Qwen2.5-Math-72B-Instruct is the 72B instruction-tuned edition of the Qwen2.5-Math mathematical family. Its maker specifically targets English and Chinese mathematical problems and describes two approaches: chain-of-thought reasoning and tool-integrated reasoning. The model receives a written mathematical condition and returns text containing a derivation, explanation or solution. Its specialization is mathematics rather than general creative writing or document processing.
Mathematical capabilities and reasoning approaches
In the text-reasoning approach, the task asks for the relevant definitions, justified transformations and a clearly separated final answer. The model card also describes tool-integrated reasoning, in which natural-language reasoning is combined with programs. The maker names finding the roots of a quadratic equation and computing a matrix's eigenvalues as examples where precise computation and symbolic or algorithmic manipulation matter.
Tool-integrated reasoning is not the same as merely displaying code in an answer. The maker's mathematical demo supplies an environment that can run programs, and the calculation result then participates in the solution. A standalone text-generation request produces text; an application that uses a computational workflow must supply the actual execution step. This distinction keeps mathematical reasoning, program proposals and returned numerical results separate.
Base, Instruct and reward-model editions
The family includes separate base models, instruction-tuned models and a mathematical reward model. The 72B-Instruct edition is intended for chat-style instructions. The Qwen2.5-Math-72B base edition is described as a completion and few-shot foundation and a starting point for further tuning. The separately named reward model has its own role and should not be treated as this model's ordinary answer generator.
The release announcement describes a mathematically specialized training pipeline. The base models use additional synthesized mathematical material, more Chinese mathematics data and initialization from the Qwen2.5 foundation. The Instruct stage uses supervised fine-tuning and reinforcement learning, with a mathematics-specific reward model guiding rejection sampling and later optimization. The maker adds tool-integrated reasoning data and English and Chinese instruction data. These explain the edition's mathematical focus; they do not imply that a separate verifier is invoked automatically for every user request.
Preparing the question
Keep the mathematical statement complete. Define variables, domain restrictions and the quantity or proposition to establish. Use notation that remains consistent between the original condition and the requested answer. A useful instruction can ask for the method, the important transformations and the final result, with a separate check against the original conditions.
The maker's quick start distinguishes the two approaches through the instructions. A text-reasoning request asks for a step-by-step solution and a boxed final answer. A tool-integrated request asks the model to combine natural-language reasoning with programs and to preserve the same final-answer convention. These are documented mathematical workflows, not a separate promise about tools exposed by every serving interface.
For illustration, the card's simple equation is 4x + 5 = 6x + 7. A useful output design separates collecting the variable terms, isolating the variable, and the final expression; the mathematical result for that illustrative condition is x = -1. Substitution gives 4(-1) + 5 = 1 and 6(-1) + 7 = 1, so both sides agree. A more involved request can provide a matrix, ask for a symbolic eigenvalue derivation and identify which numerical calculation would be delegated to the computational environment.
Context and configuration
The published release describes mathematical pretraining with a 4K context. The released model configuration sets maximum positions to 4,096, so the prompt and the worked solution need a compact length plan. Do not assign this mathematical edition the much larger context advertised for the general Qwen2.5 line. Keep relevant conditions and mathematical working together, and omit unrelated material that would consume that space.
The model card's quick-start generation uses a 512-token example setting. That value is not presented as a maximum output capacity. A desired response length can be specified for the task, but a separate output limit should come from the actual applicable configuration rather than from an example or another Qwen edition.
Substantive limits and useful results
The maker recommends this series for mathematical tasks in English and Chinese and does not recommend general-purpose tasks outside that specialization. The weights are text-generation models; a mathematical question in an image needs its symbols and conditions converted to text by a separate visual or OCR step. A multimodal demonstration that combines visual and mathematical models does not make the mathematical edition itself an image-input model.
For a tutoring workflow, supply the learner's attempted derivation and mark the transition that needs explanation. Ask for a correction in the original notation and a final answer at the requested level of detail. For a technical calculation, specify exact versus approximate output, units and rounding before choosing text reasoning or a computational workflow. These preparations connect the model's mathematical specialization to a concrete, inspectable solution.
", "aboutText": "Qwen2.5-Math-72B-Instruct is the 72B instruction-tuned edition of the Qwen2.5-Math mathematical family. Its maker specifically targets English and Chinese mathematical problems and describes two approaches: chain-of-thought reasoning and tool-integrated reasoning. The model receives a written mathematical condition and returns text containing a derivation, explanation or solution. Its specialization is mathematics rather than general creative writing or document processing.\n\nMathematical capabilities and reasoning approaches\n\nIn the text-reasoning approach, the task asks for the relevant definitions, justified transformations and a clearly separated final answer. The model card also describes tool-integrated reasoning, in which natural-language reasoning is combined with programs. The maker names finding the roots of a quadratic equation and computing a matrix's eigenvalues as examples where precise computation and symbolic or algorithmic manipulation matter.\n\nTool-integrated reasoning is not the same as merely displaying code in an answer. The maker's mathematical demo supplies an environment that can run programs, and the calculation result then participates in the solution. A standalone text-generation request produces text; an application that uses a computational workflow must supply the actual execution step. This distinction keeps mathematical reasoning, program proposals and returned numerical results separate.\n\nBase, Instruct and reward-model editions\n\nThe family includes separate base models, instruction-tuned models and a mathematical reward model. The 72B-Instruct edition is intended for chat-style instructions. The Qwen2.5-Math-72B base edition is described as a completion and few-shot foundation and a starting point for further tuning. The separately named reward model has its own role and should not be treated as this model's ordinary answer generator.\n\nThe release announcement describes a mathematically specialized training pipeline. The base models use additional synthesized mathematical material, more Chinese mathematics data and initialization from the Qwen2.5 foundation. The Instruct stage uses supervised fine-tuning and reinforcement learning, with a mathematics-specific reward model guiding rejection sampling and later optimization. The maker adds tool-integrated reasoning data and English and Chinese instruction data. These explain the edition's mathematical focus; they do not imply that a separate verifier is invoked automatically for every user request.\n\nPreparing the question\n\nKeep the mathematical statement complete. Define variables, domain restrictions and the quantity or proposition to establish. Use notation that remains consistent between the original condition and the requested answer. A useful instruction can ask for the method, the important transformations and the final result, with a separate check against the original conditions.\n\nThe maker's quick start distinguishes the two approaches through the instructions. A text-reasoning request asks for a step-by-step solution and a boxed final answer. A tool-integrated request asks the model to combine natural-language reasoning with programs and to preserve the same final-answer convention. These are documented mathematical workflows, not a separate promise about tools exposed by every serving interface.\n\nFor illustration, the card's simple equation is 4x + 5 = 6x + 7. A useful output design separates collecting the variable terms, isolating the variable, and the final expression; the mathematical result for that illustrative condition is x = -1. Substitution gives 4(-1) + 5 = 1 and 6(-1) + 7 = 1, so both sides agree. A more involved request can provide a matrix, ask for a symbolic eigenvalue derivation and identify which numerical calculation would be delegated to the computational environment.\n\nContext and configuration\n\nThe published release describes mathematical pretraining with a 4K context. The released model configuration sets maximum positions to 4,096, so the prompt and the worked solution need a compact length plan. Do not assign this mathematical edition the much larger context advertised for the general Qwen2.5 line. Keep relevant conditions and mathematical working together, and omit unrelated material that would consume that space.\n\nThe model card's quick-start generation uses a 512-token example setting. That value is not presented as a maximum output capacity. A desired response length can be specified for the task, but a separate output limit should come from the actual applicable configuration rather than from an example or another Qwen edition.\n\nSubstantive limits and useful results\n\nThe maker recommends this series for mathematical tasks in English and Chinese and does not recommend general-purpose tasks outside that specialization. The weights are text-generation models; a mathematical question in an image needs its symbols and conditions converted to text by a separate visual or OCR step. A multimodal demonstration that combines visual and mathematical models does not make the mathematical edition itself an image-input model.\n\nFor a tutoring workflow, supply the learner's attempted derivation and mark the transition that needs explanation. Ask for a correction in the original notation and a final answer at the requested level of detail. For a technical calculation, specify exact versus approximate output, units and rounding before choosing text reasoning or a computational workflow. These preparations connect the model's mathematical specialization to a concrete, inspectable solution.", "editorialOverlay": { "copy_fields": { "practical_html": "Technical example in English
Solve a quadratic with a domain check\n\nSolve x squared minus 5x plus 6 = 0 over the real numbers, then apply the additional condition x greater than 2. Show the factorisation, list the equation's roots, and clearly separate the root that remains after the condition. Check the accepted value by substitution and put the final admissible set in boxed mathematical notation.A compact factorisation-based derivation, substitution check and boxed admissible solution set.Both equation roots are considered before the strict inequality excludes the boundary value 2.qwen2.5-math-72b-instructQwen2.5-Math-72B-Instruct is a mathematical instruction model for English and Chinese problems. It supports worked text reasoning and tool-integrated mathematical workflows, with a distinct 4K release configuration rather than general Qwen2.5 long-context specifications.
This description covers the model’s capabilities. Available in Ailoot inputs, outputs and options are listed for the selected method below.
Qwen2.5-Math-72B-Instruct is the 72B instruction-tuned edition of the Qwen2.5-Math mathematical family. Its maker specifically targets English and Chinese mathematical problems and describes two approaches: chain-of-thought reasoning and tool-integrated reasoning. The model receives a written mathematical condition and returns text containing a derivation, explanation or solution. Its specialization is mathematics rather than general creative writing or document processing.
Mathematical capabilities and reasoning approaches
In the text-reasoning approach, the task asks for the relevant definitions, justified transformations and a clearly separated final answer. The model card also describes tool-integrated reasoning, in which natural-language reasoning is combined with programs. The maker names finding the roots of a quadratic equation and computing a matrix's eigenvalues as examples where precise computation and symbolic or algorithmic manipulation matter.
Tool-integrated reasoning is not the same as merely displaying code in an answer. The maker's mathematical demo supplies an environment that can run programs, and the calculation result then participates in the solution. A standalone text-generation request produces text; an application that uses a computational workflow must supply the actual execution step. This distinction keeps mathematical reasoning, program proposals and returned numerical results separate.
Base, Instruct and reward-model editions
The family includes separate base models, instruction-tuned models and a mathematical reward model. The 72B-Instruct edition is intended for chat-style instructions. The Qwen2.5-Math-72B base edition is described as a completion and few-shot foundation and a starting point for further tuning. The separately named reward model has its own role and should not be treated as this model's ordinary answer generator.
The release announcement describes a mathematically specialized training pipeline. The base models use additional synthesized mathematical material, more Chinese mathematics data and initialization from the Qwen2.5 foundation. The Instruct stage uses supervised fine-tuning and reinforcement learning, with a mathematics-specific reward model guiding rejection sampling and later optimization. The maker adds tool-integrated reasoning data and English and Chinese instruction data. These explain the edition's mathematical focus; they do not imply that a separate verifier is invoked automatically for every user request.
Preparing the question
Keep the mathematical statement complete. Define variables, domain restrictions and the quantity or proposition to establish. Use notation that remains consistent between the original condition and the requested answer. A useful instruction can ask for the method, the important transformations and the final result, with a separate check against the original conditions.
The maker's quick start distinguishes the two approaches through the instructions. A text-reasoning request asks for a step-by-step solution and a boxed final answer. A tool-integrated request asks the model to combine natural-language reasoning with programs and to preserve the same final-answer convention. These are documented mathematical workflows, not a separate promise about tools exposed by every serving interface.
For illustration, the card's simple equation is 4x + 5 = 6x + 7. A useful output design separates collecting the variable terms, isolating the variable, and the final expression; the mathematical result for that illustrative condition is x = -1. Substitution gives 4(-1) + 5 = 1 and 6(-1) + 7 = 1, so both sides agree. A more involved request can provide a matrix, ask for a symbolic eigenvalue derivation and identify which numerical calculation would be delegated to the computational environment.
Context and configuration
The published release describes mathematical pretraining with a 4K context. The released model configuration sets maximum positions to 4,096, so the prompt and the worked solution need a compact length plan. Do not assign this mathematical edition the much larger context advertised for the general Qwen2.5 line. Keep relevant conditions and mathematical working together, and omit unrelated material that would consume that space.
The model card's quick-start generation uses a 512-token example setting. That value is not presented as a maximum output capacity. A desired response length can be specified for the task, but a separate output limit should come from the actual applicable configuration rather than from an example or another Qwen edition.
Substantive limits and useful results
The maker recommends this series for mathematical tasks in English and Chinese and does not recommend general-purpose tasks outside that specialization. The weights are text-generation models; a mathematical question in an image needs its symbols and conditions converted to text by a separate visual or OCR step. A multimodal demonstration that combines visual and mathematical models does not make the mathematical edition itself an image-input model.
For a tutoring workflow, supply the learner's attempted derivation and mark the transition that needs explanation. Ask for a correction in the original notation and a final answer at the requested level of detail. For a technical calculation, specify exact versus approximate output, units and rounding before choosing text reasoning or a computational workflow. These preparations connect the model's mathematical specialization to a concrete, inspectable solution.
POST /v1/chat/completionstexttext| Field | Type | Requirement | Values & limits | Default |
|---|---|---|---|---|
Fieldmodel | Typestring | RequirementRequired | Values & limits qwen2.5-math-72b-instruct | Default— |
Fieldmessages | Typemessage[] | RequirementRequired | Values & limits Minimum items: 1 | Default— |
Fieldmessages[].role | Typestring | RequirementRequired | Values & limits Examples: system, user, assistant, tool, function Conditions: These roles are explicitly represented by Source compatibility types; the exact model role set remains model-specific. Model-specific | Default— |
Fieldmessages[].content | Typestring|content_part[]|null | RequirementOptional | Values & limits | Default— |
Fieldmessages[].tool_calls | Typetool_call[] | RequirementOptional | Values & limits | Default— |
Fieldmessages[].tool_call_id | Typestring | RequirementOptional | Values & limits Applies when: role=tool; use actual returned ID | Default— |
Fieldmessages[].name | Typestring | RequirementOptional | Values & limits | Default— |
Fieldmessages[].reasoning_content | Typestring | RequirementOptional | Values & limits Applies when: Round-trip actual returned reasoning where this model uses it | Default— |
Fieldmessages[].reasoning_details | Typeobject|array | RequirementOptional | Values & limits Model-specific | Default— |
Fieldmax_tokens | Typeinteger | RequirementOptional | Values & limits Minimum: 1 Model-specific | Default— |
Fieldmax_completion_tokens | Typeinteger | RequirementOptional | Values & limits Minimum: 1 Model-specific | Default— |
Fieldstream | Typeboolean | RequirementOptional | Values & limits | Defaultfalse |
Fieldstream_options.include_usage | Typeboolean | RequirementOptional | Values & limits Model-specific | Default— |
Fieldtemperature | Typenumber | RequirementOptional | Values & limits Model-specific | Default— |
Fieldtop_p | Typenumber | RequirementOptional | Values & limits Model-specific | Default— |
Fieldstop | Typestring|string[] | RequirementOptional | Values & limits Model-specific | Default— |
Fieldtools | Typefunction_tool[] | RequirementOptional | Values & limits Model-specific | Default— |
Fieldtools[].type | Typestring | RequirementOptional | Values & limits function Model-specific | Default— |
Fieldtools[].function.name | Typestring | RequirementRequired | Values & limits Applies when: function tool supplied | Default— |
Fieldtools[].function.description | Typestring | RequirementOptional | Values & limits | Default— |
Fieldtools[].function.parameters | TypeJSON_schema | RequirementOptional | Values & limits | Default— |
Fieldtool_choice | Typestring|object | RequirementOptional | Values & limits Model-specific | Default— |
Fieldparallel_tool_calls | Typeboolean | RequirementOptional | Values & limits Model-specific | Default— |
Fieldresponse_format | Typeobject | RequirementOptional | Values & limits Model-specific | Default— |
Fieldreasoning_effort | Typestring | RequirementOptional | Values & limits Model-specific | Default— |
Fieldreasoning | Typeobject | RequirementOptional | Values & limits Model-specific | Default— |
Fieldservice_tier | Typestring | RequirementOptional | Values & limits Model-specific | Default— |
Fieldinstructions | Typestring | RequirementOptional | Values & limits Compatibility field | Default— |
Fieldfunctions | Typefunction[] | RequirementOptional | Values & limits Model-specific | Default— |
Fieldfunction_call | Typestring|object | RequirementOptional | Values & limits Model-specific | Default— |
Fieldprompt_cache_options | Typeobject | RequirementOptional | Values & limits Model-specific | Default— |
Fieldmodalities | Typestring[] | RequirementOptional | Values & limits text | Default— |
Fieldprovider | Typeobject | RequirementOptional | Values & limits Conditions: provider.options is rejected on this Ultra text route | Default— |
Fieldcache_control.ttl | Typestring | RequirementOptional | Values & limits Conditions: 1h is rejected in actual prompt-cache locations | Default— |
Text · UTF8 text
messages[].content
| Parameter | Contract |
|---|---|
Parametercontent_type | Contractapplication/json |
Parameterrequired | Contractmodel, messages |
Parametermaterial_types | Contracttext |
Parametermessages | Contractmessage array with role/content shape |
Parameterfile_material | Contractactual UTF-8 document inserted as literal text; no file ID inferred |
Parameteroptional_controls | Contractstream, temperature, top_p, stop, max_tokens, max_completion_tokens, reasoning, response_format, tools, tool_choice |
Parametercontrol_scope | Contractmodel-specific; user function tools differ from hosted tools |
Parameteroutput_modalities | Contracttext |
Parameterhosted_operations | Contractfalse |
Parametermultimodal_input_binding | Contractnull |
Lifecycle: synchronous_or_streamed
Send exact model ID with messages.
Context length is not an output cap.
A text file may supply literal text; image/audio/file-object inputs need exact binding.
Tariff references do not add request options. Supported parameters are listed for the selected method.
| Configuration | Rate schedule | Charge |
|---|---|---|
| ConfigurationBase token rates | Rate scheduleBase rate | Charge Input · Input tokens $0.001144 / 1K tokens Output · Output tokens $0.00344 / 1K tokens Input · Cache read $0 / 1K tokens Input · Cache write $0 / 1K tokens Input · Cache write, 1 hour — / 1K tokens |
Ailoot reserves an estimated amount before a request. After the result, it settles the final charge from measured usage. Streaming settlement uses the final usage record. How reservation and settlement work →
set -eu\n: "${AILOOT_API_KEY:?Set your Ailoot API key}"\npython3 - <<'PY_REQUEST'\nimport json,os\nfrom pathlib import Path\np=json.loads('{"model": "qwen2.5-math-72b-instruct", "messages": [{"role": "user", "content": "Explain the difference between an observation and a hypothesis in three sentences."}]}')\n\nPath("request.json").write_text(json.dumps(p,ensure_ascii=False))\nPY_REQUEST\ncurl --fail-with-body --silent --show-error https://api.ailoot.ai/v1/chat/completions \\\n -H "Authorization: Bearer $AILOOT_API_KEY" -H 'Content-Type: application/json' \\\n --data-binary @request.json -D response-headers.txt -o result.json\npython3 - <<'PY_RESULT'\nimport json\nfrom pathlib import Path\nr=json.loads(Path("result.json").read_text())\nfor x in r.get("choices",[]):\n if x.get("message",{}).get("content"): print(x["message"]["content"])\nPY_RESULT\nfrom openai import OpenAI\nimport os\n\nif not os.environ.get("AILOOT_API_KEY", "").strip(): raise SystemExit("Set AILOOT_API_KEY before making a request")\nclient=OpenAI(base_url="https://api.ailoot.ai/v1",api_key=os.environ["AILOOT_API_KEY"],max_retries=0)\nresult=client.chat.completions.create(model='qwen2.5-math-72b-instruct',messages=[{"role":"user","content":"Explain observations and hypotheses in three sentences."}])\nimport base64, json\nfrom pathlib import Path\n\ndef save_result(data, stem="result"):\n # Keep every field, including usage, IDs, reasoning and tool requests.\n Path(stem + ".json").write_text(json.dumps(data, ensure_ascii=False, indent=2), encoding="utf-8")\n print(json.dumps(data, ensure_ascii=False, indent=2))\n def save_blob(encoded, suffix, label):\n raw = base64.b64decode(encoded, altchars=b"-_", validate=True)\n ext = "png" if raw.startswith(b"\\x89PNG\\r\\n\\x1a\\n") else "jpg" if raw.startswith(b"\\xff\\xd8") else "webp" if raw[:4] == b"RIFF" and raw[8:12] == b"WEBP" else suffix\n file = Path(stem + "-" + label + "." + ext)\n file.write_bytes(raw)\n print("Saved", file)\n for index, block in enumerate(data.get("content") or []):\n print("Content", index, json.dumps(block, ensure_ascii=False))\n for choice in data.get("choices") or []:\n print("Choice", choice.get("index"), json.dumps(choice.get("message", choice.get("delta", {})), ensure_ascii=False))\n for index, item in enumerate(data.get("output") or []):\n print("Output", index, json.dumps(item, ensure_ascii=False))\n if item.get("type") == "image_generation_call" and item.get("result"):\n save_blob(item["result"], item.get("output_format") or "bin", "output-" + str(index))\n for ci, candidate in enumerate(data.get("candidates") or []):\n for pi, part in enumerate((candidate.get("content") or {}).get("parts") or []):\n print("Candidate/part", ci, pi, json.dumps(part, ensure_ascii=False))\n blob = part.get("inlineData") or part.get("inline_data")\n if blob and blob.get("data"):\n mime = blob.get("mimeType") or blob.get("mime_type")\n suffix = {"image/png":"png", "image/jpeg":"jpg", "image/webp":"webp", "audio/wav":"wav", "audio/mpeg":"mp3", "video/mp4":"mp4"}.get(mime, "bin")\n save_blob(blob["data"], suffix, "candidate-" + str(ci) + "-part-" + str(pi))\n\nsave_result(result.to_dict(mode="json"))\nfrom openai import OpenAI\nimport os\nfrom pathlib import Path\n\nif not os.environ.get("AILOOT_API_KEY", "").strip(): raise SystemExit("Set AILOOT_API_KEY before making a request")\nclient=OpenAI(base_url="https://api.ailoot.ai/v1",api_key=os.environ["AILOOT_API_KEY"],max_retries=0)\nimport base64, json\nfrom pathlib import Path\n\ndef save_result(data, stem="result"):\n # Keep every field, including usage, IDs, reasoning and tool requests.\n Path(stem + ".json").write_text(json.dumps(data, ensure_ascii=False, indent=2), encoding="utf-8")\n print(json.dumps(data, ensure_ascii=False, indent=2))\n def save_blob(encoded, suffix, label):\n raw = base64.b64decode(encoded, altchars=b"-_", validate=True)\n ext = "png" if raw.startswith(b"\\x89PNG\\r\\n\\x1a\\n") else "jpg" if raw.startswith(b"\\xff\\xd8") else "webp" if raw[:4] == b"RIFF" and raw[8:12] == b"WEBP" else suffix\n file = Path(stem + "-" + label + "." + ext)\n file.write_bytes(raw)\n print("Saved", file)\n for index, block in enumerate(data.get("content") or []):\n print("Content", index, json.dumps(block, ensure_ascii=False))\n for choice in data.get("choices") or []:\n print("Choice", choice.get("index"), json.dumps(choice.get("message", choice.get("delta", {})), ensure_ascii=False))\n for index, item in enumerate(data.get("output") or []):\n print("Output", index, json.dumps(item, ensure_ascii=False))\n if item.get("type") == "image_generation_call" and item.get("result"):\n save_blob(item["result"], item.get("output_format") or "bin", "output-" + str(index))\n for ci, candidate in enumerate(data.get("candidates") or []):\n for pi, part in enumerate((candidate.get("content") or {}).get("parts") or []):\n print("Candidate/part", ci, pi, json.dumps(part, ensure_ascii=False))\n blob = part.get("inlineData") or part.get("inline_data")\n if blob and blob.get("data"):\n mime = blob.get("mimeType") or blob.get("mime_type")\n suffix = {"image/png":"png", "image/jpeg":"jpg", "image/webp":"webp", "audio/wav":"wav", "audio/mpeg":"mp3", "video/mp4":"mp4"}.get(mime, "bin")\n save_blob(blob["data"], suffix, "candidate-" + str(ci) + "-part-" + str(pi))\n\nwith client.chat.completions.stream(model='qwen2.5-math-72b-instruct',messages=[{"role":"user","content":"Explain observations and hypotheses in three sentences."}]) as stream:\n with Path("stream-events.jsonl").open("w",encoding="utf-8") as log:\n for event in stream:\n payload=event.to_dict(mode="json")\n log.write(json.dumps(payload,ensure_ascii=False)+"\\n"); log.flush()\n print(json.dumps(payload,ensure_ascii=False))\n final=stream.get_final_completion()\n save_result(final.to_dict(mode="json"),"stream-result")\njson or SSE
Keep every complete returned response, file and content part.
Keep every choice and its content/tool calls/reasoning. In SSE assemble deltas by choice/tool index, retain the final finish reason and usage.
Keep request/response IDs and headers. No generic text job retrieval URL is supplied.
| Field | Type |
|---|---|
Fieldchoices[].index | Typeinteger |
Fieldchoices[].message.content | Typestring|null |
Fieldchoices[].message.tool_calls | Typetool_call[] |
Fieldchoices[].message.reasoning_content | Typestring |
Fieldchoices[].message.reasoning_details | Typeobject|array |
Fieldchoices[].finish_reason | Typestring|null |
Fieldusage | Typeobject |
| Response | Condition | Next step |
|---|---|---|
Response400 · invalid_request_error | ConditionInvalid required fields, material representation or parameter value | Next stepCorrect the indicated fields before a new creation request. |
Ailoot Ultra qwen2.5-math-72b-instruct
Use the method paths shown above.
qwen2.5-math-72b-instructQwen2.5-Math-72B-Instruct is a mathematical instruction model for English and Chinese problems. It supports worked text reasoning and tool-integrated mathematical workflows, with a distinct 4K release configuration rather than general Qwen2.5 long-context specifications.
This description covers the model’s capabilities. Available in Ailoot inputs, outputs and options are listed for the selected method below.
Qwen2.5-Math-72B-Instruct is the 72B instruction-tuned edition of the Qwen2.5-Math mathematical family. Its maker specifically targets English and Chinese mathematical problems and describes two approaches: chain-of-thought reasoning and tool-integrated reasoning. The model receives a written mathematical condition and returns text containing a derivation, explanation or solution. Its specialization is mathematics rather than general creative writing or document processing.
Mathematical capabilities and reasoning approaches
In the text-reasoning approach, the task asks for the relevant definitions, justified transformations and a clearly separated final answer. The model card also describes tool-integrated reasoning, in which natural-language reasoning is combined with programs. The maker names finding the roots of a quadratic equation and computing a matrix's eigenvalues as examples where precise computation and symbolic or algorithmic manipulation matter.
Tool-integrated reasoning is not the same as merely displaying code in an answer. The maker's mathematical demo supplies an environment that can run programs, and the calculation result then participates in the solution. A standalone text-generation request produces text; an application that uses a computational workflow must supply the actual execution step. This distinction keeps mathematical reasoning, program proposals and returned numerical results separate.
Base, Instruct and reward-model editions
The family includes separate base models, instruction-tuned models and a mathematical reward model. The 72B-Instruct edition is intended for chat-style instructions. The Qwen2.5-Math-72B base edition is described as a completion and few-shot foundation and a starting point for further tuning. The separately named reward model has its own role and should not be treated as this model's ordinary answer generator.
The release announcement describes a mathematically specialized training pipeline. The base models use additional synthesized mathematical material, more Chinese mathematics data and initialization from the Qwen2.5 foundation. The Instruct stage uses supervised fine-tuning and reinforcement learning, with a mathematics-specific reward model guiding rejection sampling and later optimization. The maker adds tool-integrated reasoning data and English and Chinese instruction data. These explain the edition's mathematical focus; they do not imply that a separate verifier is invoked automatically for every user request.
Preparing the question
Keep the mathematical statement complete. Define variables, domain restrictions and the quantity or proposition to establish. Use notation that remains consistent between the original condition and the requested answer. A useful instruction can ask for the method, the important transformations and the final result, with a separate check against the original conditions.
The maker's quick start distinguishes the two approaches through the instructions. A text-reasoning request asks for a step-by-step solution and a boxed final answer. A tool-integrated request asks the model to combine natural-language reasoning with programs and to preserve the same final-answer convention. These are documented mathematical workflows, not a separate promise about tools exposed by every serving interface.
For illustration, the card's simple equation is 4x + 5 = 6x + 7. A useful output design separates collecting the variable terms, isolating the variable, and the final expression; the mathematical result for that illustrative condition is x = -1. Substitution gives 4(-1) + 5 = 1 and 6(-1) + 7 = 1, so both sides agree. A more involved request can provide a matrix, ask for a symbolic eigenvalue derivation and identify which numerical calculation would be delegated to the computational environment.
Context and configuration
The published release describes mathematical pretraining with a 4K context. The released model configuration sets maximum positions to 4,096, so the prompt and the worked solution need a compact length plan. Do not assign this mathematical edition the much larger context advertised for the general Qwen2.5 line. Keep relevant conditions and mathematical working together, and omit unrelated material that would consume that space.
The model card's quick-start generation uses a 512-token example setting. That value is not presented as a maximum output capacity. A desired response length can be specified for the task, but a separate output limit should come from the actual applicable configuration rather than from an example or another Qwen edition.
Substantive limits and useful results
The maker recommends this series for mathematical tasks in English and Chinese and does not recommend general-purpose tasks outside that specialization. The weights are text-generation models; a mathematical question in an image needs its symbols and conditions converted to text by a separate visual or OCR step. A multimodal demonstration that combines visual and mathematical models does not make the mathematical edition itself an image-input model.
For a tutoring workflow, supply the learner's attempted derivation and mark the transition that needs explanation. Ask for a correction in the original notation and a final answer at the requested level of detail. For a technical calculation, specify exact versus approximate output, units and rounding before choosing text reasoning or a computational workflow. These preparations connect the model's mathematical specialization to a concrete, inspectable solution.
POST /v1/messagestextjson, sse| Field | Type | Requirement | Values & limits | Default |
|---|---|---|---|---|
Fieldmodel | Typestring | RequirementRequired | Values & limits qwen2.5-math-72b-instruct | Default— |
Fieldmessages | Typemessage[] | RequirementRequired | Values & limits | Default— |
Fieldmessages[].role | Typestring | RequirementRequired | Values & limits user, assistant | Default— |
Fieldmessages[].content | Typestring | RequirementRequired | Values & limits | Default— |
Fieldmax_tokens | Typeinteger | RequirementRequired | Values & limits | Default— |
Fieldstream | Typeboolean | RequirementOptional | Values & limits | Defaultfalse |
Text · UTF-8 text
messages[].content string
| Parameter | Contract |
|---|---|
Parametercontent_type | Contractapplication/json |
Parameterrequired | Contractmodel, messages, max_tokens |
Parameteroptional_controls | Contractstream |
Parametermaterial_types | Contracttext |
Parametertext_file_material | ContractRead the actual UTF-8 document and put its text in the indicated input or message content string. |
Lifecycle: synchronous_or_streamed
Tariff references do not add request options. Supported parameters are listed for the selected method.
| Configuration | Rate schedule | Charge |
|---|---|---|
| ConfigurationBase token rates | Rate scheduleBase rate | Charge Input · Input tokens $0.001144 / 1K tokens Output · Output tokens $0.00344 / 1K tokens Input · Cache read $0 / 1K tokens Input · Cache write $0 / 1K tokens Input · Cache write, 1 hour — / 1K tokens |
Ailoot reserves an estimated amount before a request. After the result, it settles the final charge from measured usage. Streaming settlement uses the final usage record. How reservation and settlement work →
{\n "model": "qwen2.5-math-72b-instruct",\n "max_tokens": 128,\n "messages": [\n {\n "role": "user",\n "content": "Summarize the incident report."\n }\n ],\n "stream": false\n}set -eu\n: "${AILOOT_API_KEY:?Set your Ailoot API key}"\n: "${AILOOT_TEXT_FILE:?Set your actual UTF-8 document}"\nexport AILOOT_TEXT_FILE\npython3 - <<'PY_REQUEST'\nimport json, os\nfrom pathlib import Path\n\nsource_file = Path(os.environ['AILOOT_TEXT_FILE'])\nif not source_file.is_file():\n raise SystemExit('Set AILOOT_TEXT_FILE to your actual UTF-8 document')\ntext = source_file.read_text(encoding='utf-8')\nif not text.strip():\n raise SystemExit('Choose a document containing text')\npayload = {'model': 'qwen2.5-math-72b-instruct', 'max_tokens': 128, 'messages': [{'role': 'user', 'content': 'Summarize the incident report.'}]}\npayload['messages'][0]['content'] = 'Summarize this material and quote supporting source passages.\\n\\n' + text\nPath('request.json').write_text(json.dumps(payload, ensure_ascii=False), encoding='utf-8')\nPY_REQUEST\ncurl --fail-with-body --silent --show-error https://api.ailoot.ai/v1/messages \\\n -H "x-api-key: $AILOOT_API_KEY" -H 'anthropic-version: 2023-06-01' -H 'Content-Type: application/json' \\\n --data-binary @request.json -D response-headers.txt -o result.json\npython3 - <<'PY_RESULT'\nimport json\nfrom pathlib import Path\n\nresult = json.loads(Path('result.json').read_text(encoding='utf-8'))\nprint(json.dumps(result, ensure_ascii=False, indent=2))\nPY_RESULT\nimport json, os\nfrom pathlib import Path\n\nsource_file = Path(os.environ['AILOOT_TEXT_FILE'])\nif not source_file.is_file():\n raise SystemExit('Set AILOOT_TEXT_FILE to your actual UTF-8 document')\ntext = source_file.read_text(encoding='utf-8')\nif not text.strip():\n raise SystemExit('Choose a document containing text')\npayload = {'model': 'qwen2.5-math-72b-instruct', 'max_tokens': 128, 'messages': [{'role': 'user', 'content': 'Summarize the incident report.'}]}\npayload['messages'][0]['content'] = 'Summarize this material and quote supporting source passages.\\n\\n' + text\nfrom urllib.request import Request, urlopen\nfrom urllib.error import HTTPError\n\napi_key = os.environ['AILOOT_API_KEY']\nif not api_key.strip():\n raise SystemExit('Set AILOOT_API_KEY before making a request')\nheaders = {'x-api-key': 'PLACEHOLDER_KEY', 'anthropic-version': '2023-06-01', 'Content-Type': 'application/json'}\nheaders['x-api-key'] = api_key\nrequest = Request('https://api.ailoot.ai/v1/messages', data=json.dumps(payload, ensure_ascii=False).encode('utf-8'), headers=headers, method='POST')\ntry:\n with urlopen(request, timeout=120) as response:\n raw = response.read()\n Path('response-headers.txt').write_text(str(response.headers), encoding='utf-8')\nexcept HTTPError as error:\n Path('result.json').write_bytes(error.read())\n Path('response-headers.txt').write_text(str(error.headers), encoding='utf-8')\n raise\nPath('result.json').write_bytes(raw)\nimport json\nfrom pathlib import Path\n\nresult = json.loads(Path('result.json').read_text(encoding='utf-8'))\nprint(json.dumps(result, ensure_ascii=False, indent=2))\nJSON or SSE
Keep every complete returned response, file and content part.
Keep all content blocks, thinking signatures and actual tool-use IDs. Assemble all SSE block deltas; a first text block is not the complete output.
Keep request/response IDs and headers. No generic text job retrieval URL is supplied.
| Field | Type |
|---|---|
Fieldid | Typestring |
Fieldmodel | Typestring |
Fieldcontent[] | Typetext|thinking|tool_use|other content block |
Fieldstop_reason | Typestring|null |
Fieldusage | Typeobject |
| Response | Condition | Next step |
|---|---|---|
Response400 · invalid_request_error | ConditionInvalid required fields, material representation or parameter value | Next stepCorrect the indicated fields before a new creation request. |
Ailoot Ultra qwen2.5-math-72b-instruct
Use the method paths shown above.
Technical example in English
Solve a quadratic with a domain check\n\nSolve x squared minus 5x plus 6 = 0 over the real numbers, then apply the additional condition x greater than 2. Show the factorisation, list the equation's roots, and clearly separate the root that remains after the condition. Check the accepted value by substitution and put the final admissible set in boxed mathematical notation.A compact factorisation-based derivation, substitution check and boxed admissible solution set.Both equation roots are considered before the strict inequality excludes the boundary value 2.