Mathematics

Inquiry-based learning is at the heart of the controversial California Math Framework. Rather than teaching students through rote learning, which instructors believe gives a false sense of virtuosity that comes undone when students have to think for themselves and do difficult problems, students are instead taken through a process of guided discovery in which they are persuaded through example and given the given the freedom to discover solutions, construct arguments, and work with peers, until they instinctively understand mathematics. Applying the theory to practice is much harder than it…

Time and again, I play a "good" blitz chess game. In blitz chess you have 5 minutes thinking for the totality of your game. This demands quick reasoning and a certain level of dexterity - with the mouse, if you are playing online as I usually do.My blitz rating on the chess.com site hovers around 2150-2200 elo points, which puts me at the level of a strong candidate master or something like that, which is more or less how I would describe myself. But time is of course running at a slower, but more unforgiving pace in my life, and I know that my sport prowess is going to decline - hell, it has…

At the very large and very small scale, Newtonian gravity does not work the way it should. The universe should not be expanding and forget trying to explain quantum mechanics. Trying to detail why electrons can behave as both particles and waves, depending on the experimental context in which they are observed, is challenging. Louis de Broglie, Niels Bohr, Erwin Schrödinger, and David Bohm all tried but used self-consistent yet contradictory interpretations. Einstein and Bohr's debates did not lead to conclusive results and the next generation of physicists opted for equations that derived…

The late Martin Gardner held for many years a fantastic feature in the popular Scientific American magazine. It was called "Mathematical Games", and it was worth the whole magazine by itself, although SciAm always featured many interesting articles about scientific advancements. Upon picking the magazine up at a newsstand, "Mathematical Games" was the first article I would read as a teenager eager to learn about the endless tricks Gardner taught there, in his wonderful tale-telling style.This morning my mind was still half-asleep as I got under the shower, and I started to think at one…

When it comes to baseball and football, coaches always know the numbers. That helps them make informed decisions on risk and reward. Less well-known is that clinicians also often make important healthcare decisions with the aid of algorithmic tools that draw on large amounts of complex data. Data from previous patients can help predict a new patient’s risk of complications after surgery, thanks to machine learning. Yet a framework for evaluating these algorithms must continue to evolve, and in a new op-ed, Tyler Loftus of University of Florida Health, Gainesville and colleagues…

When eco-terrorists destroyed a sugar beet field in Oregon a few years ago, the local organic industry group there said they were shocked anyone would be violent, even though the organic industry there demonized science daily. The attackers could not have been unknown to local groups, it is certain they were part of the community. But how did they switch from misguided - mutagenesis chemical and radiation baths can be certified organic but GMOS are an abomination of nature - to violent? A new paper tackled the issue in the context of the Capitol Hill riots a few months ago and while they…

In western nations, there is a great deal of interest in improving standardized test scores compared to Asian students, but few schools want to do what Asian schools do most; teach to the test and teach by rote. Instead, programs focus on increasing things like 'motivation' have become popular. And so we get a mashup of math and basketball. Should we call it mathketball? A group of Copenhagen schools placed 756 1st through 5th graders in a six-week program that they found had a positive effect on their desire to learn more, provided them with an experience of increased self-determination and…

Mathematics is a language and languages can be used to create stories. It just takes imagination to create time travel or wormholes or theories of strings or lots of nice things theoretical physicists throw into arXiv. Sometimes math has to create a story because real numbers don't work, even if the physics does. Wave-particle duality, a foundation of quantum mechanics, has a fascinating science history. James Clerk Maxwell, whose equations govern the device you are reading this article on, couldn't explain everything - he died of cancer at age 46. It was left to Albert Einstein a generation…

If you believe the Chinese government, they've had basically no meaningful COVID-19 deaths since March. I'd also like to sell you a wet market in Wuhan. Believing a dictatorship that has routinely lied has been disastrous. It was disastrous for the reputation of the World Health Organisation, who claimed no travel should be curtailed and that the virus could not spread from human to human because China told them that, it was disastrous for the doctor who exposed the Wuhan cover-up (he became dead), and it was disastrous for the world economy, which could take a decade to recover. It may be…

In our daily life, we unfortunately have become used to seeing images of tumors and melanomas. You may have noticed that they’re are not entirely symmetric. This asymmetry is useful to doctors in their diagnoses, but why are they asymmetric? Instinctively, we think that symmetric objects are most often found in nature, but perhaps assymetry is even more common. To complicate things, the same object may sometimes be symmetric and sometimes not. Take soap bubbles for example. When they are small, they seem perfectly symmetric, but when we increase their radius, we see that symmetry is broken:…