Anyone Can Be a Math Person Once They Know the Best Learning Techniques
So you think you're "not a math person"? International Mathematical Olympiad coach Po-Shen Loh strongly disagrees.
Po-Shen Loh, PhD, is associate professor of mathematics at Carnegie Mellon University, which he joined, in 2010, as an assistant professor in the Department of Mathematical Sciences. As a Hertz Fellow, Professor Loh received his PhD in combinatorics of the Pure Math Department at Princeton University. His thesis discussed several original results that he discovered during his graduate study in joint projects with his advisor and other collaborators. Professor Loh studies questions that lie at the intersection of two branches of mathematics: combinatorics (the study of discrete systems) and probability theory.
Prior to his work at Princeton, Loh received the equivalent of a master's degree in mathematics from the University of Cambridge (United Kingdom) in 2005, where he was supported by a Winston Churchill Foundation Scholarship. He received his undergraduate degree in mathematics from Caltech in 2004, graduating first in his class, and his undergraduate thesis later received the Honorable Mention for the 2004 AMS-MAA-SIAM Morgan Prize.
In his spare time, Loh has maintained his involvement with the United States Mathematical Olympiad program. He is now the head coach of the national delegation, as well as a lead fundraiser for the organization. As a high school student, he won a silver medal at the 1999 International Mathematical Olympiad (IMO), and following his win continued to be active in the training of high school students at the U.S. national Math Olympiad Summer Program. In 2004, he served as the deputy leader for the U.S. team at the IMO in Athens, Greece, where our national team placed second. After completing his PhD, Loh again, served as deputy team leader for the United States at the International Mathematical Olympiad from 2010 to 2013. Afterwards Professor Loh was promoted to national head coach of the U.S.A. IMO team, and on his second attempt, Team U.S.A. won first place, in a competition with teams from over 100 countries represented.
Earlier this year, Loh received an NSF CAREER award, the most prestigious NSF award for junior faculty, which honors outstanding research combined with a commitment to teaching. Professor Loh is the founder of the educational technology startup expii.com, a crowd-sourced platform for the world to share interactive lessons in math and science.
Po-Shen Lo: I think that everyone in the world could be a math person if they wanted to. The keyword though, I want to say, is if they wanted to. That said, I do think that everyone in America could benefit from having that mathematical background in reasoning just to help everyone make very good decisions. And here I'm distinguishing already between math as people usually conceive of it, and decision making and analysis, which is actually what I think math is.
So, for example, I don't think that being a math person means that you can recite the formulas between the sines, cosines, tangents and to use logarithms and exponentials interchangeably. That's not necessarily what I think everyone should try to concentrate to understand. The main things to concentrate to understand are the mathematical principles of reasoning.
But let me go back to these sines, cosines and logarithms. Well actually they do have value. What they are is that they are ways to show you how these basic building blocks of reasoning can be used to deduce surprising things or difficult things. In some sense they're like the historical coverages of the triumphs of mathematics, so one cannot just talk abstractly about “yes let's talk about mathematical logic”, it's actually quite useful to have case studies or stories, which are these famous theorems.
Now, I actually think that these are accessible to everyone. I think that actually one reason mathematics is difficult to understand is actually because of that network of prerequisites. You see, math is one of these strange subjects for which the concepts are chained in sequences of dependencies.
When you have long chains there are very few starting points—very few things I need to memorize. I don't need to memorize, for example, all these things in history such as “when was the war of 1812?” Well actually I know that one, because that's a math fact—it was 1812—but I can't tell you a lot of other facts, which are just purely memorized. In mathematics you have very few that you memorize and the rest you deduce as you go through, and this chain of deductions is actually what's critical.
Now, let me contrast that with other subjects like say history. History doesn't have this long chain, in fact if you fully understand the war of 1812 that's great, and it is true that that will influence perhaps your understanding later of the women's movement, but it won't to be as absolutely prerequisite. In the sense that if you think about the concepts I actually think that history has more concepts than mathematics; it's just that they're spread out broader and they don't depend on each other as strongly. So, for example, if you miss a week you will miss the understanding of one unit, but that won't stop you from understanding all of the rest of the components.
So that's actually the difference between math and other subjects in my head. Math has fewer concepts but they're chained deeper. And because of the way that we usually learn when you had deep chains it's very fragile because you lose any one link—meaning if you miss a few concepts along the chain you can actually be completely lost. If, for example, you're sick for a week, or if your mind is somewhere else for a week, you might make a hole in your prerequisites. And the way that education often works where it's almost like riding a train from a beginning to an end, well it's such that if you have a hole somewhere in your track the train is not going to pass that hole.
Now, I think that the way to help to address this is to provide a way for everyone to learn at their own pace and in fact to fill in the holes whenever they are sensed. And I actually feel like if everyone was able to pick up every one of those prerequisites as necessary, filling in any gap they have, mathematics would change from being the hardest subject to the easiest subject.
I think everyone is a math person, and all that one has to do is to go through the chain and fill in all the gaps, and you will understand it better than all the other subjects actually.
Po-Shen Loh is a Hertz Foundation Fellow and Carnegie Mellon mathematics professor who thinks that history is a much harder subject than math. Do you agree? Well, your position on that might change before and after this video. Loh illuminates the invisible ladders within the world of math, and shows that it isn't about memorizing formulas—it's about processing reason and logic. With the support of the Fannie and John Hertz Foundation, Po-Shen Loh pursued a PhD in combinatorics at the Pure Math Department at Princeton University.
The Hertz Foundationmission is to provide unique financial and fellowship support to the nation's most remarkable PhD students in the hard sciences. Hertz Fellowships are among the most prestigious in the world, and the foundation has invested over $200 million in Hertz Fellows since 1963 (present value) and supported over 1,100 brilliant and creative young scientists, who have gone on to become Nobel laureates, high-ranking military personnel, astronauts, inventors, Silicon Valley leaders, and tenured university professors. For more information, visit hertzfoundation.org.
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