On the purpose of doing mathematics

Posted on February 17, 2011 by Kareem Carr

by Kareem Carr

It’s been a while since William Thurston wrote “On Proof and Progress in Mathematics”.  However, in this answer posted on MathOverflow, he clearly still articulates, better than I ever could, what I find valuable about mathematics:

It’s not mathematics that you need to contribute to. It’s deeper than that: how might you contribute to humanity, and even deeper, to the well-being of the world, by pursuing mathematics? Such a question is not possible to answer in a purely intellectual way, because the effects of our actions go far beyond our understanding. We are deeply social and deeply instinctual animals, so much that our well-being depends on many things we do that are hard to explain in an intellectual way. That is why you do well to follow your heart and your passion. Bare reason is likely to lead you astray. None of us are smart and wise enough to figure it out intellectually. Continue reading →

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Math, How do I love thee? Let me count the ways….

Posted on February 13, 2011 by Angelean Hendrix

by Angelean Hendrix

How do I love thee? Let me count the ways.
I love thee to the depth and width and height
Analysis can prove, when dimensions out of sight
For the ends of Optimizations and ideal attracting solutions.
I love thee to the level of every proof’s manipulation
And most quiet subtly, much to De Morgan’s delight.
I love thee completely, in finite cover to be right;
I love thee purely, and for challenges application raise,
I love thee for your lucidity and breadth use
In my vain attempts at convergence, and with my cloddish programming gait.
I love thee with every reference I  lose
With every hour I have to give -I love thee with the pain,
brain cells, and insights of all my life! -and, if the universe choose,
I shall but love thee better after Thesis Defend.
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In Pursuit of Increased Audience Participation

Posted on February 10, 2011 by Derek Smith

by Derek Smith

Maybe it shouldn’t, but it often amazes me when I notice similarities between tutoring 6th graders and my work as a TA. I don’t mean this in a disparaging manner; I’ve simply observed a few common (though not suggested) approaches to solving problems in mathematics. For instance, many students seem to rely strictly on divine inspiration prior to asking for help! They may remember a few facts from lecture, but leave their book and scratch paper entirely untouched. I often wonder about and occasionally experiment with techniques to increase student engagement and would like to share a positive experience I had last week.

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Advice on Attending Conferences in the Notices

Posted on February 6, 2011 by Kareem Carr

by Kareem Carr

There is a great article by Katherine Ott in the Notices this month about attending conferences.  I will just quote the first paragraph:

Like many mathematicians, I occasionally miss class in order to attend a research conference.  When I explain the reason for my upcoming absence, the incredulous look on my students’ faces says it all: You’re traveling there? To do math? And listen to math talks all day? Over the weekend? As a graduate student, you might feel the same way. After all, who wants to do work over an entire weekend? The truth is that mathematics research conferences are an integral part of being a mathematician; and yes, as a graduate student you are a mathematician! Although the idea might be unappealing or intimidating at first, graduate school is the time to begin attending research conferences. Ultimately, attending and participating in research conferences will help you write your dissertation, get a postdoc or a job, and move through the tenure process of academia.

[Original PDF Article]

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Happy Mathematician, Productive Mathematician?

Posted on February 2, 2011 by Kareem Carr

by Kareem Carr

An article by Benedict Carey in the New York Times last month highlighted a study that might shed some insight both on why mathematics is so enjoyable and how to get slightly better at resolving otherwise puzzling research problems. Carey wrote that,

In a just completed study, researchers at Northwestern University found that people were more likely to solve word puzzles with sudden insight when they were amused, having just seen a short comedy routine.

The article continues by saying that,

“What we think is happening,” said Mark Beeman, a neuroscientist who conducted the study with Karuna Subramaniam, a graduate student, “is that the humor, this positive mood, is lowering the brain’s threshold for detecting weaker or more remote connections” to solve puzzles.

We tend to emphasize the thrill that we experience at the end of solving a tricky problem as being the primary reward of hours of work. However, the article argues that the journey itself toward the goal can be enjoyable.

Continue reading →

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