If, like me, you sometimes prefer to write mathematics on paper before typing into LaTeX, you have the choice of pencil or pen as your writing tool. I’ve written before about writing in pencil. My current tools of choice are fountain pens.
A fountain pen, the ink it contains and the paper used are three independent variables that combine in a complicated way to affect the experience of writing and the results produced. Here, I focus solely on inks and ask what ink one should choose depending on different mathematics-focused requirements.
I give links to reviews on the excellent Mountain of Ink and Pen Addict websites and other pen/ink websites. Unless otherwise stated, I have tried the inks myself.
Fast Drying Time
When we write down mathematical working, perhaps in the course of doing research, we are likely to need to go back and make changes to what we have just written. A fast drying ink helps avoid smudges, and it also means we can start writing on the reverse side of a page without pausing to let the ink dry or using blotting paper. Left-handed writers may always need such an ink, depending on their particular style of writing. My favourite fast-drying ink is Noodler’s Bernanke Blue, which is named after Ben Bernanke, former chairman of the Federal Reserve. Downsides are feathering (where the ink spreads out to create rough edges) and bleeding (where ink soaks through on the other side of the page) on lesser grades of paper.
As mathematicians are major consumers of coffee, what we write risks being spilled on. (Indeed this is so normal an occurrence that Hanno Rein has written a LaTeX package to simulate a coffee stain.) An ink should be reasonably water resistant if spills are not to blur what we have written. Many popular inks have poor water resistance. One of the most water resistant is Noodler’s Bulletproof Black, which also “resists all the known tools of a forger, UV light, UV light wands, bleaches, alcohols, solvent…”. It’s great for writing cheques, as well as mathematics. (But it may not be the blackest black ink, if that matters to you.) Another water resistant ink is Noodler’s Baystate Blue (see below).
Sometimes, writing with an interestingly named pen, paper or ink can provide inspiration. While many Coloverse inks have a space or physics theme, I am not aware of any mathematically named inks.
Vibrant inks are great for annotating a printout or writing on paper with heavy lines, squares or dots. An outstanding ink in this respect is Noodler’s Baystate Blue, an incredibly intense, bright blue that jumps off the page. The downsides are bleeding and staining. An ink to be used with caution! I also like the much better behaved Pilot Iroshizuku Fuyu-gaki (orange) and Pilot Iroshizuku Kon-peki (blue).
For Marking (Grading)
For marking scripts one obviously needs to use a different colour than the student has used. Traditionally, this is red. A couple of my favourites for marking are Waterman Audacious Red and Cult Pens Deep Dark Orange.
Shading, Sheen and Shimmer
Many inks have one or more of the properties of shading, sheen and shimmer. Shading is where an ink appears darker or lighter in different parts of a stroke; sheen is where an ink shines with a different colour; and shimmer is where particles have been added to the ink that cause it to shimmer or glisten when it catches the light. The strength of all these effects is strongly dependent on the pen, the nib size and the paper, and for shimmer the pen needs to be moved around to distribute the particles before writing. (Sheen and shimmer do not show up well on the scans shown in this post.) Among my favourites are Diamine Majestic Blue (blue with purple sheen), Robert Oster Fire and Ice (teal with shading and pink sheen) and Diamine Cocoa Shimmer (brown with gold shimmer). For “monster sheen”, try Organic Studios Nitrogen Royal Blue, but note that it is hard to clean out of a pen.
Much mathematics is written on bar mats, napkins, paper towels, backs of envelopes, newspapers, tablecloths, and anything that is to hand, especially when mathematicians work together away from their desks. These surfaces are not fountain-pen friendly. One promising ink for such situations is Noodler’s X-Feather, which was created to combat feathering on cheap paper. (I have not tried this ink.)
Finally, three good all-round inks that I’ve used a lot when working on my books and papers are Diamine Asa Blue, Diamine Oxford Blue, and Diamine Red Dragon.