专业数学工具中一些有用但不为人知的功能有哪些?

Terence Tao 2017-07-08

专业数学工具中一些有用但不为人知的功能有哪些?

几天前,我和Ed Dunne聊天,他目前是《数学评论》(特别是其在线版本MathSciNet)的执行编辑。当时,我提到通过使用MathSciNet单独查找每个参考文献并将每个参考文献导出为BibTeX格式来创建包含数十个参考文献的BibTeX文件对我来说是多么费力。然后他告诉我,在每个MathSciNet参考文献下方都有一个小的链接,可以将参考文献添加到剪贴板,然后可以一次性将整个剪贴板导出为任何所需的格式。回想起来,这是网站一直存在的功能,但我从未费心去探索它,现在我可以更快地填充BibTeX文件了。

这让我意识到,也许流行的数学工具还有许多其他有用的功能,只有少数用户真正知道,所以我想创建一个博客文章,鼓励读者发布他们自己最喜欢的工具或工具功能,这些功能通常显而易见,但并不总是广为人知。以下是我从自己的工作流程中能够回忆起的一些功能(尽管对于其中一些功能,我有意识地回忆起来花了相当长的时间,因为我已经习惯了它们这么长时间!):

  • Gmail的TeX插件。一个Chrome插件,允许在通过Gmail发送的电子邮件中编写TeX符号(通过编写LaTeX代码并按热键,通常是F8)。

  • Gmail的Boomerang插件。另一个用于Gmail的Chrome插件,它有两个主要功能。首先,它可以将电子邮件从收件箱中”回旋镖”出去,在指定的稍后日期返回(例如,从今天起一周后)。我发现这对于整理收件箱中关于我将来需要处理但由于旅行或等待其他数据到达而目前无法处理的邮件很有用。其次,它可以以指定的延迟(例如,到明天早上)发送电子邮件,给人时间在必要时取消电子邮件。(感谢Julia Wolf告诉我关于Boomerang的信息!)

这让我想起,Gmail上的撤销发送功能已经让我免于尴尬几次(但必须首先设置它;它会将电子邮件延迟一小段时间,例如30秒,在此期间可以撤销电子邮件)。

  • Inkscape中的LaTeX渲染。我曾经使用纯文本在图像中编写数学公式,这看起来总是很糟糕。我花了几年时间才意识到Inkscape具有在其中编译LaTeX的功能。

  • TeXnicCenter中的书签。我可能只使用了TeXnicCenter提供的一小部分功能,但我很喜欢的一个小功能是能够用一个热键(Ctrl-F2)为TeX文件的一部分(例如,末尾的参考文献或当前正在编辑的位置)添加书签,然后可以用一些进一步的热键(F2和shift-F2)在书签位置之间快速循环。

实际上,有许多Windows键盘快捷键值得尝试(当然,对于Mac或Linux系统也是如此)。

  • Detexify对我来说是查找我不太记得的符号的TeX代码(或在寻找与我心中大致形状相似的新符号时)的最快方式。

  • 为了在我的博客上编写LaTeX,我使用Luca Trevisan的LaTeX到WordPress Python脚本(以及我编写的一个小批处理文件来实际运行python脚本)。

  • 使用手机上的摄像头记录黑板计算或幻灯片(或会议中心的wifi密码,或任何其他书写或显示的信息)。如果手机设置得当,这可能比用笔和纸写下来快得多。(我想这个特别的技巧现在被广泛使用,但我仍然看到当别人使用手机而不是笔来记录东西时,人们会感到惊讶。)

  • 使用我的在线日历不仅记录预定的未来约会,还安排时间来完成特定任务(例如,在周二保留下午2-3点来阅读论文X,或完成差事Y)。我发现,在那些我之前已经安排了这种特定时间块的日子里,我能够完成”待办事项”列表中更大比例的任务,相比之下,在那些我留下了几个小时未安排的日子里(尽管有时这些时间对于发现意想不到的新事物也很有用)。(我在网上的某个地方学到了这个小技巧,但我早已丢失了原始参考。)

无论如何,我非常想听听其他读者在他们的工作中发现了哪些其他小工具或功能。

What are some useful, but little-known, features of the tools used in professional mathematics?

A few days ago, I was talking with Ed Dunne, who is currently the Executive Editor of Mathematical Reviews (and in particular with its online incarnation at MathSciNet). At the time, I was mentioning how laborious it was for me to create a BibTeX file for dozens of references by using MathSciNet to locate each reference separately, and to export each one to BibTeX format. He then informed me that underneath to every MathSciNet reference there was a little link to add the reference to a Clipboard, and then one could export the entire Clipboard at once to whatever format one wished. In retrospect, this was a functionality of the site that had always been visible, but I had never bothered to explore it, and now I can populate a BibTeX file much more quickly.

This made me realise that perhaps there are many other useful features of popular mathematical tools out there that only a few users actually know about, so I wanted to create a blog post to encourage readers to post their own favorite tools, or features of tools, that are out there, often in plain sight, but not always widely known. Here are a few that I was able to recall from my own workflow (though for some of them it took quite a while to consciously remember, since I have been so used to them for so long!):

  • TeX for Gmail. A Chrome plugin that lets one write TeX symbols in emails sent through Gmail (by writing the LaTeX code and pressing a hotkey, usually F8).

  • Boomerang for Gmail. Another Chrome plugin for Gmail, which does two main things. Firstly, it can “boomerang” away an email from your inbox to return at some specified later date (e.g. one week from today). I found this useful to declutter my inbox regarding mail that I needed to act on in the future, but was unable to deal with at present due to travel, or because I was waiting for some other piece of data to arrive first. Secondly, it can send out email with some specified delay (e.g. by tomorrow morning), giving one time to cancel the email if necessary. (Thanks to Julia Wolf for telling me about Boomerang!)

Which just reminds me, the Undo Send feature on Gmail has saved me from embarrassment a few times (but one has to set it up first; it delays one’s emails by a short period, such as 30 seconds, during which time it is possible to undo the email).

  • LaTeX rendering in Inkscape. I used to use plain text to write mathematical formulae in my images, which always looked terrible. It took me years to realise that Inkscape had the functionality to compile LaTeX within it.

  • Bookmarks in TeXnicCenter. I probably only use a tiny fraction of the functionality that TeXnicCenter offers, but one little feature I quite like is the ability to bookmark a portion of the TeX file (e.g. the bibliography at the end, or the place one is currently editing) with one hot-key (Ctrl-F2) and then one can cycle quickly between one bookmarked location and another with some further hot-keys (F2 and shift-F2).

Actually, there are a number of Windows keyboard shortcuts that are worth experimenting with (and similarly for Mac or Linux systems of course).

  • Detexify has been the quickest way for me to locate the TeX code for a symbol that I couldn’t quite remember (or when hunting for a new symbol that would roughly be shaped like something I had in mind).

  • For writing LaTeX on my blog, I use Luca Trevisan’s LaTeX to WordPress Python script (together with a little batch file I wrote to actually run the python script).

  • Using the camera on my phone to record a blackboard computation or a slide (or the wifi password at a conference centre, or any other piece of information that is written or displayed really). If the phone is set up properly this can be far quicker than writing it down with pen and paper. (I guess this particular trick is now quite widely used, but I still see people surprised when someone else uses a phone instead of a pen to record things.)

  • Using my online calendar not only to record scheduled future appointments, but also to block out time to do specific tasks (e.g. reserve 2-3pm at Tuesday to read paper X, or do errand Y). I have found I am able to get a much larger fraction of my “to do” list done on days in which I had previously blocked out such specific chunks of time, as opposed to days in which I had left several hours unscheduled (though sometimes those hours were also very useful for finding surprising new things to do that I had not anticipated). (I learned of this little trick online somewhere, but I have long since lost the original reference.)

Anyway, I would very much like to hear what other little tools or features other readers have found useful in their work.