Math across disciplines

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by Jeremy Lane

Math and Statistics subject editor

In his inaugural post, our new math and statistics editor, Jeremy Lane, brings us news and views from the world of math and its role in society.

International ranking of math departments: useful tool or gaming the system?

In October, Nassif Ghoussoub reblogged a fascinating piece of investigative blogging inspired by a recent global ranking of universities by subject area published by US News and World Report (USNWR).

In the post, mathematician and biologist Lior Pachter explores how, despite not having a PhD program until 2012, the relatively unknown King Abdulaziz University (KAU) managed to place seventh in USNWR’s Mathematics ranking, above giants such as MIT and Cambridge. Pachter reveals that KAU games the ranking system by employing roughly a quarter of highly cited mathematicians (according to Thomson-Reuters) in very lucrative adjunct contracts that only require the mathematician’s physical presence on campus for two weeks every year, thus artificially inflating its faculty’s publication numbers.

More troubling than simple rankings, however, Pachter also notes that – like other Saudi universities – KAU is gender segregated. Among the department’s list of 118 past and present adjuncts, there is only one woman. He points out other programs at KAU which suffer similar deficiencies, noting that their yearly conference on genomic medicine has had zero female participants for the last two years.

The post ends by linking to a recent preprint which demonstrates how sensitive ranking systems can be to changes in the rather arbitrary way variables (such as impact factors) are weighted. This raises the question: who is to blame for the situation at KAU? The university’s administrators, the adjuncts who enable them, or academia’s collective obsession with citations?

The subject has since appeared in an article in the Daily Californian and a blog post by biologist Jonathan Eisen.

Math doesn’t excuse you from being a decent human being

The October issue of Notices of the American Mathematical Society had a short article by Abigail Thompson titled Does diversity trump ability: and example of the misuse of mathematics in the social sciences. In the article, Thompson deconstructs the mathematics of a popular social sciences article: Groups of diverse problem solvers can outperform groups of high-ability problem solvers, by Hong and Page, which was published by the Proceedings of the National Academy of Sciences in 2004.

The Hong and Page article proves a mathematical theorem that translates roughly to: “for large enough groups of people, diverse groups will almost always outperform highly skilled but homogeneous groups at a given task.” Thompson’s deconstruction, however, says that “Once the unnecessary technicalities are removed and basic errors corrected, the theorem is revealed to be little more than a straightforward restatement of its hypotheses,” and further claims that “a careful examination of Theorem 1’s statement shows that it has no real-world applications.”

In a recent blog post, Isabella Laba, a UBC professor, addresses Thompson’s article in the broader context of diversity in the mathematical community:

“I have satisfied myself that Thompson is not unfair in her mathematical analysis. Her article, however, does not exist in a vacuum. It will be read in mathematics departments, organizations and committees where “diversity” is viewed as a bureaucratic imposition made on them by distant administrators who don’t understand research, even as their few women faculty often find themselves alienated and sidelined.”

She then goes on to explain how, mathematically justified or not, diversity is important and should be fostered rather than justified away with mathematical arguments. Just because you can apply mathematical logic to an issue, such as diversity, doesn’t mean you should. Some issues concern our humanity, not our ability to do math.

Math and the biological sciences

Continuing in this theme, I’m reminded of two recent obituaries for the great French mathematician Alexander Grothendieck, who passed away in November. The first, by Ed Frenkel, praises Grothendieck’s passion for pacifism and ends with the quote,

“A party of one, he was unafraid to be himself and to speak his truth. The man who had advanced mathematics in the most profound ways did not believe that math was the answer to everything. He taught us that life is more valuable than any equation.”

Contrast this with an obituary written by Mumford and Tate, which was submitted to Nature and subsequently subjected to major revisions for being too technical. The original rejected obituary appears on Mumford’s blog as Can One Explain Schemes to Biologists (bringing to mind last year’s online furor over E.O. Wilson’s piece on why great scientists don’t need math), and is accompanied by a lengthy commentary suggesting that the post was severely edited by Nature because their readers were too math illiterate to understand it.

The obituary describes Grothendieck’s humanistic enterprises:

“With a breathtakingly naive spirit (that had served him well doing math) he believed he could start a movement that would change the world.”

It concludes by saying,

“As a friend, Grothendieck could be very warm, yet the nightmares of his childhood had left him a very complex person. He was unique in almost every way. His intensity and naivety enabled him to recast the foundations of large parts of 21st century math using unique insights that still amaze today. The power and beauty of Grothendieck’s work on schemes, functors, cohomology, etc. is such that these concepts have come to be the basis of much of math today. The dreams of his later work still stand as challenges to his successors.”

Though undoubtedly written with different goals and audiences in mind, the difference of opinion with respect to Grothendieck’s humanistic enterprises is hard to miss. I feel inclined to agree with Frenkel’s.

For more on the divide between mathematics and biology, see this lengthy piece (also by Lior Pachter, mentioned above) on the obituary by Mumford and Tate.

That’s all for this episode of math and statistics – remember that we’re always looking for more blogs in this category, so if you have one – or are planning to start one for 2015 – let us know!

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