My name has the perfect number of characters.
“Butterworth is slightly impatient with this chicken and egg question - which comes first, zeal or hard work? He says that “if, for whatever reason, you start working hard at mathematics when all your classmates don’t, then the teacher is going to favour you, so you’re going to get external rewards, and you’re going to get the internal rewards of being able to do something rather well that your mates aren’t so good at, and so you’ll start off a virtuous circle of external rewards, internal rewards, you work a bit harder, you get even farther ahead of your classmates, who aren’t actually putting in the time. So it wouldn’t be surprising that if random people who for some reason select to pursue maths on the whole get rewarded because they are going to be better than their peers.”
— Do Math
“Mathematics is a process of staring hard enough with enough perseverance at the fog of muddle and confusion to eventually break through to improved clarity. I’m happy when I can admit, at least to myself, that my thinking is muddled, and I try to overcome the embarassment that I might reveal ignorance or confusion. Over the years, this has helped me develop clarity in some things, but I remain muddled in many others. I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication.”
“Mathematics sings when we feel it in our whole brain. People are generally inhibited about even trying to share their personal mental models. People like music, but they are afraid to sing. You only learn to sing by singing.”
— Bill Thurston from the Forward to Crocheting Adventures with the Hyperbolic Planes.
“Perelman’s aversion to public spectacle and to riches is mystifying to many. I have not talked to him about it and I can certainly not speak for him, but I want to say I have complete empathy and admiration for his inner strength and clarity, to be able to know and hold true to himself. Our true needs are deeper – -yet in our modern society most of us reflexively and relentlessly pursue wealth, consumer goods and admiration. We have learned from Perelman’s mathematics. Perhaps we should also pause to reflect on ourselves and learn from Perelman’s attitude toward life.”
In empirical studies of friendship networks participants are typically asked, in interviews or questionnaires, to identify some or all of their close friends, resulting in a directed network in which friendships can, and often do, run in only one direction between a pair of individuals. Here we analyze a large collection of such networks representing friendships among students at US high and junior-high schools and show that the pattern of unreciprocated friendships is far from random. In every network, without exception, we find that there exists a ranking of participants, from low to high, such that almost all unreciprocated friendships consist of a lower-ranked individual claiming friendship with a higher-ranked one. We present a maximum-likelihood method for deducing such rankings from observed network data and conjecture that the rankings produced reflect a measure of social status. We note in particular that reciprocated and unreciprocated friendships obey different statistics, suggesting different formation processes, and that rankings are correlated with other characteristics of the participants that are traditionally associated with status, such as age and overall popularity as measured by total number of friends.
This article was published by Wired on December 9, 2009. This is not a new news but I still find it amazing. The first time I saw this, I was like, “WHOOAAH! These are beautiful!”
This article was about the Mandelbulb. A group of math geeks created a three-dimensional analogue for the mesmerizing Mandelbrot fractal. The 3-D renderings were generated by applying an iterative algorithm to a sphere. The same calculation is applied over and over to the sphere’s points in three dimensions. In spirit, that’s similar to how the original 2-D Mandelbrot set generates its infinite and self-repeating complexity.