But when I went to college at Harvard, I took a course in topology, which is the study of spaces. The questions were really complicated and different and interesting in a way I had never expected. And it was just kind of like I fell in love. One way I might describe it is to say that I study symmetries of mathematical objects. All those rotations are symmetries. There are a lot of other ways symmetries come up, and they can get really, really complicated. So we use neat mathematical objects to think about them, called groups.
A lot of mathematics ultimately is artistic rather than useful. When I arrived as a professor at George Mason, I knew I wanted to do more than research and mathematics. I love teaching, but I felt like I wanted to do something for the world that was not part of the ivory tower of just solving problems that I thought were really curious and interesting.
One is to be available to answer quantitative questions. Someone once described to me the advice he gives to journalists. A favorite one is distinguishing between causation and correlation. Part of the problem, I think, is that scientists themselves always want to know more than they can with the tools they have.
Like, you might be interested in knowing whether taking hormones is helpful or harmful to women who are postmenopausal. What you can answer is the question of whether women who take hormones whom you enroll in your study — those specific women — have an increase or decrease in, say, heart disease rates or breast cancer rates or stroke rates compared to a control group or to the general population.
Or people like me? Or the population as a whole? Partly our goal is to help change the culture of journalism so that people recognize the importance of using quantitative arguments and thinking about quantitative issues before they come to conclusions.
On an individual level, if we have the ability to think quantitatively, we can make better decisions about our own health, about our own choices with regard to risk, about our own lifestyles. On a collective level, the impact of being educated in general is huge. We aspire to a literate society because it allows for public engagement, and I think this is also true for quantitative literacy. What is this payoff? Consider a baby playing with blocks. The infant struggles to grasp the object, and through hours of trial and error learns to use its hands in order to achieve the desired effect.
Are we to conclude that the only benefit the child gets from successfully placing the square block in the square hole is the satisfaction of a goal achieved and a slightly more organized playpen? Of course not. The real progress the baby has made is in developing motor skills, hand-eye coordination, and spatial intuition.
These skills are more general and have much greater utility than the task for which they were initially developed. Similarly, the greatest benefit that comes from successfully studying mathematics is the ability to think carefully. Indeed, it is precisely because students of mathematics do not realize that solving the problems they're working on requires a new way of thinking that these problems seem so difficult.
It may sound like intellectual snobbery to say that learning to think carefully requires studying mathematics, but the simple fact is that human mind is not built to understand the way the world works; rather, it's built to stay alive in the plains and savannas, and thus is prone to all sorts of faulty thinking: self-deception is the key to lying convincingly, which can be a useful survival strategy.
Wishful thinking, confirmation bias, and myriad other forms of incorrect reasoning are what come naturally to human beings, and learning to avoid these common errors takes real work.
Like the baby putting the square block into the square hole, solving mathematical problems requires learning to think in a new way, culminating in the form of reasoning known as mathematical rigor , which is so powerful that it is the only human activity which leads to undeniable absolute objective truth. Once you've seen the proof of a theorem , to deny the theorem is to misunderstand what it says.
Mathematical thinking is the basis of all of the sciences. You cannot be a scientist without learning mathematical thinking. Even scientists who don't make use of more advanced mathematical techniques need to be able to deduce which predictions follow from their hypotheses and which do not. Engineers who don't learn how to think like a mathematician leave themselves and their clients open to errors which can prove to be costly or fatal. Even if you have no intention of going into a technical field, mathematical thinking is the key to solving problems, to avoiding being taken in by scam artists, to making successful decisions.
You don't have to be Sherlock Holmes to benefit from making careful observations and sound deductions. Only if you know the difference between valid and invalid reasoning can you spot the errors, intentional or not, in the reasoning of salespeople, lawyers, and politicians who want your money and votes. Careful thinking is necessary to distinguish fact from fiction, which is a skill we all require if we're going to live in a democracy where citizens sit on juries and elect leaders.
Ultimately, this is why we should all study mathematics, even if we never end up using the particulars of algebra or calculus. This website will present a variety of applications that illustrate the innovative ways that the mathematical sciences are being used in a wide range of disciplines. For more information about SIAM visit the website: www. O'Leary and John M. Welcome to WhyDoMath Mathematical and computational analyses have proved to be uniquely insightful for solving a myriad of problems in science, society and our everyday lives.
Jones Wavelets Patrick J.
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