The Societal Impact of Chess, Part 3: Chess and Mathematics
Below is another excerpt from Chessays: Travels Through the World of Chess, Chapter 6, Far Transfer (visit our website for more details HERE)
(...) And if the case of Armenia doesn’t independently win us over, the next course of action is to loudly proclaim that chess is particularly well-suited for developing one’s mathematical skills.
To be fair, this claim doesn’t seem to be nearly as widely implausible as the others, as there are certain undeniable similarities between chess and mathematical thinking writ large—just as there are with the very many other games and puzzles out there that combine analytical reasoning with pattern recognition.
The problem, as ever, is understanding what the hell we are actually talking about.
Most of the time, so far as I can make it out, the claim boils down to something like:
Playing chess regularly will dramatically increase your child’s mathematics test scores!
Well, this is precisely the sort of statement that lends itself to empirical analysis. Does it? Under what circumstances?
So far as I’ve been able to determine, the support for such a statement ranges from exceptionally thin to non-existent. And—once again— this is hardly a criticism of chess, per se, or an expression of some nefarious anti-chess conviction I cling to that children shouldn’t be encouraged to play chess (or perhaps even actively discouraged from doing so), but simply a dispassionate line of inquiry: you say X occurs. Very well. Demonstrate to me that this is, in fact, the case.
More worryingly, I can’t help but feel that we’re sliding insidiously into a particularly troubling line of argument here. You might well disagree with the passionate advocate who forthrightly avers that chess should be an integral part of every child’s educational experience because chess is unquestionably the greatest intellectual activity known to mankind.
Such a statement might strike you as demonstrating a conspicuous lack of awareness of other worthy intellectual activities or being just plain wrong or something in between, but it is undeniably a logically consistent culmination of a certain perspective: Chess is the greatest thing since sliced bread, educationally-speaking, so every child should be exposed to it.
On the other hand, the claim, All students should play chess because it will help their math scores, represents another type of rationalization altogether. Suddenly, we are justifying chess by way of its impact on math scores—which, among other things, should necessarily lead any thoughtful person to respond: “Hang on a minute, if the goal is to improve math scores, wouldn’t it be better to focus directly on a way of doing that?”
Presumably the thinking—once again never explicit—goes something like: “Well yes, in principle. But everyone knows that most students are not the slightest bit interested in working directly on ways to improve their math scores, so instead we’ll hook them on chess, and then—presto!—their math scores will automatically improve without them paying the slightest bit of outward attention to them.” Behold the seductive appeal of overhyped far transfer.
It’s logically possible, of course, that such a correlation between chess and math scores does exist, or exists in some narrow contexts, at least. But it definitely sounds fishy: What is it exactly about chess, the critical mind inevitably finds itself inquiring, that makes it possess such a magical quality? Would it also work the same—or perhaps even better—for makruk and janggi? Or go? And if not, why not?
And given that I’ve never seen one whit of evidence to support such a claim—which, if it existed, would surely be emphatically capitalized on by zillions of chess-in-schools supporters during their latest conference in downtown Yerevan—I’m doubly skeptical.
But that is not all. This putative chess-mathematics link also ends up inadvertently illuminating the largest of all elephants in our educational room, which is, What the hell are we trying to do here anyway? In particular, given the specific mathematical context in which we now find ourselves: What do we actually mean by “math skills”?
Because to anyone who’s actually had some experience of mathematics beyond the high school or early undergraduate level, the prevailing view is that the standard mathematics curriculum is all too often not terribly relevant for developing one’s mathematical understanding either.
Most people’s view of mathematics, after having been forced to endure mandatory mathematics courses in school for well over a decade, is that it is an activity that involves the manipulation of an abstruse, largely incoherent list of terms and quantities—often by way of memorization—the purpose of which is constantly justified through a mysteriously averred “real world relevance” that they almost never directly perceive.
Beyond that, more sociologically speaking, there is the widespread belief that there are two types of people in the world—those who “get” mathematics and those who don’t—and that those who do are intrinsically “smarter.”
All of this is totally wrong. Yet it is, unquestionably, the core mathematics-related message that almost all educational systems produce en masse, and one that is perpetually reinforced by teachers, parents and the students themselves.
And a few pages ago when I admitted that there are “certain undeniable similarities between chess and mathematical thinking writ large,” what I had in mind by that was not at all something in keeping with the standard, cookie-cutter, “being good at mathematics” sense above that is routinely associated with getting 19/20 on a school math test, but instead rather a deeper sense of combining logical analysis and pattern recognition so typical of the genuine mathematical experience.
Now none of this, I’m certain, is the slightest bit controversial. If you were to talk to one hundred random people with higher degrees in mathematics, I have no doubt whatsoever that you would find that virtually all of them would unhesitatingly agree with the sentiment I’ve just expressed.
But the key question is: does it matter? Given that mathematics curricula seem to have been doing the same sort of thing for decades, if not centuries, it’s hard not to conclude that most people in charge don’t seem to think that it does.
And even if there was sudden, widespread agreement that a change must now occur, that it’s suddenly time for our educational systems to make a significantly enhanced effort to better communicate the true nature of mathematical thinking to our students—that, in itself, hardly implies that the best, or most efficient, or easiest way to do so is through the use of chess.
Personally, when I ponder the whole chess-math relationship, I have mixed views about it.
On the one hand, the sense of profound aesthetic appreciation that I experience when seeing a beautiful combination in chess certainly feels very similar to being presented with a beautiful mathematical theorem (yes, there are lots of extremely beautiful mathematical theorems; the fact that such a phrase might well strike you as an oxymoron is really the whole problem in a nutshell) while solving a chess problem indubitably provokes a momentary sort of “aha moment” that is reminiscent of whenever I’ve managed to enhance my mathematical understanding.
On the other hand, such “aha moments” are hardly uniquely provoked by chess (or uniquely related to mathematics), and routinely occur whenever any puzzle or conceptual nut is cracked, from a logic puzzle to a sudoku to a particularly difficult wordle. And when it comes to aesthetics, there is an inescapable sense of chess representing a form of “narrow beauty” that is strikingly at odds with its mathematical counterpart.
This one is considerably fuzzier and correspondingly harder to describe, but what I mean is that an intrinsic aspect of genuinely beautiful mathematics is its breadth. Encountering a mathematical result that manages to comprehensively link two domains previously imaged to be completely distinct—the paradigmatic example is algebra and geometry—is an indescribably beautiful experience, leaving you convinced that you’re now perceiving reality in a profoundly different way.
It intuitively feels decidedly more beautiful and vastly more significant than any development within the domain of any particular subfield, no matter how ingenious or otherwise impressive it might be.
And chess, by its very nature, is always naturally limited to a very particular subfield—i.e. that of chess. Which means that however penetrating the particular chess-related insight is, and thus however beautiful it is within that context, it can never, by definition, go beyond that context and enter the realm of the outstandingly beautiful and truly profound that so vividly characterizes the higher forms of mathematical understanding.
But don’t just take my word for it. Let’s turn to someone who really knows what he’s talking about, such as the renowned mathematician G.H. Hardy:
“A chess problem is genuine mathematics, but it is in some way ‘trivial’ mathematics. However ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful…
The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is ‘significant’ if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas.
Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences. No chess problem has ever affected the general development of scientific thought; Pythagoras, Newton, Einstein have in their times changed its whole direction.
The seriousness of a theorem, of course, does not lie in its consequences, which are merely the evidence for its seriousness. The inferiority of the chess problem…lies not in its consequences, but in its content.”
Hardy, you might have noticed, continually refers to chess problems rather than games, because it is when confronting a specific problem that the parallels between chess and mathematics become manifest. Later on, he addresses this distinction explicitly:
“Surely a chess master, a player of great games and great matches, at bottom scorns a problemist’s purely mathematical art. He has much of it in reserve himself, and can produce it in an emergency: ‘if he had made such and such a move, then I had such and such a winning combination in mind.’ But the ‘great game” of chess is primarily psychological, a conflict between one trained intelligence and another, and not a mere collection of small mathematical theorems.”
And so, once more, we are back to the competitive aspect of chess as its most fundamentally distinguishing characteristic: chess as a sport.
Rather than chattering away incoherently about “analytical skills” or dogmatically trying to shoehorn chess into the “helping your math” box, perhaps we should simply focus on that: In what ways might chess, as a sport, provide certain educational advantages?
A BIT OF BACKGROUND:
My name is Howard Burton and I am a documentary filmmaker and author. I produced a recently released 4-part documentary, THROUGH THE MIRROR OF CHESS: A CULTURAL EXPLORATION, about the remarkable impact of chess on culture, art, science and sport. I also wrote a book, CHESSAYS: TRAVELS THROUGH THE WORLD OF CHESS, about all sorts of chess-related issues that I encountered during my time spent as a tourist in the chess world. Visit our website for more details HERE.
