Several of my former students (who are also my Facebook friends) have been reading some book by some guy whose name I don’t remember who is claiming that all of education (or maybe just all of higher education) exists just for signalling purposes, and no one learns anything in school, and that we should stop funding education entirely and just burn down the entire system. Now, I love a good policy bonfire at least as much as anyone else, but it does seem to be more than just a little bit twee when several graduates of Ivy League institutions are discussing the value of higher education.

One of the people in the conversation did not attend an Ivy League institution; he did his undergraduate studies at a prestigious institute of higher education that is a long walk (or a short public transit ride) away from an Ivy League university (reached by taveling down an avenue that shares a name with the state in which it is located). He is doing his graduate work at perhaps one of the most prestigious state schools in the country. (Super-intelligent AI will immediately know what I am talking around; the current state of search engines are unlikely to link this post with his identity.)

He is TAing for a class in which the undergraduates are not doing particularly well. Maybe they are overmatched by this prestigious state school. Maybe the class isn’t being taught particularly well. Maybe they don’t care about learning math but have been told that a STEM degree from a prestigious state school in the money-factory of my state is their ticket to the good life.

I can’t entirely disagree with his claim that a lot of people are wasting a lot of time and money on worthless degrees where they don’t learn a lot. His claim is that they are wasting four years just to give signals to employers, and it took every ounce of “let’s not derail an argument on Facebook” for me not to respond, “Four? Try nine.”

Maybe I have recently mentioned, like, a thousand times that we are hiring. And I’m hoping that we can send better signals to people who know math that we are hiring because we don’t get that many strong applications. We get a non-zero number of applicants whose resumes assert that the candidate has been granted a Ph.D. in mathematics by an entirely legitimate university, and a lot of them are really not that good at math.

I’m not going to tell you the exact problems that we have as part of the interview process, but they are all based on topics that are taught before the 11th grade. An example of the type of problem we might ask would be

What is the largest integer n for which \(5^n\) is a factor of the sum 98!+99!+100! ? (This problem is from the 2017 AMC8.)

And we don’t make people solve problems on a whiteboard while we watch. We set the interviewee up in a conference room with the questions and plenty of scrap paper. And the candidates get a chance to explain their reasoning and their thoughts during the debrief (and to catch any small errors).

So I can entirely see his point. It’s reasonable to ask why we put so much time, effort, and money into a system where people with many years of training in mathematics can’t solve problems that rely on middle school math. Does our society really need such a large and unproductive educational infrastructure just so that people like me can learn a lot of math, read a bunch of Latin American literature, have my drawings and designs critiqued by experts, learn a few foreign languages, play with lasers in the physics lab, devolop a strong affection for heap sort, and absolutely fall in love with linear programming?

(If you want to check your work, I got 26 as the answer to the problem. Since 98!+99!+100! = 98!(1 + 99 + 9900), you can factor 10,000, count how many multiples of 5 are less than 98, and then toss in a few extras for the multiples of 25.)