From a Bunch of Old Timers

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This page was created by Becky Painter '13, Iris Hee Rhang Yoon '13 and Xingda Zhai '13, the researchers from the summer of 2010, to induct you into the Math Images Project quickly. In this page, we will walk you through the process of writing a good Math Images Page based on our 10 weeks' experience. You are of course most welcome to explore the process yourselves.

Brainstorming Ideas

The start of everything is hard; so it is with writing a Math Images Project (MIP) page.

How can you brainstorm ideas? Well, perhaps the most effective way is to ask yourself questions, like those in the list below.

  • What are some of the mathematical questions that I really wanted to learn about but never really had the chance?
  • What are some famous mathematical problems that are mentioned all the time but no one has really done a good job explaining?
  • What are some of the contributions in math by those famous mathematician/scientists/engineers whom you always hear about but never really know what their contributions are?
  • Is there a beautiful picture that can be used as a starting point for a math topic?
  • Is there a math problem, theorem, shape, or subject that seems visual or easy to illustrate?
  • What are some of the concepts/topics that you found hard to understand in math class and thought could be explained better?

You can also look through the collection of images that Gene has and see which images interest you, or search for fascinating ideas in popular mathematics books such as

  • How Round is your circle?: Where Engineering and Mathematics Meet by John Bryant and Christopher Sangwin (delightful reading)
  • Mathematics for the Million: How to Master the Magic of Numbers by Lancelot Hogben (the guy is a FRS and he is really good)
  • Who Gave you the Epsilon?: & Other Tales of Mathematical History by Marlow Anderson, Victor Katz and Robin Wilson (an MAA publication)
  • The Math Book by Clifford A. Pickover (especially good for great images)
  • Heart of Mathematics by Edward B. Burger (presents great intuitive approaches to difficult math problems) etc

After flipping through some books and checking out some websites, you'll probably have a topic in mind for your first page... but don't start writing yet! We have a few words of caution:

  • Pick a very narrow topic for your first page. As you look through the other pages on the site, you might realize that most pages require a lot of work. This is most certainly an understatement. One of the reasons why there are so many unfinished pages on the site is that they take much more time than you might anticipate. If you have a broad topic (like the Fibonacci numbers) you may want to wait to tackle the subject until you have experience writing a page so that you know what you're getting yourself into.
  • Pick a topic that suits your mathematical ability. It's great to challenge yourself, but writing about a subject you've seen before (at least for the first page) will make the learning process less painful. You'll still need to do a ton of research, and you'll learn a lot in the process, but it's good to start where you're comfortable.

Picked a topic? Now you're ready to start research!


Research in MIP is different from other research in the natural sciences. We are not trying to prove a hypothesis by experimental data. What we are doing is taming the scary beast of mathematics into a more amiable pet. Say you have settled on some images and topics you want to talk about. You now need to roughly go through in your head which ones are manageable in scope and difficulty. Then, you need to start teach yourself these topics by using online resources and books. This part is research; you are investigating a subject that you will write about.

Sometimes, you need to use primary literature, i.e. an original published book, paper or journal; this is one of the most rewarding aspects of this project. Slogging through a seemingly simple paper and finally having the eureka moment in the end gives you great satisfaction. For example, I, Xingda, was working on The Logarithms, Its Discovery and Development and I had to go through John Napier's original (well, not quite 100% original since he wrote in Latin and I read the translation) 1616 publication. It had hardly any mathematical notation and few illustrations but it contained many ingenious ideas that forced me to marvel at his originality. I thought logarithms are just, you know, logarithms. But their history and invention is nothing but that. In the end, I had a much better idea how logarithms worked. That, my friend, is research.

Words of caution about research:

  • Don't use wikipedia as a starting point! It's too easy to copy their layout, pictures, derivations, etc. We need to be unique! Also see the last paragraph of Starting To Write, below.
  • Keep track of your sources (including pictures). It's a hassle to find them all at the end. Also, see the last paragraph of Starting To Write, below.
  • Actually use the library! Many websites use other websites (especially wikipedia) to get information because it's so easy. However, if you can find relevant information in a book, you'll have a unique take on the subject.

Narrowing Down The Scope

You might have understood many difficult topics or ideas and have many things to say about them, but you need to narrow down the scope of coverage. The trick of good science writing is to know what to say and how much to say about it. You must not over-burden the readers with too much information and you must have a focus or central idea that runs through the whole page. To do so, you might want to start with a conclusion first. What is the idea you want the readers to take away, and what are the absolutely crucial ideas that you need to cover before reaching that conclusion? In this way, you have the bare skeleton of the page, and you then need to add flesh to make it a lively page.

Starting to Write

Putting your ideas on screen can seem hard, but it is actually very easy. Our advice is "just put everything you have on the page". Good writers, science and non-science ones alike, start by simply filling up the blank pages in front of them. Let the ideas flow first and allow nothing to stop you. Just write as much as possible and don't think about editing at all. It's like creating a sculpture of a person. Starting with a solid slab of stone or clay, we work out the rough shape first, not lingering on details such as nose or eyes. Then we go on to finer details.

Remember, images and illustrations are best for most people who are visual learners, so use many of them (of course, don't abuse them). They are wonderful aids to understanding and also to making your page very attractive. Maybe half of the time, you won't be able to find the image you need on the internet, so start learning to use Photoshop, PowerPoint, Geometer's Sketchpad and Matlab. Familiarity with them serves you greatly in all disciplines.

It's ok to use other people's ideas and images, so long as you credit them. So, whenever you take something from a book or website, note it down and create footnote. Don't do it when you are finishing the page because you are likely to have forgotten where you got the quote or image. When using an image created by someone else, make sure that it is okay for you to use it. If you do not see a statement saying that the image is free to use (like there is on most Wikipedia images), you should try to contact the copyright holder and ask their permission to use the image. Most people are really nice and will give you permission.

Should you have template/software related problems, you should direct them to an expert.

You might also want to check out Top 5 things you need to know how to do on the wiki.

Revising and Editing

Your first draft of a page probably won't have all the content you want, and it certainly will be possible to make your page even better. You can find ways to improve your page on your own, by reading your drafts. Ask yourself questions like, "Do I mean exactly what is exactly on the page? Are there some links missing in my explanations?" The Page Building Help page has a list of features of good pages, which you can refer to regularly.

Math Images pages are editable by anyone, so you are never working truly alone. Another Math Images user can contribute to your page at any time. However, asking people you know for help with math questions is a good way to learn more math and make pages really strong.

You should also ask other page creators for feed back (and read their pages in return). Peer feedback is a great way to find ways to improve your page. You will learn more about math and writing as you notice features in others' writing to emulate or avoid. Modern day research no longer follows the patterns of the days of Micheal Faraday or Thomas Edison, when they locked themselves up and guarded their secrets dearly. Collaboration is the future of research (a result of globalization), and you should embrace it!

For more books and other references for good science writing, see

  • Am I Making Myself Clear?: A Scientist's Guide to Talking to the Public by Cornelia Dean
  • Explaining Research: How to Reach Key Audiences to Advance Your Work by Dennis Meredith
  • Don't Be Such a Scientist: Talking Substance in an Age of Style by Randy Olson
  • For examples of good science writing by contemporary great scientists, check out The Next Fifty Years: Science in the First Half of the Twenty-first Century, edited by John Brockman.

The Finishing Touch

Once you feel your page is done, you need to send it to final review. Make sure to write a response to the checklist at the top of your discussion page. When one of the final reviewers decides your page is good to go, they will mark it as being ready for the public.

Examples of pages

Here are examples of some pages that we, the class of summer 2010, made that we think are pretty sweet. Check them out.

From Becky:

From Iris:

From Xingda: