If you’re studying a high school or undergraduate college math topic and you have a question, the answer is probably somewhere online. Finding it is just a matter of coming up with the right search terms. Or if searching doesn’t work out, you can always ask on Quora. But another way to use Quora is for an overview of what math concepts are available to study.
How Quora Works
I worked on a project last year where I mined Quora for competitive programming questions, which gave me some insight into how Quora works. I’m not planning the same deep investigation of the Mathematics topic that I did for the Competitive Programming topic. But it’s interesting to see the similarities and differences between the two topics.
To generate engaging Q&A content, Quora relies on high volume combined with smart filtering. They collect as much content as they can by making it as easy as possible to submit questions and answers, rarely deleting questions, and even paying people to submit questions. Then as users interact with content, the Quora software uses signals like upvotes, downvotes, shares, comments, and follow requests to decide what to show in each user’s feed. It’s far from a perfect system, but there’s enough quality content and the feed algorithms are well-tuned enough that users keep coming back, despite the low-quality content mixed in with the good stuff.
Quora rarely deletes or closes questions. A question that is 100% spam will usually get deleted. But questions that are merely redundant or poorly-written get to stick around. The Mathematics topic has thousands (tens of thousands? hundreds of thousands?) of basic math problems. For example, there’s this inane word problem about eggs, which has accumulated over 100 answers. There are many more like it.
When I was classifying Quora competitive programming questions last year, I relied on the all_questions page. This page gave me an unfiltered list, so I could make my own judgements rather than having the feed algorithm do it for me. Because the Competitive Programming topic has on the order of 25k questions, I could look at them all manually. (25,000 multiplied by a few seconds per question equals a reasonable number of hours for a year-long project). Because the Mathematics topic is better known, there are more like 400k questions for that topic. So the only option is to rely on the feed.
The Mathematics Feed
The feed for the Mathematics topic is reasonably good. There are enough people writing quality answers that you can skim through the feed and always find something interesting. Your personal feed gets even better if you give the algorithm feedback by following interesting people and upvoting interesting content. Occasionally the algorithm throws in a “how many eggs” type problem, probably because people keep asking them so the algorithm assumes they want answers. Downvote those to keep your feed clean. It’s unlikely that the people asking them even bother to check back for answers. They’re just farming views.
As an example of the kind of quality content that shows up on the math feed, here are a few of the answers I found this week:
The math feed has many textbook-style questions, some more interesting than others. The best answers explain something general about mathematical thinking, rather than just solving a specific problem. In his answer to this one, Alon Amit explores the range of this function, using graphs that gradually zoom out to show its squiggly behavior. He also explains why it behaves the way it does using elementary analysis concepts.
This is another answer from Alon Amit. In this one, he tackles a simple-looking equation that nevertheless is impossible to definitively solve using algebra (though you can guess and check). This kind of question is one way to experience the wide breadth of math topics at a high level without taking a lot of classes or reading a lot of books. As one commenter put it:
I had NEVER EVER thought about this, I have taken soooo much math..
A long Quora tradition is the naïve question which nevertheless attracts interesting answers. In this one, Jeff Suzuki distinguishes between what the question writer apparently thinks math is (calculating results) and what math actually is (problem-solving). As he says in his answer:
A problem is something you don’t know how to solve; problem solving occurs when you create a solution.
If I tell you “Here’s how you multiply multidigit numbers,” and then ask you to multiply multidigit numbers, you’re not problem solving: you’re practicing a skill.
Who wrote their PhD thesis in the shortest amount of time? (Charles Slade)
This question is more about mathematicians than math. Charles Slade relates the story of Adrian Ocneanu, who met a professor at a conference and so impressed him that the professor offered him a PhD on the spot. It sounds like a tall tale, but evidence suggests that it’s accurate.
What is the single hardest math problem you ever attempted to solve? (James G. Bridgeman)
Another story, this one about how grad student James G. Bridgeman spent a long but fruitful week proving “that any graded comodule over the Lazard ring could be realized as the complex bordism comodule of a CW-spectrum” (whatever that means), and what his advisor thought about his accomplishment.
Reading About Math
There’s no substitute for reading specific math topics in the right order (as in a textbook) and then doing problems to check your comprehension. But it can also be useful to skim through the Quora math feed to get a high-level view of what kind of math is out there and read math stories that provide insight into how math happens in the real world.