by Keith Devlin @profkeithdevlin

This tweet came up in my feed the other day. I sensed a topic for a “Devlin’s Angle” or maybe an NPR “Math Guy” slot, although the latter has pretty well retired itself now. (But I did recently do a live-streamed video conversation with my long-time NPR host Scott Simon that can be viewed here.)

I was curious to know who are regarded as today’s most influential mathematicians. Fields Medal winners? Presidents of major mathematical societies? Chairs of mathematics departments at major universities? There are many ways to classify “influence”. Which one had been chosen by this outfit called academicinfluence.com? So I took the bait and clicked on the link.

What came up was not what I anticipated.

Finding myself grouped with, and above, mathematical giants such as Terence Tao, Tim Gowers, Peter Sarnak, Ingrid Daubechies, and Andrew Wiles, it was clear that this was not a categorical ranking, nor was it a list drawn up by a panel of judges. There was an algorithm at work. 

Now, like any academic with a Y-chromosome, I probably have a higher opinion of myself than anyone else does, but the only way I end up ranked #1 here is by way of a Moneyball algorithm. In fact, I’d written about this phenomenon in Devlin’s Angle back in February 2016, with the title Theorem: You are exceptional.

If you measure enough characteristics, every one of us can end up at the top of the rankings, whatever the domain. This is what motivates world class athletes who find themselves coming in second and third but never first, to switch from single disciplines to triathlons, pentathlons, or decathlons. It’s also how Billy Bean built a pennant-winning Oakland A’s baseball team out of good but not great players (the Moneyball story).

With modern computers able to handle massive datasets, the approach can be adopted to take account of very large numbers of features. Though in fact, the numbers don’t need to be astronomical to achieve powerful results. As I showed in that earlier post, if you measure 200 characteristics, 98.24% of the population will find themselves classified as exceptional (i.e., in the 1%). Amazon, Netflix, Google and the rest of the online giants use this theorem to provide us with offers that very closely match our needs and desires, no matter how bizarre the combinations might seem.

Case in point. A few weeks ago, a social-distanced-induced pang of nostalgia caused me to go on Amazon and order some cans of British Mushy Peas (a popular working class accompaniment to fish and chips), and Amazon promptly offered me two jars of Olive Bruschetta from Italy. The only way I can think of to make that link (which I followed, to my subsequence gastronomic enjoyment) was by combining Amazon’s knowledge of my affinity for Italy and many things Italian with the food-processing fact that mushing peas is similar to crushing olives. Graph theory in action. (Netflix has more trouble with me, since I never bother to “like” or “dislike” movies I try.)

So, back to the “influential mathematicians” list. The organization that produced it, Academic Influence, is a serious enterprise with the stated mission of connecting learners to leaders. Their goal is to provide “objective rankings of people, places, and institutions.” The site is fully interactive, allowing you to enter various categories, time periods, and the like.

For instance, I looked for the world’s most influential universities over the past twenty years, coming up with Harvard, London, and Stanford, in that order, and for the most influential universities in mathematics over the same period, which returned Princeton, Harvard, and MIT. The ranked lists all extend to the top fifty, by the way.

It’s fun looking at the rankings for mathematicians you get for time periods going back as far as 4,000bce, and trying to figure out how exactly the algorithm defines “influential.” It clearly gathers its data from material that can be found online and quantified. That probably explains why Fields Medal winning mathematician Paul Cohen comes up as a lowly #17 in the ranking for influential sets theorists of the period 1960 to 1980, whereas any set theorist around at the time would rank him an unequivocal #1 in that category in terms of influence on the field. (I suspect that quality of work or contributions is not directly measured, but inferred from citation counts. It’s all based on numbers. It would be wise to bear that in mind when interpreting results from the site.)

The heavy dependency on online sources likely also explains how my ranking arose. I’ve written a LOT of stuff, both in print and online, that has been read by a lot of people. Ditto some of the other mathematicians on the top ten list. I also developed and gave the world’s first ever math MOOC back in 2012. 

Of course, (linear) rankings are really of little value except as topics for magazine articles. More interesting is to look at the groups of academics or academic institutions the algorithm produces, since that can provide a context that gives some indication of what is actually being measured.

To be sure, I felt a degree of affirmation from being on the list, but it comes down purely to the career path I found myself following. Early on in my career, I realized I was not good enough to rise to the very top levels in terms of mathematics research, and once I accepted that fact and recognized my other limitations, I broadened my activities to put more emphasis on teaching and engaging in expository work of varying kinds. 

But there is a lesson here for anyone trying to build a career in mathematics. The vast number of characteristics that the ranking algorithm presumably draws on are all choices we can make as to what to focus on. (The figure of 1,001 in my title has mere iconic value. The real number is of course far higher.) According to that “Exceptionality Theorem” I mentioned earlier, eventually you will develop a profile relative to which you will be in the top ranking. And maximizing our own potential is what it is really all about, no? Mathematics is broad enough, and deep enough, that there is room for everyone to do that.

Moreover, it is within the discipline that we find the true rewards. For most of us, those rewards come from how we interact with and affect others, not what awards or accolades we receive.

And that brings me to the real message of this post. Given the “Exceptionality Theorem”, while it feels momentarily  nice to find yourself ranked highly in something you care about, just what does it really signify? Simply that what you have accomplished or becomed skilled at is a good fit to a metric created by some other person or organization, to which society ascribes some degree of accrediting authority. 

Well, society typically defines scholastic achievement by performance in standardized tests. The unspoken contrapositive is that if you don’t do well in the test, you are a “failure” in the domain the test is purported to measure. But that’s not a valid conclusion. Tests simply provide an exclusionary filter. They say little if what you do simply does not fit.

We lose a lot by not having mechanisms to identify and measure people’s “strengths spectrum.” We need to do for students what Amazon and Netflix do to target customers, and find ways for society to identify and benefit from the broad, rich tapestry of talents individuals exhibit.

Assessment should identify and measure people’s accomplishments, not quantify the degree to which they fit a particular mold.

I leave you with these words from the late Sir Kenneth Robinson.