# Maths Mystery solved with a little help from Microsoft Word

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OK, we admit this story is a stretch but there’s a point behind the link between this interesting story, Microsoft Word and it’s PDF support.

Thomas Royen is a retired statistician who has solved a long standing mathematical question. The Gaussian correlation conjecture (GCC) had beaten experts for years before Herr Royen comes along and solves it without the complex methods of 21st Century maths.  Quanta has Herr Royen’s story and an explanation of GCC.

His discovery took years to be appreciated, in part because he published his findings using Microsoft Word with its Equation editor. Which is why the story attracted the attention of us MS Office nerds.

Herr Royen wrote up his paper with Word and published it as a PDF here.

### PDF back to Word

We decided to import his PDF back into Word to see how a document with so many formula and symbols looked back in the original format.  Microsoft calls this ’round-tripping’.

A PDF made with Word should convert easily and well when imported back into Word.  After all, the formatting instructions and details are there in the PDF and in a format that Word should understand.

We opened PDF in Word and, sure enough it looked like the original.  The original PDF (left) and Word conversion (right):

Looks are deceiving …

### Equations don’t convert

Clicking on an equation doesn’t make the Equation Editor appear. That’s because Word converts any equation into an image when converting to PDF.

We suspect that the second equation in this example was written in standard Word text, not the Equation Editor.

The failure to make proper equations from the PDF is a problem because other mathematicians don’t want to retype equations (time, risk of error).

Little wonder Herr Royen had to re-write his paper using LaTeX, the standard for math and scientific papers.

### PDF features not perfect

Word 2016 for Windows has good PDF support but it’s not perfect.

You can make a PDF from an Office document (Word, Excel or PowerPoint).  That’s been possible for many years either directly from Office (Save As …) or using a third-party tool.

Importing a PDF into Word depends a lot on the way the PDF was created. It’s not a perfect or ideal process. That’s not Microsoft’s fault because PDF to Word conversion is difficult and can’t ever do all that we’d like.

Google Docs can convert PDF’s that Microsoft Office can’t cope with.

A lot of Office elements; Equations, Charts, SmartArt, Diagrams etc are saved to PDF as images. That’s OK until someone tries to convert that PDF back to a Word document.  All they get are image in Word, not the original, editable objects.

There are also privacy issues with Microsoft’s conversion to PDF.  Back in 2015 we discovered that images with shapes overlaid are sent to a PDF version with the original image intact.   Images can also contain location and other hidden information.

### Office documents instead of PDF

Sometimes, sending an Office document is better than a PDF. If document has specialist Office objects (Charts, SmartArt, Icons, Equation etc) and the receiver might want to edit the document – send an Office document instead.

The Office document is fully editable, including the special objects.

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