Best Erdős AI Tools & Models - Premium Erdős News

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OpenAI's reasoning model independently solves an 80-year-old problem: from research assistant to scientific discoverer

OpenAI's general reasoning model independently solved the Erdős unit distance conjecture, a problem that had puzzled the academic community for 80 years in the field of combinatorial geometry, without human guidance. The problem was proposed by mathematician Erdős in 1946, and its core is to explore how many pairs of unit distances can exist between n points on a plane.

15.3k 16 hours ago

Anthropic Launches Claude Mythos, Solving the Erdős Mathematical Conjecture with a Concise Proof

Anthropic's Claude Mythos model solved the century-old Erdős unit distance conjecture in combinatorial geometry through a clever proof, following OpenAI's GPT-5.5. This breakthrough used an agent collaboration paradigm, not a single model, intensifying AI competition in pure mathematics discovery.....

14.6k 18 hours ago

Anthropic Launches Claude Mythos, Solving the Erdős Mathematical Conjecture with a Concise Proof

Overcoming a 56-Year-Old Puzzle! Google AlphaProof Nexus Revolutionizes the Mathematics Field

Google DeepMind launched the AI framework AlphaProof Nexus, achieving significant breakthroughs in the field of mathematical research through a four-level agent architecture. It successfully solved two 56-year-old Erdős problems. The system starts by interacting with the base model and Lean compiler, gradually increasing the complexity of reasoning, demonstrating the strong potential of AI in formal verification and mathematical reasoning.

15.7k 16 hours ago

Overcoming a 56-Year-Old Puzzle! Google AlphaProof Nexus Revolutionizes the Mathematics Field

Breakthrough in OpenAI Inference Model: AI Successfully Refutes Erdős Unit Distance Conjecture

On May 20, 2026, OpenAI's reasoning model overturned Paul Erdős' 1946 'unit distance conjecture,' solving a core problem in discrete geometry that had persisted for nearly 80 years. Unlike previous AI achievements, this result gained widespread academic recognition, marking a key breakthrough from AI 'retrieval' to 'original creation.'....

32.3k 1 days ago

Models

GPT-4.1 mini

Openai

$2.8

Input tokens/M

$11.2

Output tokens/M

Context Length

o3-mini

Openai

$7.7

Input tokens/M

$30.8

Output tokens/M

200

Context Length

GPT-5 Codex

Openai

Input tokens/M

Output tokens/M

Context Length

Claude 3 Opus

Anthropic

$105

Input tokens/M

$525

Output tokens/M

200

Context Length

Gemini 2.0 Flash

Google

$0.7

Input tokens/M

$2.8

Output tokens/M

Context Length

Claude Haiku 4.5

Anthropic

Input tokens/M

$35

Output tokens/M

200

Context Length

Gemini 2.5 Flash

Google

$2.1

Input tokens/M

$17.5

Output tokens/M

Context Length

Claude Sonnet 4.5

Anthropic

$21

Input tokens/M

$105

Output tokens/M

200

Context Length

Claude 3 Sonnet

Anthropic

$21

Input tokens/M

$105

Output tokens/M

200

Context Length

Gemini 2.5 Flash-Lite

Google

$0.7

Input tokens/M

$2.8

Output tokens/M

Context Length

qwen3-coder-plus

Alibaba

Input tokens/M

$16

Output tokens/M

Context Length

Qianfan-Lightning

Baidu

Input tokens/M

Output tokens/M

128

Context Length

wan2.5-i2i-preview

Alibaba

Input tokens/M

Output tokens/M

Context Length

qwen3-max

Alibaba

Input tokens/M

$24

Output tokens/M

256

Context Length

qwen3-vl-plus

Alibaba

Input tokens/M

$10

Output tokens/M

256

Context Length

Doubao-Seed-Translation

Bytedance

$1.2

Input tokens/M

$3.6

Output tokens/M

Context Length

qwen3-livetranslate-flaltimeash-re-2025-09-22

Alibaba

Input tokens/M

$240

Output tokens/M

Context Length

qwen3-omni-30b-a3b-captioner

Alibaba

$15.8

Input tokens/M

$12.7

Output tokens/M

Context Length

qwen3-tts-flash

Alibaba

Input tokens/M

Output tokens/M

Context Length

qwen3-tts-flash-realtime

Alibaba

Input tokens/M

Output tokens/M

Context Length

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