It’s an old joke that mathematicians need just a pencil, paper, and a bin, while philosophers are even more frugal because they don’t need the bin. Yet nowadays more and more of the time of mathematicians, indeed all scientists, is spent at the computer. Whereas twenty years ago I would handwrite a draft of a paper before typing it in, I now do almost all the drafting directly in at the keyboard.

But in response to computers dominating our lives, and in a move away from the (mythical?) paperless office, people are increasingly reverting to analogue tools, encouraged by the pleasure of handling stationery and, for those of us who were brought up in an analogue world, nostalgia.

This is a good time to employ retro tools in a digital world because we can now buy online an increasingly wide variety of stationery from all around the world.

What might you gain by writing mathematics with a pencil and paper as opposed to typing it at the computer? Sitting at a desk with a pencil in hand you are free from the distractions of the windows on your computer screen. The analogue process, with its delays of turning a page, sharpening the pencil, and rubbing out mistakes, has the benefit of slowing you down and thereby promoting your flow of thought and creativity. And the touch of the paper and the smell of cedar as you sharpen the pencil refresh the senses.

Donald Knuth has another reason for writing with a pencil, as explained in this 2008 interview.

I love keyboards, but my manuscripts are always handwritten. The reason is that I type faster than I think. There’s a synchronization problem. I can think of ideas at about the rate I can write them down with a pencil. But with typing I’m going faster, so I have to sync, and my thoughts have to start up and stop again in a way that involves more of my brain.

Yet more reasons for using pencils are given in the video Why Use Pencils? by T. J. Cosgrove. One of T. J.’s points is that the graphite produced by a pencil does not fade, unlike inks.

It is also worth noting that in some recently published research psychologists found evidence that students who take notes with pencil (or pen) and paper outperform those who take notes on a laptop.

So there are some good reasons for writing with a pencil. How should you choose one from among the many different types available?

I don’t know of a good source of advice on pencils for mathematicians (maybe I will write something in due course), but this blog post on pencils for musicians is largely applicable if you replace “music” by “mathematics”. The post is by Caitlin Elgin, from the wonderful Manhattan pencil shop pictured in the photo above, which I took when I visited it last year.

Most of my calculations are done with pencil. I have been using this brand https://www.staedtler.com/en/products/pencils-accessories/pencils/tradition-112-pencil-with-eraser-tip/ for a long time now.

I’d be very interested to see a followup post on specific pencils – as someone who uses pen and paper a lot for my maths, I’m intrigued to know more about pencils instead (and it would be nice to have some advice to follow before diving into the rabbithole of premium pencil brands).

I use three brands, the Caran d’Ache Technograph F, the Faber-Castell 9000 F and the Staedtler Mars Lumograph F. For mathematical formulae the best is the F rate, HB is soft.