How to raise a genius: lessons from a 45-year study of super-smart children

How to raise a genius: lessons from a 45-year study of super-smart children, by Tom Clynes, 07 September 2016, in Nature | News Feature.

On a summer day in 1968, professor Julian Stanley met a brilliant but bored 12-year-old named Joseph Bates. The Baltimore student was so far ahead of his classmates in mathematics that his parents had arranged for him to take a computer-science course at Johns Hopkins University, where Stanley taught. Even that wasn’t enough. Having leapfrogged ahead of the adults in the class, the child kept himself busy by teaching the FORTRAN programming language to graduate students.

Unsure of what to do with Bates, his computer instructor introduced him to Stanley, a researcher well known for his work in psychometrics — the study of cognitive performance. To discover more about the young prodigy’s talent, Stanley gave Bates a battery of tests that included the SAT college-admissions exam, normally taken by university-bound 16- to 18-year-olds in the United States.

Read the rest of the story

Tim Gowers: In case you haven’t heard what’s going on in Leicester …

[Reposted from Tim Gowers’ Blog, 15 Sept 2016]

Strangely, this is my second post about Leicester in just a few months, but it’s about something a lot more depressing than the football team’s fairytale winning of the Premier League (but let me quickly offer my congratulations to them for winning their first Champions League match — I won’t offer advice about whether they are worth betting on to win that competition too). News has just filtered through to me that the mathematics department is facing compulsory redundancies.

The structure of the story is wearily familiar after what happened with USS pensions. The authorities declare that there is a financial crisis, and that painful changes are necessary. They offer a consultation. In the consultation their arguments appear to be thoroughly refuted. The refutation is then ignored and the changes go ahead.

Here is a brief summary of the painful changes that are proposed for the Leicester mathematics department. The department has 21 permanent research-active staff. Six of those are to be made redundant. There are also two members of staff who concentrate on teaching. Their number will be increased to three. How will the six be chosen? Basically, almost everyone will be sacked and then invited to reapply for their jobs in a competitive process, and the plan is to get rid of “the lowest performers” at each level of seniority. Those lowest performers will be considered for “redeployment” — which means that the university will make efforts to find them a job of a broadly comparable nature, but doesn’t guarantee to succeed. It’s not clear to me what would count as broadly comparable to doing pure mathematical research.

How is performance defined? It’s based on things like research grants, research outputs, teaching feedback, good citizenship, and “the ongoing and potential for continued career development and trajectory”, whatever that means. In other words, on the typical flawed metrics so beloved of university administrators, together with some subjective opinions that will presumably have to come from the department itself — good luck with offering those without creating enemies for life.

Oh, and another detail is that they want to reduce the number of straight maths courses and promote actuarial science and service teaching in other departments.

There is a consultation period that started in late August and ends on the 30th of September. So the lucky members of the Leicester mathematics faculty have had a whole month to marshall their to-be-ignored arguments against the changes.

It’s important to note that mathematics is not the only department that is facing cuts. But it’s equally important to note that it is being singled out: the university is aiming for cuts of 4.5% on average, and mathematics is being asked to make a cut of more like 20%. One reason for this seems to be that the department didn’t score all that highly in the last REF. It’s a sorry state of affairs for a university that used to boast Sir Michael Atiyah as its chancellor.

I don’t know what can be done to stop this, but at the very least there is a petition you can sign. It would be good to see a lot of signatures, so that Leicester can see how damaging a move like this will be to its reputation.

Alexandra O Fradkin: Who’s the Oldest: Conversation with Kindergartners

[Reposted from Alexandra O Fradkin’s blog Musings of a Mathematical Mom]

Yesterday, I overheard a wonderful conversation between our Kindergarten teacher and the Kindergartners.  The kids needed to line up to exit the classroom and the teacher told them to line up by age, oldest to youngest.  Immediately, one of the kids (K1 from now on) had a question.  “But how can we do it?  I’m five, K2 is five, and K3 is 5, so that means we’re all the same age!”

Teacher: Are you all the exact same age?
K1: Yes.
Teacher: So you were all born on the exact same day?
K1: Noooo. (giggling from the other kids)
Teacher: Ah, so some of you were born before others.  When are your birthdays?
K1: July.
K2: May.
K3: May.
Teacher: When in May?
K2: May 5.
K3: May 17.
Teacher: So who is older, who was born first?
K1: K2 is older.
Teacher: Why?
K1: Because she is taller!
Teacher: So taller people are always older than shorter ones?
All kids: Noooo.
Teacher: So in order to figure out who is older we need to determine what comes first, May 5 or May 17?
Silence.
Teacher: Well when you count, do you say 5 or 17 first?
K1: 17.
Teacher: So we count 1, 2, 3, 4, 17, and then five comes at some point later?
K1 (after much giggling): Noooo, it’s 1,2,3,4,5.
Teacher: So who’s older?
All kids: K2!

After that conversation it still took them a moment to get into the correct order, but they did it, and off they went! I love hearing kids of this age group reason because they are, for the most part, still not afraid of being wrong and they will say whatever comes to mind. This allows you to analyze how they think and is just plain lots of fun.

Alexandra O Fradkin: Story Math in Kindergarten: Two of Everything

[Reposted from Alexandra O Fradkin’s blog Musings of a Mathematical Mom]

Friday is story day in our Kindergarten math class.  For our first book we read Two of Everything, a Chinese folktale.  We then had a wonderful discussion and the kids asked some very insightful questions.

Here is a brief synopsis of the story: A poor elderly couple find an old brass pot in their garden and it turns out to be magic.  Whenever you put something into the pot, two of that thing come out!  The couple started doubling everything and soon became very rich.  One day, the husband accidentally pushed his wife into the pot and then fell into it himself.  After some initial arguing, the two couples realized that they could become the best of friends and use the pot to create two of everything, one for each couple.

At the end of the story, one of the kids asked, “But would there also be two pots?”  What a great question!  I said that I thought there would be only one pot, but some kids disagreed.  They spent several minutes debating whether it was possible to put the pot inside of itself to create a second one.

The discussion then moved on to how one would make lots of something.  The kids suggested that you could just keep putting the same object into the pot over and over again, creating one more each time.  I then asked them what would happen if we put two of the same object into the pot at the same time.  They all immediately yelled out that you would get three of that object.  My next question was whether only one of the objects would be doubled or both.  This led one of the kids (and then the rest) to realize that in fact, four of that object would come out.

I wanted to ask them about putting three or more objects into the pot, but it was time to move on.  Perhaps that was for the best because they already had a lot to take in.  I hope to come back to this topic and can’t wait to read more stories with them.  I feel that stories engage this age group like nothing else does.  And I absolutely love the questions and thoughts that the kids come up with!

Alexandra O Fradkin: Playing Math Detectives: First Week of Second Grade Math

[Reposted from Alexandra O Fradkin’s blog Musings of a Mathematical Mom]

The first week in our second grade class we did lots of time traveling. We played the role of math detectives and helped people from different time periods solve problems. We also learned about some ancient number systems.

On the first day we went back to several million years ago. (The idea for our scenario was taken from the wonderful book by Julia Brodsky, Bright, Brave, Open Minds: Engaging Young Children in Math Inquiry.) During this time period, there lived ferocious saber-toothed tigers with sharp teeth, crocodiles with awful jaws, and the first cave people, who had no strong jaws, long teeth, or sharp claws. How could we help those early people survive in their unfriendly world of dangers? The kids came up with making weapons out of sticks and stones, building fires, hiding in caves, running away, and climbing trees. I think they would have had a good chance of survival!

On the second day, we went back just 10-20-30 thousand years, to a time before numbers were invented but people had a need for keeping track. The kids’ task was to help a farmer determine whether his shepherd was bringing back all of his sheep at the end of day or whether he was stealing or losing some along the way.

The kids were split up into groups and each group got a bag of coins (which stood for sheep). They were told that when they were ready, I would take the “sheep” on a walk and bring them back. They would have to determine whether any were missing. The main rule was that they were not allowed to count in any way!

Here is their solution:img_2955

They made holes/homes for each of the coins/sheep, and when I brought back two fewer coins than they gave me, they were easily able to detect that because they had two empty holes. I was very impressed with their inventiveness. We then discussed and looked at pictures of how people actually did use dots, tally marks, stones, and knots to keep track of animals, money, and anything else they needed to.

img_2954

Finally, on the third day we went back only several thousand years, to several locations around the globe. We visited the Babylonians, the Mayans, and the Romans, and learned how they wrote the numerals 1 through 10 in their number systems. The detective work consisted of helping them decide how they should write 11.

The kids examined the patterns closely, made suggestions, and discussed the merits of each one. In the end, they came up with versions that I think the ancient people would have been happy with.

Here is a picture of what it looked like (the Babylonian version did later get modified to be a horizontal wedge followed by a vertical one).

img_2962

Next week we will begin our in-depth exploration of the Hindu-Arabic number system. More specifically, we’ll focus on the usefulness and meaning of place value and the importance of zero!

The Humanistic Mathematics Network Newsletter

The Humanistic Mathematics Network Newsletter (HMNN) was founded by Alvin White in the summer of 1987. The Newsletter was later renamed The Humanistic Mathematics Network Journal (HMNJ). The last issue of the HMNJ was published in 2004. The open access digital archive of the full run of the HMNN/HMNJ (1987-2004) is now available at http://scholarship.claremont.edu/hmnj/.

This journal does not accept new content. A related current journal is the Journal of Humanistic Mathematics.

The 7 biggest problems facing science

The 7 biggest problems facing science, according to 270 scientists, by Julia Belluz, Brad Plumer, and Brian Resnick on September 7, 2016 in Vox.

I love this example of deductive resoning:

  •  Academia has a huge money problem
  • Too many studies are poorly designed
  • Replicating results is crucial — and rare
  • Peer review is broken
  • Too much science is locked behind paywalls
  • Science is poorly communicated
  • Life as a young academic is incredibly stressful

Conclusion:

  • Science is not doomed

Read the whole text.

Jack Abramsky: MathsWorldUK

I am writing to you, friends and colleagues, in an appeal to boost the number of Friends and donor sponsors of MathsWorldUK.
For those of you who are unfamiliar with MWUK, we are a registered company and a registered charity set up with the long-term aim of establishing in the United Kingdom the first National Exploratorium devoted entirely to mathematics and its applications. We will not be in competition with the Science Museum in London, because our philosophy is radically different from that of the SM. The new Mathematics Gallery (to be named the Winton Gallery) at the Science Museum will open in December. It will be essentially static with about 90 exhibits from the permanent collection of artefacts owned by the museum. Each artefact will be accompanied by a short description of around 90 words about some mathematical idea that the exhibit might exemplify. Our approach will be for fully interactive exhibits designed to illustrate some mathematical idea or mathematical application, with the visitor doing his or own individual exploration of the ideas underpinning each exhibit. So one approach is static, the other is active. The two spaces will complement each other, rather than be in competition with each other. A further fundamental difference is that The Science Museum’s primary function is to present scientific achievement, with mathematics as a small subsidiary of that endeavour, whereas the Exploratorium (note the emphasis on exploration, and hence discovery) will  put mathematics in all its manifestations and applications at the very heart of its activity.
Schools Competition MATRIX:  The top two prizewinning schools

Schools Competition MATRIX: The top two prizewinning schools

You can find out more about MWUk on its website (which will shortly be updated)
We have just hosted an extraordinary and wonderful conference at the University of Leeds called MATRIX with over 100 delegates from 15 countries.  This was the second MATRIX conference; the first was held in Dresden two years ago. MATRIX stands for Mathematics, Awareness, Teaching, Resources and Information eXchange. The conference was for museum folk around the world and others interested in improving public awareness and understanding of mathematics. We co-hosted this conference with the National Museum of Mathematics (MoMath) in New York and the University of Leeds. Full details of the conference are on our website, together with the winning entries for a schools competition that was run for the conference. Attached is a photograph of Hanna Fry with the top two school teams; Hannah gave out the prizes.
There are now over 50 mathematics ‘museums’ around the world with about 10 more due to open in 2017. Germany alone has 10 museums, either dedicated to mathematics or with substantial mathematical galleries. The UK has no such mathematical space. The new Musee Henri Poincare is due to open in Paris in 2020. The Director, already appointed, is Cedric Villani; he  is also the Director of the Institut Henri Poincare in Paris. Cedric Villani is a Fields Medallist in Mathematics (the equivalent of being a Nobel Prize winner in maths), who also wrote the recent best-seller Birth of a Theorem: a mathematical adventure. He was at our MATRIX conference.
MWUK has been invited by the Chairman of the House of Commons Select Committee on Numeracy and Mathematics to participate at a Conference on the Northern Powerhouse, to be held in Manchester, on 15th September. We have also recently had a meeting with Sadiq Khan’s mayoral team at City Hall in London.
I am not one who partakes in sponsored walks, cycle rides, marathons, treks or whatever. So I cannot appeal to you to sponsor me to do some incredible feat of physical activity and then denote the proceeds of such sponsorship to a charity of my choosing. Instead I am appealing directly on behalf of our charity. We urgently need donations to support the appointment of a full time director of fund-raising and to purchase some much needed equipment.
On our website you will be able to make a donation directly to MWUK, and also to request a form to become a Friend of MathsWorldUK if you so wish. All donations, large or small, will be greatly appreciated. Also, please forward this message to any of your contacts whom you feel may be interested in the MWUK project.
Thank you, in advance, for your consideration.
Jack Abramsky

Misha Gavrilovich: Expressing the statement of the Feit-Thompson theorem with diagrams in the category of finite groups

Misha Gavrilovich’s paper Expressing the statement of the Feit-Thompson theorem with diagrams in the category of finite groups, available from

is a follow-up to his paper in The De Morgan Gazette,

M. Gavrilovich, Point-set topology as diagram chasing computations, The De Morgan Gazette, 5 no. 4 (2014), 23-32

The paper raises important questions about optimal approaches to exposition of elementary group theory: quite a number of group-theoretic concepts (for example, solvable, nilpotent group, p-group and prime-to-p group, abelian, perfect, subnormal subgroup, injective and surjective homomorphism) can be expressed as diagram chasing in the category theoretic language.