DeepSeek Math V2 specialises in natural-language theorem proving and self-verifiable mathematical reasoning. It is built on DeepSeek V3.2 Exp Base. The manufacturer’s starting point is that a correct final answer can still rest on invalid reasoning, while a theorem often requires a complete derivation rather than a numerical answer. The model therefore focuses on generating proofs, identifying their defects and improving the argument before finalising the response.
Proof verification. The training method teaches a verifier to read a problem together with a proposed proof, identify issues and judge the proof’s quality. Its criteria distinguish a complete, rigorous derivation from an otherwise sound solution with minor errors, and from a fundamentally invalid argument. A practical proof-review request should use the same distinction: show where the reasoning breaks, explain why the issue matters and separate a missing detail from a gap that prevents the conclusion.
Meta-verification. The research also reviews the verifier’s own criticism. A claimed defect must actually appear in the proposed proof and must justify the assessment. This addresses the risk of assigning a reasonable-looking judgement while inventing a problem that the proof does not contain. For a review task, provide the original proof along with any existing critique and ask whether the critique accurately represents the relevant step. The useful artifact is a checked explanation of the objection and its consequences.
Proof generation and self-analysis. DeepSeek trains the generator using verifier feedback and explicitly rewards accurate evaluation of its own work. The model is encouraged to acknowledge genuine errors, fix the issues it can resolve and present the best proof together with an honest assessment of its completeness. Verification and generation improve in an iterative training cycle; harder generated proofs become material for improving the verifier. The resulting model can both generate and verify mathematical arguments.
Prepare the problem precisely. Include definitions, quantifiers, domains and all assumptions. State whether you want existence, uniqueness, an inequality, a construction or a counterexample. If a permitted lemma is supplied, give its exact statement and explain whether it may be used directly or also needs to be proved. The manufacturer’s proof prompts require a justified solution even when the task asks for an answer, and do not treat a reference to another text as a substitute for the missing argument.
The expected answer can contain an overview of the idea, a full proof and a separate self-evaluation. For an inequality, ask the model to check the domain restrictions and equality conditions. For a counting problem, ask it to justify that the cases are exhaustive and do not overlap. For an existing proof, identify the step under dispute and request either a repair or an explanation of why the proposed conclusion remains unproved. Algebra, geometry, number theory, combinatorics and inequalities are represented in the manufacturer’s mathematical evaluation tasks.
Refinement. The published workflow can feed a proof and its self-analysis back to the same model to address remaining defects. In the manufacturer’s reported single-attempt research setting, the proof budget is 128K tokens; some difficult arguments remain incomplete when that budget is exhausted. In your own work, use a specific objection as the next input, and ask which part of the proof changes when that objection is resolved. Keep the earlier definitions and assumptions visible. The revised artifact should state what has been established and which difficulty remains.
Math V2’s output is a natural-language proof and critique. Formal proof systems such as Lean check a different kind of artifact; DeepSeek Prover V2 is a separate formal-reasoning specialisation. An assessment that no flaw was found still merits mathematical review, particularly when the proof depends on an omitted case or an unstated lemma. The producer’s research notes that its most difficult problems can remain unresolved even with refinement.
", "aboutText": "DeepSeek Math V2 specialises in natural-language theorem proving and self-verifiable mathematical reasoning. It is built on DeepSeek V3.2 Exp Base. The manufacturer’s starting point is that a correct final answer can still rest on invalid reasoning, while a theorem often requires a complete derivation rather than a numerical answer. The model therefore focuses on generating proofs, identifying their defects and improving the argument before finalising the response.\n\nProof verification. The training method teaches a verifier to read a problem together with a proposed proof, identify issues and judge the proof’s quality. Its criteria distinguish a complete, rigorous derivation from an otherwise sound solution with minor errors, and from a fundamentally invalid argument. A practical proof-review request should use the same distinction: show where the reasoning breaks, explain why the issue matters and separate a missing detail from a gap that prevents the conclusion.\n\nMeta-verification. The research also reviews the verifier’s own criticism. A claimed defect must actually appear in the proposed proof and must justify the assessment. This addresses the risk of assigning a reasonable-looking judgement while inventing a problem that the proof does not contain. For a review task, provide the original proof along with any existing critique and ask whether the critique accurately represents the relevant step. The useful artifact is a checked explanation of the objection and its consequences.\n\nProof generation and self-analysis. DeepSeek trains the generator using verifier feedback and explicitly rewards accurate evaluation of its own work. The model is encouraged to acknowledge genuine errors, fix the issues it can resolve and present the best proof together with an honest assessment of its completeness. Verification and generation improve in an iterative training cycle; harder generated proofs become material for improving the verifier. The resulting model can both generate and verify mathematical arguments.\n\nPrepare the problem precisely. Include definitions, quantifiers, domains and all assumptions. State whether you want existence, uniqueness, an inequality, a construction or a counterexample. If a permitted lemma is supplied, give its exact statement and explain whether it may be used directly or also needs to be proved. The manufacturer’s proof prompts require a justified solution even when the task asks for an answer, and do not treat a reference to another text as a substitute for the missing argument.\n\nThe expected answer can contain an overview of the idea, a full proof and a separate self-evaluation. For an inequality, ask the model to check the domain restrictions and equality conditions. For a counting problem, ask it to justify that the cases are exhaustive and do not overlap. For an existing proof, identify the step under dispute and request either a repair or an explanation of why the proposed conclusion remains unproved. Algebra, geometry, number theory, combinatorics and inequalities are represented in the manufacturer’s mathematical evaluation tasks.\n\nRefinement. The published workflow can feed a proof and its self-analysis back to the same model to address remaining defects. In the manufacturer’s reported single-attempt research setting, the proof budget is 128K tokens; some difficult arguments remain incomplete when that budget is exhausted. In your own work, use a specific objection as the next input, and ask which part of the proof changes when that objection is resolved. Keep the earlier definitions and assumptions visible. The revised artifact should state what has been established and which difficulty remains.\n\nMath V2’s output is a natural-language proof and critique. Formal proof systems such as Lean check a different kind of artifact; DeepSeek Prover V2 is a separate formal-reasoning specialisation. An assessment that no flaw was found still merits mathematical review, particularly when the proof depends on an omitted case or an unstated lemma. The producer’s research notes that its most difficult problems can remain unresolved even with refinement.", "editorialOverlay": { "copy_fields": { "practical_html": "Technical example in English
Repair a divisibility proof\n\nReview this proposed proof: 'If 6 divides ab, then 6 divides a or 6 divides b, because every prime factor of 6 must divide one of the factors.' Here a and b are integers. Identify the invalid implication, provide a counterexample and state a correct related proposition with proof. Separate your proof from a self-check of its completeness.A precise flaw explanation, an integer counterexample, a corrected proposition with proof and a separate self-check.Verify the counterexample meets the premise and defeats both alternatives in the claimed conclusion.DeepSeek-Math-V2-ultraDeepSeek’s model for natural-language mathematical proofs and self-verification, built on DeepSeek V3.2 Exp Base. It can develop a solution, examine its logical gaps and refine the argument, with a detailed proof and an evaluation of the remaining issues.
This description covers the model’s capabilities. Available in Ailoot inputs, outputs and options are listed for the selected method below.
DeepSeek Math V2 specialises in natural-language theorem proving and self-verifiable mathematical reasoning. It is built on DeepSeek V3.2 Exp Base. The manufacturer’s starting point is that a correct final answer can still rest on invalid reasoning, while a theorem often requires a complete derivation rather than a numerical answer. The model therefore focuses on generating proofs, identifying their defects and improving the argument before finalising the response.
Proof verification. The training method teaches a verifier to read a problem together with a proposed proof, identify issues and judge the proof’s quality. Its criteria distinguish a complete, rigorous derivation from an otherwise sound solution with minor errors, and from a fundamentally invalid argument. A practical proof-review request should use the same distinction: show where the reasoning breaks, explain why the issue matters and separate a missing detail from a gap that prevents the conclusion.
Meta-verification. The research also reviews the verifier’s own criticism. A claimed defect must actually appear in the proposed proof and must justify the assessment. This addresses the risk of assigning a reasonable-looking judgement while inventing a problem that the proof does not contain. For a review task, provide the original proof along with any existing critique and ask whether the critique accurately represents the relevant step. The useful artifact is a checked explanation of the objection and its consequences.
Proof generation and self-analysis. DeepSeek trains the generator using verifier feedback and explicitly rewards accurate evaluation of its own work. The model is encouraged to acknowledge genuine errors, fix the issues it can resolve and present the best proof together with an honest assessment of its completeness. Verification and generation improve in an iterative training cycle; harder generated proofs become material for improving the verifier. The resulting model can both generate and verify mathematical arguments.
Prepare the problem precisely. Include definitions, quantifiers, domains and all assumptions. State whether you want existence, uniqueness, an inequality, a construction or a counterexample. If a permitted lemma is supplied, give its exact statement and explain whether it may be used directly or also needs to be proved. The manufacturer’s proof prompts require a justified solution even when the task asks for an answer, and do not treat a reference to another text as a substitute for the missing argument.
The expected answer can contain an overview of the idea, a full proof and a separate self-evaluation. For an inequality, ask the model to check the domain restrictions and equality conditions. For a counting problem, ask it to justify that the cases are exhaustive and do not overlap. For an existing proof, identify the step under dispute and request either a repair or an explanation of why the proposed conclusion remains unproved. Algebra, geometry, number theory, combinatorics and inequalities are represented in the manufacturer’s mathematical evaluation tasks.
Refinement. The published workflow can feed a proof and its self-analysis back to the same model to address remaining defects. In the manufacturer’s reported single-attempt research setting, the proof budget is 128K tokens; some difficult arguments remain incomplete when that budget is exhausted. In your own work, use a specific objection as the next input, and ask which part of the proof changes when that objection is resolved. Keep the earlier definitions and assumptions visible. The revised artifact should state what has been established and which difficulty remains.
Math V2’s output is a natural-language proof and critique. Formal proof systems such as Lean check a different kind of artifact; DeepSeek Prover V2 is a separate formal-reasoning specialisation. An assessment that no flaw was found still merits mathematical review, particularly when the proof depends on an omitted case or an unstated lemma. The producer’s research notes that its most difficult problems can remain unresolved even with refinement.
POST /v1/chat/completionstexttext| Field | Type | Requirement | Values & limits | Default |
|---|---|---|---|---|
Fieldmodel | Typestring | RequirementRequired | Values & limits DeepSeek-Math-V2-ultra | 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 $0.004572 / 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": "DeepSeek-Math-V2-ultra", "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='DeepSeek-Math-V2-ultra',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='DeepSeek-Math-V2-ultra',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 DeepSeek-Math-V2-ultra
Use the method paths shown above.
DeepSeek-Math-V2-ultraDeepSeek’s model for natural-language mathematical proofs and self-verification, built on DeepSeek V3.2 Exp Base. It can develop a solution, examine its logical gaps and refine the argument, with a detailed proof and an evaluation of the remaining issues.
This description covers the model’s capabilities. Available in Ailoot inputs, outputs and options are listed for the selected method below.
DeepSeek Math V2 specialises in natural-language theorem proving and self-verifiable mathematical reasoning. It is built on DeepSeek V3.2 Exp Base. The manufacturer’s starting point is that a correct final answer can still rest on invalid reasoning, while a theorem often requires a complete derivation rather than a numerical answer. The model therefore focuses on generating proofs, identifying their defects and improving the argument before finalising the response.
Proof verification. The training method teaches a verifier to read a problem together with a proposed proof, identify issues and judge the proof’s quality. Its criteria distinguish a complete, rigorous derivation from an otherwise sound solution with minor errors, and from a fundamentally invalid argument. A practical proof-review request should use the same distinction: show where the reasoning breaks, explain why the issue matters and separate a missing detail from a gap that prevents the conclusion.
Meta-verification. The research also reviews the verifier’s own criticism. A claimed defect must actually appear in the proposed proof and must justify the assessment. This addresses the risk of assigning a reasonable-looking judgement while inventing a problem that the proof does not contain. For a review task, provide the original proof along with any existing critique and ask whether the critique accurately represents the relevant step. The useful artifact is a checked explanation of the objection and its consequences.
Proof generation and self-analysis. DeepSeek trains the generator using verifier feedback and explicitly rewards accurate evaluation of its own work. The model is encouraged to acknowledge genuine errors, fix the issues it can resolve and present the best proof together with an honest assessment of its completeness. Verification and generation improve in an iterative training cycle; harder generated proofs become material for improving the verifier. The resulting model can both generate and verify mathematical arguments.
Prepare the problem precisely. Include definitions, quantifiers, domains and all assumptions. State whether you want existence, uniqueness, an inequality, a construction or a counterexample. If a permitted lemma is supplied, give its exact statement and explain whether it may be used directly or also needs to be proved. The manufacturer’s proof prompts require a justified solution even when the task asks for an answer, and do not treat a reference to another text as a substitute for the missing argument.
The expected answer can contain an overview of the idea, a full proof and a separate self-evaluation. For an inequality, ask the model to check the domain restrictions and equality conditions. For a counting problem, ask it to justify that the cases are exhaustive and do not overlap. For an existing proof, identify the step under dispute and request either a repair or an explanation of why the proposed conclusion remains unproved. Algebra, geometry, number theory, combinatorics and inequalities are represented in the manufacturer’s mathematical evaluation tasks.
Refinement. The published workflow can feed a proof and its self-analysis back to the same model to address remaining defects. In the manufacturer’s reported single-attempt research setting, the proof budget is 128K tokens; some difficult arguments remain incomplete when that budget is exhausted. In your own work, use a specific objection as the next input, and ask which part of the proof changes when that objection is resolved. Keep the earlier definitions and assumptions visible. The revised artifact should state what has been established and which difficulty remains.
Math V2’s output is a natural-language proof and critique. Formal proof systems such as Lean check a different kind of artifact; DeepSeek Prover V2 is a separate formal-reasoning specialisation. An assessment that no flaw was found still merits mathematical review, particularly when the proof depends on an omitted case or an unstated lemma. The producer’s research notes that its most difficult problems can remain unresolved even with refinement.
POST /v1/messagestextjson, sse| Field | Type | Requirement | Values & limits | Default |
|---|---|---|---|---|
Fieldmodel | Typestring | RequirementRequired | Values & limits DeepSeek-Math-V2-ultra | 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 $0.004572 / 1K tokens Input · Cache read $0 / 1K tokens Input · Cache write $0 / 1K tokens Input · Cache write, 1 hour — / 1K tokens |
Ailoot reserves an estimated amount before a request. After the result, it settles the final charge from measured usage. Streaming settlement uses the final usage record. How reservation and settlement work →
{\n "model": "DeepSeek-Math-V2-ultra",\n "max_tokens": 128,\n "messages": [\n {\n "role": "user",\n "content": "Summarize the incident report."\n }\n ],\n "stream": false\n}set -eu\n: "${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': 'DeepSeek-Math-V2-ultra', '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': 'DeepSeek-Math-V2-ultra', '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 DeepSeek-Math-V2-ultra
Use the method paths shown above.
Technical example in English
Repair a divisibility proof\n\nReview this proposed proof: 'If 6 divides ab, then 6 divides a or 6 divides b, because every prime factor of 6 must divide one of the factors.' Here a and b are integers. Identify the invalid implication, provide a counterexample and state a correct related proposition with proof. Separate your proof from a self-check of its completeness.A precise flaw explanation, an integer counterexample, a corrected proposition with proof and a separate self-check.Verify the counterexample meets the premise and defeats both alternatives in the claimed conclusion.