√2 = p / q
gcd(p, q) = 1A workspace for mathematical reasoning
Conjecta
Turn a mathematical question into a line of reasoning you can inspect.
Plan a route, explore useful lemmas, call computation and formal tools, then keep the decisive steps visible.
Proposition
√2 ∉ ℚ
p² = 2q²
2 ∣ pp = 2k ⇒ q² = 2k²
2 ∣ qgcd(p, q) ≥ 2
⊥What Conjecta changes
Not just an answer. A route you can inspect.
Difficult mathematics rarely moves in a straight line. Conjecta keeps exploration, verification, and revision in one visible process—so the useful artifact is the reasoning, not only the final sentence.
Question
Strategy
Lemmas
Verification
One continuous workspace
From first question to checked result
You set the problem and remain in control. Conjecta makes the intermediate work legible as the route develops.
-
01
State the problem
Describe the theorem, attach context, and mark what a satisfactory result must establish.
-
02
Build a proof route
Break the goal into lemmas, compare strategies, and revise when a branch stops paying off.
-
03
Check decisive steps
Use computation, retrieval, structural checks, or Lean where the argument needs firmer ground.
-
04
Keep the useful trail
Review the route, continue the same project, and retain context worth reusing in later work.
Designed for serious problems
The work stays visible.
Each layer answers a different question: where to go, what to trust, and what to carry forward.
EXPLORE
Strategy is not a black box
See the working plan, candidate lemmas, alternative branches, and the reason the system changes direction.
VERIFY
Verification lives inside the process
Computation and formal tooling can test the steps that matter, with their outcomes kept beside the argument.
REMEMBER
Context can accumulate
Projects preserve the conversation and the proof state, while reusable knowledge can support the next problem.
Begin with the question you already have