MACHINE-CHECKED MATHEMATICS

Proof, not plausibility.

Every step of your derivation, checked by computer algebra. A counterexample when it breaks. An honest abstention when it can't be settled.

Request early access How it works
HOW IT WORKS

Paste the derivation. Get a verdict per step.

01
Paste it as you wrote it

Your LaTeX, your macros. Or a photo of the whiteboard.

02
Every step gets checked

Symbolically, then confirmed numerically — integrals, matrices, branch cuts, units. Both must agree.

03
The break gets a line number

Not a wall of red — the step, and the values that break it.

VERIFICATION LEDGER ✓ 3 ✗ 1
0 def t = cos(κL)
1 alg t² + sin²(κL) = 1
2 alg P× = 1 − t² = cos²(κL)
WHY IT FAILS
at κL0.7
lhs0.41502
rhs0.58498
why1 − t² is sin²(κL)
3 alg P× + t² = 1
WHAT A VERDICT IS MADE OF

Four engines have to agree.

Symbolic, numeric, interval, and a second CAS — run independently on every claim. One dissent and the step abstains rather than guesses.

THE CLAIM
∫₀∞ sin(t)/t dt = π/2
PASS

SYMBOLIC

Reduces lhs − rhs in closed form.

simplify → 0

NUMERIC

Samples it again, at 30 digits.

1.570796326795

INTERVAL

Encloses the difference in a ball — no luck involved.

0 ∈ enclosure

SECOND CAS

A different algebra system, asked the same question.

Maxima agrees
THE WORKSPACE

What's inside

CHAT
A collaborator that checks its own math
  • Every claim it writes is verified in the loop and lands in a live ledger — PASS, FAIL, or ABSTAIN.
  • Paste LaTeX or a photo of the whiteboard.
  • Quotes from papers are filed as sources, never counted as checks.
CHAINS
Whole results, audited end to end
  • Keep a result as an ordered chain of blocks; one click re-verifies all of it.
  • The seams are checked too: definitions carry forward, a quietly redefined symbol is caught with both bindings named, units are compared.
  • The first failing block is named, and every audit run is kept as history.
LIBRARY
Papers as evidence
  • Seed a paper by arXiv ID — LaTeX source, equations exactly as the author wrote them.
  • References fetch themselves; search answers with quoted passages.
  • A built-in reader renders each paper with its own macros.
EARLY ACCESS

Lemma AI is in early access.

Invite-only while it's built with working researchers in photonics and mathematical physics. Tell us what you're deriving.

Request access

Or just write to a.faghihifar@gmail.com