AI and Human Mathematicians Claim Ten Major Breakthroughs in Math and CS in 2026

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The year 2026 has seen a series of significant advances at the intersection of artificial intelligence and pure mathematics, according to a detailed review published by DEV Community. Notable achievements include an AI system called LeanMind co-developing a formally verified proof of the Sylvester-Gallai conjecture — reportedly the first major open problem solved by AI without substantial human guidance. Researchers from Oxford and MIT also claimed to have fully proved the long-standing Hadamard conjecture using combinatorial design theory and quantum annealing. Additionally, the matrix multiplication exponent was pushed below a key threshold using deep reinforcement learning, while Carnegie Mellon University produced a fully machine-checked formal proof of the Kepler conjecture in Lean. These developments are being highlighted as potential paradigm shifts in how mathematical research is conducted, with formal verification and machine learning playing increasingly central roles.

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Why GitHub Blocks Search Results Beyond Page 10: The Deep Pagination Problem

GitHub's Search API deliberately returns a 422 error when users request results beyond the first 1,000 entries, blocking access to page 11 and beyond with 100 results per page. The restriction exists because of a fundamental database limitation: SQL's OFFSET clause cannot jump directly to a position in a B-tree index and must scan and discard every preceding row one by one. This means fetching page 50,000 of a 20-results-per-page query forces the database to walk through nearly a million rows before returning any data, making query cost proportional to the offset rather than the page size. A real-world test on a 5-million-row PostgreSQL table confirmed the issue, with an OFFSET of 999,980 causing the engine to scan exactly one million rows before delivering just 20 results. GitHub's hard cap is a deliberate safeguard against this performance problem, which can silently affect any application using offset-based pagination on large datasets.

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ProgrammingDEV Community ·

DCAB 0.12.0 adds test case for Word comment 'done' state change in XML metadata

The Document Change Assurance Benchmark (DCAB) version 0.12.0 introduces a new deterministic test case called review.modern_comment_done_state_changed, targeting a specific boundary in WordprocessingML document structure. The case examines how a comment's 'done' status can shift from done='0' to done='1' inside word/commentsExtended.xml without altering any visible text, anchors, or other package members. This distinction matters for document review tools because stored metadata changes may not be reflected in a document's visible content or classic comment data. The release passed continuous integration testing across Python 3.11 to 3.13 and includes validation support via an optional DocFence 0.27 adapter. DCAB now contains 23 paired synthetic test cases, with release artifacts and the full corpus available on GitHub and Hugging Face.

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ProgrammingDEV Community ·

Developer builds ephemeral encrypted chat where server never stores messages

A developer has released elm.chat, an open-source encrypted chat application built on Cloudflare Durable Objects and Workers, designed so that no message content is ever stored server-side. Each chat room is a temporary space where encryption keys are derived in the browser using HKDF-SHA-256, keeping the server blind to message content. Messages and files are encrypted with AES-GCM-256 before being relayed through a Durable Object, which handles routing but never persists transcripts. When a new participant joins, chat history is synced directly from already-connected peers rather than loaded from a server, meaning if no peer holds a message, it is permanently lost. The project is licensed under AGPL-3.0, though the developer acknowledges that connection metadata such as IP addresses and timing remain visible to Cloudflare.

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ProgrammingDEV Community ·

Six Prompting Techniques to Get Better Code Outputs From Claude

Developers often get subpar results from Claude not because of the model's limitations, but due to poorly structured prompts, according to a guide published on DEV Community. The article recommends six practical techniques, including specifying precise requirements, using XML tags to separate instructions from code context, and asking Claude to outline its approach before writing any code. Providing real code examples from your codebase helps Claude match existing conventions, while breaking large tasks into sequential stages — plan, implement, review, fix — produces more consistent results. The guide also advises using the /clear command in Claude Code to reset context between unrelated tasks, preventing earlier conversation history from degrading responses on new problems.

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