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My question is similar to this one: https://math.stackexchange.com/questions/1833459/math-without-pencil-and-paper Except I'm not physically disabled.

Pencil and paper have been used for centuries to calculate things. It works, but it is not environmentally friendly and storing paper is a hassle. Doing it using desktop computers isn't efficient because the keyboard and mouse limits you. But nowadays, we have tablets, styluses, kindles and all sorts of small high dpi devices to play with.

Therefore I wonder if any mathematician or student have found something that beats pencil and paper? I suspect the answer is (still) no, but I wonder if someone has tried? How far off are we until we can go fully digital? With far off I mean what were the limiting factors? Low dpi, stylus sensitivity, low display contrast or something else?

Edit: Even though this question is opinion-based I like @JoeTaxpayer's answer. The writing in his screenshot looks a little smushy... Not as "detailed" as you can write on paper. :) So if the iPad is the best for handwriting, I will have to wait many more years before I can replace my pen & paper with an electronic device.

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    $\begingroup$ I find that pen and paper beat pencil and paper :) $\endgroup$
    – John Coleman
    Aug 17, 2017 at 13:53
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    $\begingroup$ Totally OT, but since you mentioned it: Pencil and paper are far more environmentally friendly than anything electronic. Paper comes from trees that are specifically grown for pulp. Pulp trees are a crop, just like corn. When you're done with paper, it can be recycled or left to biodegrade. Electronic devices contain all sorts of toxic and/or radioactive materials that, if the devices are recycled at all, end up in a poor village in China, where workers are exposed to the stuff all day long every day. See e.g. content.time.com/time/photogallery/0,29307,1870162,00.html $\endgroup$
    – shoover
    Aug 17, 2017 at 15:45
  • $\begingroup$ @JohnColeman But pens use ink which is non-erasable. How does that work? Don't you do mistakes that you have to erase out? $\endgroup$
    – Björn Lindqvist
    Aug 19, 2017 at 18:51
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    $\begingroup$ @BjörnLindqvist To me, the smooth nature of a good pen is more important than the fact that pencil can be erased. I tend to hate the feel of writing with a pencil and also don't like the scratchy sound that it often makes. If I make a mistake, I cross it out. This isn't for others to read, it is for myself. I always use pen when I prepare for lectures or play around with research ideas. Ultimately, it is a matter of taste. De gustibus non est disputandum. $\endgroup$
    – John Coleman
    Aug 19, 2017 at 19:00
  • $\begingroup$ @JohnColeman Many mathematicians prefer pencil to pen (to an extent that is a noticeable contrast to most groups of adults). $\endgroup$
    – Jessica B
    Aug 27, 2017 at 8:45

5 Answers 5

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Here's a sample of the iPad's resolution. The original is a page wide (8in) but clipped a bit short. The writing tends to be a bit bigger than I'd have with pencil and paper. The graph was just a snapshot, using Desmos. This ability to mix an image onto a page has value depending on the use case. There are times that when drawing graphs by hand, the graph paper image comes in handy. Last, editing after the fact, to correct a mistake or just to add lines to better show some process, is very handy.

enter image description here

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Taking a break from a convoluted computation...

To me the key limiting factor is space. I can spread out several sheets over the table and have various bits and pieces directly visible. I cannot do this to the same extent on my tablet or my computer. Therefore I also use loose sheets not something that is bound together.

One might argue I could set up a system with one or even several larger screens and that would solve this problem, but than this is still costly and maybe a hassle to get right (though I think much less so than it used to be until somewhat recently). And then, I would be bound to the place where I have this set up.

I do not know how it actually would compare, but the production of all the screens and the energy they consume should be non-negligible, too.

You asked for alternatives. It may not be feasible for you, but consider a blackboard. It's rather the opposite to being an innovation, but in some mathematicians' opinion still the best medium.

A drawback is that it is hard to save one's work. But there modern innovations can enter the workflow. Take a photo before erasing.

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  • $\begingroup$ I taught using a Smart Board (interactive white board) which has advantages over the blackboard. You can write on it & erase like a regular blackboard but you can also type from the computer. You can even type on it without the physical board. You can insert images and use tools to make perfect shapes. You can save what you wish and delete the rest. Saving is better than a photo since you can reopen on the computer or the Smart Board. Add as many pages as you wish to each file. When I need images for test questions that I write, I use the versatile tools on the Smart Board & copy & paste $\endgroup$
    – Amy B
    Aug 18, 2017 at 3:08
  • $\begingroup$ I never used anything like this, but I'd imagine it to be very convenient for certain tasks. $\endgroup$
    – quid ♦
    Aug 18, 2017 at 10:21
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    $\begingroup$ I started to comment yesterday about something like that, but then I saw how much they cost -- about \$2000 - \$3000 vs less than \$100 for a regular whiteboard. $\endgroup$
    – shoover
    Aug 18, 2017 at 16:37
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    $\begingroup$ @shoover I worked in a school where they were provided. Many elementary schools and high schools have them and those that don't can get grants to pay for them. Once the school has them, you can get a code to use the software on your personal computer. I no longer work at that school but have been allowed to continue using the software on my personal computer. $\endgroup$
    – Amy B
    Aug 20, 2017 at 4:41
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Your question is just an opinion call, so I need not cite any authoritative sources. ☺

Regarding desktops, writing LaTeX is sometimes more convenient than writing by hand with a stylus or pen. A limiting factor is UI. LaTeX is just a language, and text is typed into a text editor which is good for natural languages, but not for formal languages. IMHO, a visual modal editor for abstract syntax tree with ergonomic keyboard would be ideal. Emacs is close to this, but it is still not visual, and it is not modal. The prices of real ergonomic keyboards are about 500 USD. Just for comparison, I rarely write text on paper because keyboard is more convenient. Keyboard has its advantages.

Regarding styluses, limiting factors are screen cost, UI, and physical differences. I am a poor man living in a poor country, so I bought a device with a screen of size 133 mm by 75 mm. I desperately need a way to split writing into sheets and arrange them on a higher level. Actually, this need will show up independently of screen size. No matter how big a screen is, it is not able to hold all writing. Stylus feels different from pen: there is no friction between stylus and screen. Maybe it is not a problem, but it is kind of unusual.

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Pencil and paper will always been unbeatable for many applications, but sometimes electronic devices are more useful to me.

For example, Wacom tablet + Microsoft OneNote + Movavi Screen Capture is what I use to create instructional videos on a MAC. The whole setup is inexpensive and the pressure sensitivity creates "realistic" writing that is a bit more aesthetic than electronic-writing that has a constant-thickness. (the tablet is like 80 bucks, OneNote is free, Movavi is not free but was worth purchasing since it has quite a bit more functionality than Quicktime's screen capture),

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You may wish to consider Rocketbook. The basic idea of their products is to write on paper but easily convert the output to electronic storage. I found the android app rather unsuccessful, but I am told it works well on apple.

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