Last semester I was working through a 200-page lecture notes PDF — the kind that gets scanned from printed transparencies, emailed as a file attachment, and opens with a slightly-off angle on every page. I wanted to pull the key equations into my own notes. What followed was an education in how PDFs actually store (or don't store) mathematical content.
**Born-digital PDFs** (generated from LaTeX, Word, or typesetting software) contain actual vector math. Extraction from these is fast and 95%+ accurate — the formula structure is essentially already there.
**Scanned PDFs** are just photographs of printed pages packaged into a container. There's no text layer. Extraction works through image recognition, and accuracy depends entirely on scan quality. My professor's notes were this kind.
**Hybrid PDFs** have a text layer added by OCR software after scanning. Quality varies wildly — sometimes great, sometimes the "text" layer is completely wrong. These are the most unpredictable.
**1. Resolution.** The scan was done at 150 DPI instead of 300. At low resolution, small symbols — subscripts, primes, dots — become a few pixels wide. The model can't reliably distinguish `\prime` from a stray speck. Rescanning at 300 DPI fixed more than half my problems.
**2. Encryption.** Some PDFs are password-protected or have content restrictions that prevent any tool from reading the content stream. The PDF appears to open fine, but nothing can extract from it. Removing the password (File → Export as PDF in Preview, without the password lock) solved this.
**3. Formulas stored as vector paths.** Some PDF generators draw equations as shapes rather than encoding them as characters. To any extraction tool, these formulas are invisible — just abstract geometry. The only way around this is to render the page as an image and run visual recognition on that instead.
Not the direct-PDF workflow I was hoping for, but reliable. The image-based pipeline doesn't care whether the original was scanned or born-digital — it just sees pixels and reads the math.
PDF is a presentation format, not a data format. It's optimized for how things look, not for what they mean. Mathematical notation in particular gets mangled in transit — rendered, rasterized, path-converted — in ways that destroy the underlying structure.
