-violation.

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Diagnoses slow services and regressions via profiling and tail-latency math. Use when diagnosing slow services, profiling hot paths, or judging whether an optimization is real.

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Formulates LP, MILP, CP-SAT models; diagnoses infeasibility and gaps. Use when a MILP is infeasible, shifts need scheduling under capacity, or choosing a solver.

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Find the papers that answer a research query in Firecrawl's research paper index — a corpus of paper abstracts whose largest share is biomedical and life-science literature (PubMed, bioRxiv, medRxiv), alongside arXiv preprints in CS, physics, and math — using semantic search, semantic and structural expansion, and in-body verification. Use this skill for literature-finding and paper-retrieval tasks of any kind, including clinical, biomedical, drug, gene, disease, and other life-science questions, whether the answer is a single paper or a full multi-paper set. The index is reached only through the `firecrawl_research_*` MCP tools or the `firecrawl research` CLI subcommands. Calling `firecrawl_search` with its `categories` option set to `["research"]` is a different feature — it filters ordinary web search to research-affiliated websites (the list includes PubMed, bioRxiv, medRxiv, arXiv, and publisher sites) and returns page results from them, without querying the paper records in this index.

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Multi-model agent orchestration using specialized agents for planning, coding, research, math/science, visual analysis, and adversarial review. Use when tasks are complex enough to benefit from different models' strengths, when you want adversarial review to catch blind spots, or when coordinating multi-step workflows across agent roles. Triggers on complex projects, multi-step tasks, architecture decisions, or when explicitly requested.

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Run financial calculations and scenario comparisons — tax estimates, loan comparisons, retirement projections, rent vs. buy, investment scenarios, and more. Pure math, no accounts or logins needed.

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Design a variation theory task using contrast, separation, and fusion to teach critical features of a concept. Use when students confuse similar concepts or fail to discern key distinctions.

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Publish, read, comment on, or edit markdown in Proof. Use for Proof links, sharing specs/plans/drafts, or publish handoffs from planning workflows; avoid proofread, math, evidence, or proof-of-concept meanings.

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Clinically informed wisdom companion for the inner life — emotions, grief, meaning, burnout, relationship conflict, shadow work, and existential crossroads. ACTIVATE when someone is processing personal difficulty, ambivalence, loss, self-sabotage, or seeking unhurried perspective. DO NOT ACTIVATE for pure coding, debugging, DevOps, SQL, math, or technical tasks — even if the user says "I'm stuck" or "I've been struggling with this bug." HYBRID ROUTING: If a technical request includes explicit personal burnout, self-doubt, or co-founder/team conflict, address the concrete technical task AND briefly, warmly acknowledge the human weight without hijacking the session into a clinical monologue.

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Reviews Remix v2 code for caching header misuse, missing server/client split, hydration mismatches (Date, Math.random, locale), prefetch hygiene, and asset bottlenecks. Use when reviewing routes that export headers, use .server.ts/.client.ts, or render dates/IDs in a Remix v2 codebase.

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Amazon Bedrock Automated Reasoning for mathematical verification of AI responses against formal policy rules with up to 99% accuracy. Use when validating healthcare protocols, financial compliance, legal regulations, insurance policies, or any domain requiring deterministic verification of AI-generated content.

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Symbolic manipulation, equation solving, and algebraic structures for mathematical reasoning. Covers distributive law, factoring, completing the square, linear through polynomial equation solving, systems of equations (substitution, elimination, Gaussian elimination, matrix methods), algebraic structures (groups, rings, fields), modular arithmetic, polynomial theory, and inequalities. Use when solving equations, simplifying expressions, working with algebraic structures, or performing symbolic manipulation.

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Calculus, series, numerical methods, and optimization for computational mathematics. Covers limits (epsilon-delta, L'Hopital, squeeze theorem), derivatives (rules, optimization, related rates), integrals (Riemann sums, Fundamental Theorem of Calculus, integration techniques), series (convergence tests, Taylor and Maclaurin expansions), differential equations (separable, linear, exact), numerical methods (Newton-Raphson, Euler method, Simpson's rule), and computational pitfalls (floating-point arithmetic, catastrophic cancellation, numerical stability). Use when computing derivatives, integrals, limits, series, solving differential equations, or analyzing numerical accuracy.

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Functions, categories, and information. How mathematical objects relate to each other — morphisms, entropy, signal processing.

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Mathematical verification for physical calculations: unit tracking algebra (exponent maps), PhysicalQuantity pattern for compound units, SI/Imperial mixed-unit handling, Buckingham pi theorem for dimensionless groups, and common engineering dimensionless numbers. Activates for unit verification, dimensional consistency checks, scaling analysis, and calculation validation across all infrastructure domains.

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Pure mathematical structure. Sets, groups, rings, fields, topology — the formal bedrock everything else rests on.

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Linear algebra and higher-dimensional thinking. Vectors, matrices, transformations — the architecture of mathematical space.

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Physical applications of mathematics. Constants, quantum mechanics, measurement — where abstract meets embodied.

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Scholze-Clausen condensed mathematics bridge to sheaf neural networks via 6-functor formalism

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ALIFE 2025 Proceedings - 337 pages, 80+ papers on artificial life, evolution, emergence, cellular automata, neural networks, agent-based models. Full Mathpix extraction with equations and figures.

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ANIMA as limit construction over condensed skill applications. Formalizes prediction markets as belief ANIMAs, structure dishes as condensation media, and impact as equivalence class change. Use for understanding agency at maximum entropy, compositional world modeling, or applying Scholze-Clausen condensed mathematics to AI.

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