David Mumford on Grothendieck and magazine “Nature”

Can one explain schemes to biologists

December 14, 2014

John Tate and I were asked by Nature magazine to write an obituary for Alexander Grothendieck. Now he is a hero of mine, the person that I met most deserving of the adjective “genius”. I got to know him when he visited Harvard and John, Shurik (as he was known) and I ran a seminar on “Existence theorems”. His devotion to math, his disdain for formality and convention, his openness and what John and others call his naiveté struck a chord with me.

So John and I agreed and wrote the obituary below. Since the readership of Nature were more or less entirely made up of non-mathematicians, it seemed as though our challenge was to try to make some key parts of Grothendieck’s work accessible to such an audience. Obviously the very definition of a scheme is central to nearly all his work, and we also wanted to say something genuine about categories and cohomology. Here’s what we came up with:

Continue reading

Andreas Schleicher: Seven big myths about top-performing school systems

A paper by Andreas Schleicher, , at the BBC website. The list of “seven big myths”:

  1. Disadvantaged pupils are doomed to do badly in school
  2. Immigrants lower results
  3. It’s all about money
  4. Smaller class sizes raise standards
  5. Comprehensive systems for fairness, academic selection for higher results
  6. The digital world needs new subjects and a wider curriculum
  7. Success is about being born talented

In my [AB] humble opinion,  this appears to be the case when the negations of myths are myths, too (with a possible exception of no. 7). School systems cannot, and should not, be compared without first having a close look at socio-economic, cultural, and political environments of their home countries.

Unconscious biases

From  The New York Times: Is the Professor Bossy or Brilliant? Much Depends on Gender. By Claire Cain Miller, February 6, 2015

Male professors are brilliant, awesome and knowledgeable. Women are bossy and annoying, and beautiful or ugly.

These are a few of the results from a new interactive chart that was gaining notice on social media Friday. Benjamin Schmidt, a Northeastern University history professor, says he built the chart using data from 14 million student reviews on the Rate My Professors site. It allows you to search for any word to see how often it appeared in reviews and how it broke down by gender and department.

The chart makes vivid unconscious biases. The implications go well beyond professors and college students, to anyone who gives or receives feedback or performance reviews.

It suggests that people tend to think more highly of men than women in professional settings, praise men for the same things they criticize women for, and are more likely to focus on a woman’s appearance or personality and on a man’s skills and intelligence. […]

Studies have also shown that students can be biased against female professors. In one, teachers graded and returned papers to students at the exact same time, but when asked to rate their promptness, students gave female professors lower scores than men. Biases cut both ways — teachers have also been found to believe girls are not as good in math and science, even when they perform similarly to boys.

Ivor Grattan-Guinness obituary

From The Guardian, by Tony Crilly

Energetic historian of mathematics and logic

When Ivor Grattan-Guinness, who has died aged 73 of heart failure, became interested in the history of mathematics in the 1960s, it was an area of study widely considered to be irrelevant to mathematics proper, or something that older mathematicians did on retirement. As an undergraduate at Oxford, he found that mathematics was presented drily, with no inkling of the original motivations behind its development. So Ivor set himself the task of asking “What happened in the past?” – as opposed, he said, to taking the heritage viewpoint of asking “How did we get here?”

Read in full.

Ivor Owen Grattan-Guinness, historian of mathematics and logic, born 23 June 1941; died 12 December 2014

MBE to a maths clubs volunteer

From BBC:

A man who runs free maths classes for primary age children has been recognised in the New Year Honours list with an MBE.

Gbolahan Bright has been running the Bright Academy maths clubs for primary age children in London and Essex for the past 20 years.

“I have gained a lot from this society. I have been blessed and it would have been ungrateful of me if I did not give back,” he said.

Of the 500 or so children who have taken the classes, about 50 gained their GCSE while still at primary school.

Read more.

Film and discussion: “Colours of Math”

18 November 2014, , at Pushkin House.  From an advertisement:

The independent documentary “Colours of Math” (2012) by Ekaterina Eremenko – a German-based, American-trained, Russian-born documentary producer and mathematician – has been an unlikely runaway success.  It has been translated into 12 languages, and screened around the world.

With six mathematicians from different countries and six senses that lead them in their journey of discovery, the movie gives an insight into the mystery of abstract mathematical ideas and creative thinking.

The screening (60 min) is followed by a round table discussion. What is happening in contemporary mathematics? Are there particular national schools of thought and traditions of education? Prominent mathematicians will share their views on these questions.


Professor Sergey Foss, Heriot Watt University

Professor Leonid Parnovski, University College London

Professor Eugene Shargorodsky, Kings College London

Dr June Barrow-Green, Open University

The Imitation Game Cryptography Competition

From Charles Walkden, University of Manchester:

Dear all,

The Imitation Game Cryptography Competition:  www.maths.manchester.ac.uk/cryptography_competition_the_imitation_game

`The Imitation Game‘ is a biopic of Alan Turing starring Benedict Cumberbatch in the lead role (also starring Keira Knightley, Charles Dance,…) and will be released in cinemas on Nov 14th.

The film’s distributors asked us to get involved in the publicity and promotion for the film by running a one-off on-line `Imitation Game Cryptography Competition‘, www.maths.manchester.ac.uk/cryptography_competition_the_imitation_game.

It’s free to enter and is open to everybody.  There are some great prizes for you to win: film posters signed by the cast, DVD bundles, soundtracks, etc,  The competition runs until 14th Nov.
Please can you spread the word to anyone and everyone (and feel free to take part yourself!).
PS:  The School’s annual `Alan Turing Cryptography Competition’ will run again from Jan 2015, with registration opening on 1st Dec.  Unlike the Imitation Game competition, this is only open to school children in Year 11 or below – but again please spread the word!
Andrew, Charles, Kees, Sebastian, Helen

Ofsted: Low-level classroom disruption hits learning

From BBC http://www.bbc.co.uk/news/education-29342539 :

Low-level, persistent disruptive behaviour in England’s schools is affecting pupils’ learning and damaging their life chances, inspectors warn.

The report says too many school leaders, especially in secondary schools, underestimate the prevalence and negative impact of low-level disruptive behaviour and some fail to identify or tackle it at an early stage.


Source: Poll conducted by YouGov for Ofsted, http://www.ofsted.gov.uk/news/failure-of-leadership-tackling-poor-behaviour-costing-pupils-hour-of-learning-day

This is one of many low-level school issues that affect undergraduate mathematics teaching.  In a mathematics lecture, weaker students are more prone to “loosing the thread” than in most other courses. Also, students for whom English is not the first language,  in particular,  most from overseas are more sensitive to the signal-to-noise ratio than natives,  and, at a certain level of background noise,  their understanding of the lecture becomes seriously degraded. In my opinion,  this is one of many neglected issues of undergraduate mathematics education. I in my lectures always insist on complete silence in the audience (and usually start my first lecture with  a brief explanation of the concept of signal-to-noise ratio).

Mother’s thyroid level ‘may predict child’s poor maths’

From BBC:

Children born to mothers who have low levels of thyroid hormones during pregnancy tend to do worse in maths in early primary school, a study says.

Dutch researchers tracked 1,196 healthy children from birth to age five, having recorded their mothers’ thyroxine levels at 12 weeks of pregnancy.

They then looked at the children’s test scores for language and arithmetic.

Those born to mothers with low levels of thyroxine were twice as likely to have below average arithmetic scores.

However, the scientists – led by Dr Martijn Finken at the VU University Medical Centre in Amsterdam – said the five-year-olds’ language results were no different.

The maths results were the same even after taking into consideration the child’s family background.

Read the whole article.