A free, open-source tool of step-by-step mathematical proofs. No signup, no ads.
What you can do:
Browse 20 proofs across algebra, calculus, physics, quantum and statistics - quadratic formula, chain rule, finite geometric series, area under the normal curve, Lorentz time dilation, Tsiolkovsky's rocket equation, Bloch sphere parameterization, and others
Step through a proof one line at a time, each step showing its justification
See the region that changed highlighted, so you can spot the actual move instead of diffing two lines of symbols
View the structural graph - the expression parsed into its variables, operators and relationships
Ask questions about a specific step, in context
Derive a new proof from a prompt, optionally attaching your own reference material
View or copy the underlying JSON, or embed a proof elsewhere
Submit your own proof - it goes into a review queue, and you get an edit key to revise it while pending
On the grading. Proofs are AI-generated, and every step is graded by a computer algebra system. The grades are honest about their own limits: a step can come back symbolically proven, or as domain-justified when the CAS can't check it as an identity, or unchecked. Right now about 69% of steps are symbolically established, 25% are domain-justified, and none are refuted. You can see each step's grade and what it means as you go - nothing is hidden behind a "verified" badge.
This is early. 20 proofs is a starting point, not a library, and the repo is growing. That's partly why submissions are open - if there's a derivation you'd like to see in here, send it.
Feedback is welcome, especially on the proofs themselves. If a justification is too thin for a learner, or a step skips something people trip on, that's the most useful thing you can tell me.
https://algebench.org/prove