Read | Chris Aldrich

🔖 What is good mathematics? | Terry Tao

Bookmarked What is good mathematics? (arxiv.org)

Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously. As a case study, the story of Szemer'edi's theorem is presented.

This looks like a cool little paper.

Update 3/17/17

Some thoughts after reading

And indeed it was. The opening has lovely long (though possibly incomplete) list of aspects of good mathematics toward which mathematicians should strive. The second section contains an interesting example which looks at the history of a theorem and it’s effect on several different areas. To me most of the value is in thinking about the first several pages. I highly recommend this to all young budding mathematicians.

In particular, as a society, we need to be careful of early students in elementary and high school as well as college as the pedagogy of mathematics at these lower levels tends to weed out potential mathematicians of many of these stripes. Students often get discouraged from pursuing mathematics because it’s “too hard” often because they don’t have the right resources or support. These students, may in fact be those who add to the well-roundedness of the subject which help to push it forward.

I believe that this diverse and multifaceted nature of “good mathematics” is very healthy for mathematics as a whole, as it it allows us to pursue many different approaches to the subject, and exploit many different types of mathematical talent, towards our common goal of greater mathematical progress and understanding. While each one of the above attributes is generally accepted to be a desirable trait to have in mathematics, it can become detrimental to a field to pursue only one or two of them at the expense of all the others.

As I look at his list of scenarios, it also reminds me of how areas within the humanities can become quickly stymied. The trouble in some of those areas of study is that they’re not as rigorously underpinned, as systematic, or as brutally clear as mathematics can be, so the fact that they’ve become stuck may not be noticed until a dreadfully much later date. These facts also make it much easier and clearer in some of these fields to notice the true stars.

As a reminder for later, I’ll include these scenarios about research fields:

A field which becomes increasingly ornate and baroque, in which individual
results are generalised and refined for their own sake, but the subject as a
whole drifts aimlessly without any definite direction or sense of progress;

A field which becomes filled with many astounding conjectures, but with no
hope of rigorous progress on any of them;

A field which now consists primarily of using ad hoc methods to solve a collection
of unrelated problems, which have no unifying theme, connections, or purpose;

A field which has become overly dry and theoretical, continually recasting and
unifying previous results in increasingly technical formal frameworks, but not
generating any exciting new breakthroughs as a consequence; or

A field which reveres classical results, and continually presents shorter, simpler,
and more elegant proofs of these results, but which does not generate any truly
original and new results beyond the classical literature.

A new fossil could push back the start of life on Earth | The Economist

Read A new fossil could push back the start of life on Earth (The Atlantic)

The putative fossils formed just a few hundred million years after Earth itself

Science remains male-dominated | The Economist

Read Women in research Science remains male-dominated (The Economist)

But a new report says females are catching up

MARCH 8th was International Women’s Day. That seemed to Elsevier, an academic publisher, a good occasion to publish a report looking at the numbers and performance of female scientists around the world. The report, “Gender in the Global Research Landscape”, analysed the authorship of more than 62m peer-reviewed papers published in 27 subject areas over the past 20 years, in 11 mostly rich countries and in the European Union as a whole. The papers and their citations are indexed in Scopus, a database that is run by Elsevier.

In the EU, and in eight of the 11 countries considered, the share of women authors grew from about 30% in the late 1990s to about 40% two decades later. Brazil and Portugal are closest to equality, each just a percentage point shy of it. In Japan, by contrast, barely a fifth of researchers are female—a fact that may reflect the particularly uncool image science has among Japanese schoolgirls.

Women are best represented in subjects related to health care. In nursing and psychology, for example, they outnumber men in several countries, including America and Britain. Less than a quarter of researchers who publish papers in the physical sciences are women. Perhaps as a consequence of this, inventors who register patents are still almost all men. In the places covered by the report the share of patent applications by women ranges from 8% of those filed in Japan to 26% in Portugal. Women are, however, making progress, even in the still-male-heavy world of engineering. Though they constitute only between 10% and 32% of authors of papers in that field in the places the report looks at, the share of those papers in which a woman is the lead author is between 35% and 52%.

All of this is qualified good news. Women do, nevertheless, still suffer from a “leaky pipeline” phenomenon that sees them drop out of scientific careers at a higher rate than men do. At Imperial College, London, regarded by many as Britain’s leading technological university, about 35% of undergraduates are women. But that percentage falls with each step up the career ladder. At the moment, only 15% of Imperial’s professors are women.

Partly, this stems from the fact that when those professors were undergraduates the sex ratio was even worse. But it also reflects the problem of career-building which women face in all areas, not just science. Even in the most progressive countries, they still shoulder the lion’s share of child care and housework. Boosting their numbers in the laboratory will take more than merely convincing girls that science is cool.

The minimum age of criminal responsibility continues to divide opinion | The Economist

Read The minimum age of criminal responsibility continues to divide opinion by The Data Team (The Economist)

A proposal to let Philippine criminal courts try nine-year-olds has drawn sharp criticism. But in 35 American states, children of any age can be convicted and sentenced

COMMON law has long held that committing a crime requires both a prohibited act and a “mens rea”, or “guilty mind”—the criminal knowing that the act was wrong. There is no global consensus regarding the youngest age at which a child can be deemed to have such intent, and thus can be tried and convicted of a criminal offence. Ten years ago the United Nations Committee on the Rights of the Child recommended an “absolute minimum” age of 12 for criminal responsibility, and urged countries “to continue to increase it to a higher age level”. The Philippines appears poised to move in the opposite direction: lawmakers there have proposed reducing the cut-off from 15 years old to nine. The bill has prompted sharp criticism both at home and abroad, and legislators are still arguing over its text.

Not long ago the Philippines earned a reputation for a relatively progressive stance on this issue. It introduced its current minimum age of criminal responsibility (MACR) in 2006, making it one of just 19 countries whose MACR is 15 or older. However, Rodrigo Duterte, the president, has adopted a harsh “tough-on-crime” agenda. The bill’s supporters say it would stop adult criminals from recruiting children under the age of criminal responsibility for drug-trafficking. Human-rights advocates counter that there is no evidence that this would reduce crime. Instead, says Leo Ratledge of Child Rights International Network, a British charity, it would punish victims of exploitation rather than those who exploit them.

The other members of the MACR-above-14 club are an incongruous bunch. Predictably, they include places like Norway and Sweden, which take a generally liberal approach to criminal justice. However, the top of the table is occupied by less developed countries that happen to have revised their juvenile-justice laws in recent years: in Timor-Leste and Mozambique, the MACR is now 16. Although most European states sit comfortably above the UN recommendation, there are notable exceptions. Scotland can hand out criminal records to eight-year-olds, though legislation is being mooted that will raise the minimum age limit to 12. In the rest of Britain, ten-year-olds can be tried for a crime. This British colonial legacy is reflected in the relatively low MACRs seen in South Africa, Australia and New Zealand. Similarly, Nigeria, India, Pakistan and Bangladesh are among the 21 countries that set a MACR of seven, the lowest national age globally.

In some cases the law is not clear-cut. The MACR in Comoros is based on puberty. It can differ by sex (as in Iran) or type of offence (Malaysia), while Poland and France entrust the issue to judges’ discretion. Nonetheless, even a vague minimum of “puberty” provides more protection than simply having no MACR at all. Just a handful of countries have no national MACR. The most striking is the United States. Although America sets a threshold of 11 years old for federal offences, the overwhelming share of crimes are policed at the state level. And 35 out of the 50 states have not set a MACR, putting them in a club with Cuba, Malaysia (exclusively for terrorism) and Sudan (for drug offences).

Hillbilly sellout: The politics of J. D. Vance’s “Hillbilly Elegy” are already being used to gut the working poor | Salon.com

Read Hillbilly sellout: The politics of J. D. Vance’s “Hillbilly Elegy” are already being used to gut the working poor (Salon)

Conservatives and the media treated Vance's memoir like "Poor People for Dummies." Watch his damaging rhetoric work

Study debunks old concept of how anesthesia works | Phys.Org

Read Study debunks old concept of how anesthesia works (phys.org)

Anesthesia induces unconsciousness by changing the function of proteins that reside on the surface of a thin membrane that forms a barrier around all cells, according to new research from Weill Cornell Medicine scientists. The findings challenge a century-old concept of how anesthetics work and may help guide the development of new agents associated with fewer side effects.

Why some infinities are bigger than others | Aeon Essays

Read Why some infinities are bigger than others by A. W. Moore (Aeon Essays)

Georg Cantor showed that some infinities are bigger than others. Did he assault mathematical wisdom or corroborate it?

Lofty goals here, but I’m not quite sure he’s really make the case he set out to in these few words. The comments on the article are somewhat interesting, but seem to devolve into the usual pablum seen on such posts. Nothing stuck out to me as a comment by a solid mathematician, which might have been interesting.

There Is No Deep State | The New Yorker

Read There Is No Deep State by David Remnick (The New Yorker)

The problem in Washington is not a conspiracy against the President; it’s the President himself.

📖 Read pages 55 – 86 of 776 of Learning PHP, MySQL & JavaScript with JQUERY, CSS & HTML5 by Robin Nixon

I’ve been promising myself that I would do some brushing up on programming skills this year and this seems like a fairly reasonable text with some simple examples.