For grad students & researchers

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The problem

Typing LaTeX takes longer than doing the math.

Every grad student loses hours a week to formatting. The bottleneck isn't thinking — it's syntax.

Notation friction

You know the math. Typing \frac{\partial}{\partial x}, aligning environments, and balancing braces is what slows the page down.

Notes don't translate

Whiteboard shorthand, voice memos, scratch PDFs — none of it lands cleanly in a paper draft without manual re-typing.

Drafts need PDFs

Advisors and collaborators want a rendered PDF, not a snippet. Round-tripping through Overleaf for one section is overhead.

Output

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theorem-3.texcompiled · 1 page

Input — messy notes

Thm (Cauchy-Schwarz).
for u,v in inner prod space V:
  |<u,v>|^2 <= <u,u> * <v,v>
equality iff u,v linearly dep.

proof sketch:
let t in R. consider
  <u + tv, u + tv> >= 0
expand: <u,u> + 2t<u,v> + t^2<v,v> >= 0
quadratic in t nonneg => discriminant <= 0
=> 4<u,v>^2 - 4<u,u><v,v> <= 0  ∎

Output — rendered PDF

Theorem (Cauchy–Schwarz). For u, v ∈ V, |⟨u, v⟩|² ≤ ⟨u, u⟩ · ⟨v, v⟩, with equality iff u, v are linearly dependent.

Proof.

For t ∈ ℝ, ⟨u + tv, u + tv⟩ ≥ 0. Expanding:

⟨u, u⟩ + 2t⟨u, v⟩ + t²⟨v, v⟩ ≥ 0.

The discriminant is ≤ 0, hence ⟨u, v⟩² ≤ ⟨u, u⟩⟨v, v⟩. ∎

theorem-3.pdf · ready

Pricing

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