Once upon a time, while in college, I decided to take my first intro-to-proofs class. I was so excited. "This is it!" I thought, "now I get to learn how to think like a mathematician." You see, for the longest time, my mathematical upbringing was very... not mathematical. As a student in high school and well into college, I was very good at being a robot. Memorize this formula? No problem. Plug in these numbers? You got it. Think critically and deeply about the ideas being conveyed by the mathematics? Nope. It wasn't because I didn't want to think deeply. I just wasn't aware there was anything to think about. I thought math was the art of symbol-manipulation and speedy arithmetic computations. I'm not good at either of those things, and I never understood why people did them anyway. But I was excellent at following directions. So when teachers would say "Do this computation," I would do it, and I would do it well. I just didn't know what I was doing. By the time I signed up for that intro-to-proofs class, though, I was fully aware of the robot-symptoms and their harmful side effects. By then, I knew that math not just fancy hieroglyphics and that even people who aren't super-computers can still be mathematicians because—would you believe it?—"mathematician" is not synonymous with "human calculator." There are even—get this—ideas in mathematics, which is something I could relate to. ("I know how to have ideas," I surmised one day, "so maybe I can do math, too!") One of my instructors in college was instrumental in helping to rid me of robot-syndrome. One day he told me, "To fully understand a piece of mathematics, you have to grapple with it. You have to work hard to fully understand every aspect of it." Then he pulled out his cell phone, started rotating it about, and said, "It's like this phone. If you want to understand everything about it, you have to analyze it from all angles. You have to know where each button is, where each ridge is, where each port is. You have to open it up and see how it the circuitry works. You have to study it—really study it—to develop a deep understanding." "And that" he went on to say, "is what studying math is like."
A nice little essay on mathematics for old and young alike–and particularly for those who think they don’t understand or “get” math. It’s ultimately not what you think it is, there’s something beautiful lurking underneath.
In fact, I might say that unless you can honestly describe mathematics as “beautiful”, you should read this essay and delve a bit deeper until you get the understanding that’s typically not taught in mathematics until far too late in most people’s academic lives.
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Six years ago I received an email from a colleague in the mathematics department at UC Berkeley asking me whether he should participate in a study that involved “collecting DNA from the brigh…
Not sure how I had missed this in the brouhaha a few weeks back, but it’s one of the more sober accounts from someone who’s actually got some math background and some reasonable idea about the evolutionary theory involved. It had struck me quite significantly that both Gowers and Tao weighed in as they did given their areas of expertise (or not). Perhaps it was worthwhile simply for the attention they brought? Gowers did specifically at least call out his lack of experience and asked for corrections, though I didn’t have the fortitude to wade through his hundreds of comments–perhaps this stands in part because there was little, if any indication of the background and direct identity of any of the respondents within the thread. As an simple example, while reading the comments on Dr. Pachter’s site, I’m surprised there is very little indication of Nicholas Bray’s standing there as he’s one of Pachter’s students. It would be much nicer if, in fact, Bray had a more fully formed and fleshed out identity there or on his linked Gravatar page which has no detail at all, much less an actual avatar!
This post, Gowers’, and Tao’s are all excellent reasons for a more IndieWeb philosophical approach in academic blogging (and other scientific communication). Many of the respondents/commenters have little, if any, indication of their identities or backgrounds which makes it imminently harder to judge or trust their bonafides within the discussion. Some even chose to remain anonymous and throw bombs. If each of the respondents were commenting (preferably using their real names) on their own websites and using the Webmention protocol, I suspect the discussion would have been richer and more worthwhile by an order of magnitude. Rivin at least had a linked Twitter account with an avatar, though I find it less than useful that his Twitter account is protected, a fact that makes me wonder if he’s only done so recently as a result of fallout from this incident? I do note that it at least appears his Twitter account links to his university website and vice-versa, so there’s a high likelihood that they’re at least the same person.
I’ll also note that a commenter noted that they felt that their reply had been moderated out of existence, something which Lior Pachter certainly has the ability and right to do on his own website, but which could have been mitigated had the commenter posted their reply on their own website and syndicated it to Pachter’s.
Hiding in the comments, which are generally civil and even-tempered, there’s an interesting discussion about academic publishing that could have been its own standalone post. Beyond the science involved (or not) in this entire saga, a lot of the background for the real story is one of process, so this comment was one of my favorite parts.
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After Sir Michael Atiyah’s presentation of a claimed proof of the Riemann Hypothesis earlier this week at the Heidelberg Laureate Forum, we’ve shared some of the immediate discussion in the aftermath, and now here’s a round-up of what we’ve learned.
I’m not sure I agree wholly with some of the viewpoint taken here, but I will admit that I was reading some of the earlier reports and not as much of the popular press coverage. Most reports I heard specifically mentioned the proof hadn’t been seen or gone over by others and suggested caution both as a result of that as well as the fact that Atiyah had had some recent false starts in the past several years. Some went as far as to mention that senior mathematicians in the related areas had not commented at all on the purported proof and hinted that this was a sign that they didn’t think the proof held water but also as a sign of respect for Atiyah so as not to besmirch his reputation either. In some sense, the quiet was kind of a kiss of death.
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The Riemann hypothesis, a formula related to the distribution of prime numbers, has remained unsolved for more than a century
One of the lesser articles I’ve seen on the topic thus far…
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