👓 Learning How to Learn Math | Math3ma | Tai-Danae Bradley

Read Learning How to Learn Math by Tai-Danae BradleyTai-Danae Bradley (math3ma.com)
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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🔖 Collaborative Workshop for Women in Mathematical Biology | IPAM

Bookmarked Collaborative Workshop for Women in Mathematical Biology (IPAM)

June 17-21, 2019

This workshop will tackle a variety of biological and medical questions using mathematical models to understand complex system dynamics. Working in collaborative teams of 6, each with a senior research mentor, participants will spend a week making significant progress with a research project and foster innovation in the application of mathematical, statistical, and computational methods in the resolution of problems in the biosciences. By matching senior research mentors with junior mathematicians, the workshop will expand and support the community of scholars in mathematical biosciences. In addition to the modeling goals, an aim of this workshop is to foster research collaboration among women in mathematical biology. Results from the workshop will be published in a peer-reviewed volume, highlighting the contributions of the newly-formed groups. Previous workshops in this series have occurred at IMA, NIMBioS, and MBI.

This workshop will have a special format designed to facilitate effective collaborations.

  • Each senior group leader will present a problem and lead a research group.
  • Group leaders will work with a more junior co-leader, someone with whom they do not have a long-standing collaboration, but who has enough experience to take on a leadership role.
  • Additional team members will be chosen from applicants and invitees. We anticipate a total of five or six people per group.

It is expected that each group will continue to work on their project together after the workshop, and that they will submit results to the Proceedings volume for the workshop.

The benefit of such a structured program with leaders, projects and working groups planned in advance is based on the successful WIN, Women In Numbers, conferences and is intended to provide vertically integrated mentoring: senior women will meet, mentor, and collaborate with the brightest young women in their field on a part of their research agenda of their choosing, and junior women and graduate students will develop their network of colleagues and supporters and encounter important new research areas to work in, thereby fostering a successful research career. This workshop is partially supported by NSF-HRD 1500481 – AWM ADVANCE grant.

ORGANIZING COMMITTEE

Rebecca Segal (Virginia Commonwealth University)
Blerta Shtylla (Pomona College)
Suzanne Sindi (University of California, Merced)
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🔖 Sierpinski number | Wikipedia

Bookmarked Sierpiński number (Wikipedia)
In number theory, a Sierpinski or Sierpiński number is an odd natural number k such that {\displaystyle k\times 2^{n}+1} is composite, for all natural numbers n. In 1960, Wacław Sierpiński proved that there are infinitely many odd integers k which have this property. In other words, when k is a Sierpiński number, all members of the following set are composite:
{\displaystyle \left\{\,k\cdot {}2^{n}+1:n\in \mathbb {N} \,\right\}.}
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👓 Mathematics matters | Bits of DNA

Read Mathematics matters by Lior PachterLior Pachter (Bits of DNA)
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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👓 "The Danger of a Single Story" in Mathematics | Roots of Unity

Read "The Danger of a Single Story" in Mathematics (Scientific American Blog Network)
The Lathisms podcast shares the varied stories of Hispanic and Latinx mathematicians
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👓 Atiyah Riemann Hypothesis proof: final thoughts | The Aperiodical

Read Atiyah Riemann Hypothesis proof: final thoughts by Katie Steckles and Christian Lawson-Perfect (The Aperiodical)
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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👓 Skepticism surrounds renowned mathematician’s attempted proof of 160-year-old hypothesis | Science | AAAS

Read Skepticism surrounds renowned mathematician’s attempted proof of 160-year-old hypothesis (Science | AAAS)
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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🔖 Sylvester’s Line Problem | Wolfram MathWorld

Read Sylvester's Line Problem (Wolfram MathWorld)

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through every two of them passes through a third unless they are all on a single line. This problem was proposed by Sylvester (1893), who asked readers to "Prove that it is not possible to arrange any finite number of real points so that a right line through every two of them shall pass through a third, unless they all lie in the same right line."

Woodall (1893) published a four-line "solution," but an editorial comment following his result pointed out two holes in the argument and sketched another line of enquiry, which is characterized as "equally incomplete, but may be worth notice." However, no correct proof was published at the time (Croft et al. 1991, p. 159), but the problem was revived by Erdős (1943) and correctly solved by Grünwald (1944). Coxeter (1948, 1969) transformed the problem into an elementary form, and a very short proof using the notion of Euclidean distance was given by Kelly (Coxeter 1948, 1969; Chvátal 2004). The theorem also follows using projective duality from a result of Melchior (1940) proved by a simple application of Euler's polyhedral formula (Chvátal 2004).

Additional information on the theorem can be found in Borwein and Moser (1990), Erdős and Purdy (1991), Pach and Agarwal (1995), and Chvátal (2003).

In September 2003, X. Chen proved a conjecture of Chvátal that, with a certain definition of a line, the Sylvester-Gallai theorem extends to arbitrary finite metric spaces.

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🔖 Sylvester’s Problem, Steinberg’s Solution | Cut the Knot

Bookmarked Sylvester's Problem, Gallai's Solution (cut-the-knot.org)
T. Gallai's proof has been outlined by P. Erdös in his submission of the problem to The American Mathematical Monthly in 1943. Solution Given the set Π of noncollinear points, consider the set of lines Σ that pass through at least two points of Π. Such lines are said to be connecting. Among the connecting lines, those that pass through exactly two points of Π are called ordinary.
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🔖 Sylvester–Gallai theorem | Wikipedia

Bookmarked Sylvester–Gallai theorem (Wikipedia)

The Sylvester–Gallai theorem in geometry states that, given a finite number of points in the Euclidean plane, either
* all the points lie on a single line; or
* there is a line which contains exactly two of the points.
It is named after James Joseph Sylvester, who posed it as a problem in 1893, and Tibor Gallai, who published one of the first proofs of this theorem in 1944.

A line that contains exactly two of a set of points is known as an ordinary line. According to a strengthening of the theorem, every finite point set (not all on a line) has at least a linear number of ordinary lines. There is an algorithm that finds an ordinary line in a set of n points in time proportional to n log n in the worst case.

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🔖 The Erdős Discrepancy Problem (6.09.2017) | Terence Tao | YouTube

Bookmarked The Erdős Discrepancy Problem (6.09.2017) at Instytut Matematyczny Uniwersytetu Wrocławskiego by Terence TaoTerence Tao (YouTube)

The discrepancy of a sequence f(1), f(2), ... of numbers is defined to be the largest value of |f(d) + f(2d) + ... + f(nd)| as n and d range over the natural numbers. In the 1930s, Erdős posed the question of whether any sequence consisting only of +1 and -1 could have bounded discrepancy. In 2010, the collaborative Polymath5 project showed (among other things) that the problem could be effectively reduced to a problem involving completely multiplicative sequences. Finally, using recent breakthroughs in the asymptotics of completely multiplicative sequences by Matomaki and Radziwiłł, as well as a surprising application of the Shannon entropy inequalities, the Erdős discrepancy problem was solved in 2015. In his talk TT will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.

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🔖 The Erdős Discrepancy Problem | Terence Tao | YouTube

Bookmarked The Erdős Discrepancy Problem at Institute for Pure & Applied Mathematics (IPAM) by Terence TaoTerence Tao (YouTube)
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🔖 Tao’s resolution of the Erdős discrepancy problem | AMS | K. Soundararajan

Bookmarked Tao’s resolution of the Erdős discrepancy problem by K. Soundararajan (Bulletin of the American Mathematical Society, Volume 55, Number 1, January 2018, Pages 81–92)

This article gives a simplified account of some of the ideas behind Tao’s resolution of the Erdős discrepancy problem.
http://dx.doi.org/10.1090/bull/1598 | PDF

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🔖 The Erdős discrepancy problem | Polymath1Wiki

Bookmarked The Erdős discrepancy problem (Polymath1Wiki)
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