Two-dimensional Divergence Theorem is equivalent to Green’s Theorem — Singapore Maths Tuition

The special planar version of Divergence Theorem is actually equivalent to Green’s Theorem, even though on first sight they look quite different.

via Two-dimensional Divergence Theorem is equivalent to Green’s Theorem — Singapore Maths Tuition


Professor Sir Christopher Zeeman, FRS

In Memoriam: Sir Christopher Zeeman

Sir Christopher Zeeman, Founding Professor of Mathematics at the University of Warwick, passed away peacefully in his sleep on Saturday 13 February at home in Woodstock, aged 91. The University offers its sincere condolences to Lady Rosemary Zeeman, and his six children.

Founder of Mathematics at Warwick

In 1965, Sir Christopher founded the Mathematics department as Warwick came into being. He described his approach at that time: “I was 38 and had developed some fairly strong ideas on how to run a department and create a Mathematics Institute: I wanted to combine the flexibility of options that are common in most American universities, with the kind of tutorial care to be found in Oxford and Cambridge.”

warwick_maths_dept_1965.jpgSir Christopher’s determination and ingenuity in establishing the new department were legendary. In its infancy, he famously wrote to David Epstein, Rolf Schwarzenberger, Colin Rourke, Brian Sanderson and Luke Hodgkin asking them to join him at the new University, but they all turned him down. Not one to take no for an answer, he wrote to them all again saying: “But the other four say yes”, and successfully appointed all five topologists.

He also persuaded the University to buy a defunct country club for £8,000 and paid a local sign-writer £5 to come and paint “Mathematics Institute” on the front door. Thus the Mathematics Institute was born.

His style of leadership was informal, but inspirational, and he rapidly gained Warwick international recognition for the quality of its mathematical research. He remained here until 1988, during which time his popular lectures had become ‘standing room only’.

In 2005, 40 years after he first established mathematics at Warwick, our new mathematics and statistics building was named in his honour.

Professor Sir Christopher Zeeman


Today’s Mathematics Institute has over 900 undergraduate and 150 postgraduate students, led by over 60 academic staff. The Institute is currently ranked third in the UK for research, and 90% of this research is rated ‘internationally excellent’ or ‘world leading’. Its degree courses are noted for their breadth, their innovative approach and the high quality of students and academics who they continue to inspire.


Sir Christopher holds a special place in the memories of many of our graduates and staff. Professor David Rand remembers Sir Christopher as a “brilliant mathematician, exceptional lecturer, remarkable polymath and deep-thinking leader and administrator [who] had a remarkable influence on the University.” Patrick Dunne, Warwick alumnus and Council member, knew Sir Christopher as a “brilliant mathematician who founded the Warwick maths department with principles that have stood the test of time.” Katy Bell, who studied Mathematics in 1969, was inspired to study at Warwick after Professor Zeeman gave an enthusiastic presention at her school. “My love and fascination with Mathematics has continued and I think that this is in no small part due to the way in which he was able to transfer his love of the subject to others.”

Alumna Margaret Gunn recalls, “I was particularly pleased and honoured that he attended my 21st birthday party in 1968 and discussed plumbing with my father for much of the evening.” Sir Christopher’s inspiring lectures on Catastrophe Theory were extremely popular, and especially enjoyed by alumnus Andrew Rome: “He headed up the Maths department during my undergraduate years (1981-84) and the pinnacle of that experience was the Catastrophe Theory course in year 3. I still have his book on the topic … I keep it out of a desire to maintain memories of exceptional years.”

To read more fond memories of Professor Sir Christopher Zeeman, follow this link.

Contributions to his field and recognition

Among mathematicians, Sir Christopher was best known for his work in geometric topology and singularity theory, making significant contributions in knot theory, the piecewise linear category and dynamical systems. Among the wider scientific community he is perhaps best known for spreading awareness of catastrophe theory.

Having received an MA and PhD from the University of Cambridge, Sir Christopher became a Fellow of Gonville and Caius College in 1953. He was elected a Fellow of the Royal Society in 1975 and was later awarded the Society’s Faraday Medal in 1988. Sir Christopher was awarded the Senior Whitehead Prize from the London Mathematical Society in 1982, becoming its first Forder lecturer, and then President from 1986-88.

In 1978, he gave a televised series of Christmas Lectures at the Royal Institution, introducing a new generation to mathematics, from which grew the Mathematics Masterclasses for primary and secondary school children that now flourish across the UK. Sir Christopher was the first mathematician to give these lectures since they began in 1825.

In this Royal Institution Mathematics Masterclass, Sir Christopher Zeeman explains why there is only one perfect observation point for each perspective drawing.

A decade later, Sir Christopher became Principal of Hertford College, Oxford, and was appointed an honorary fellow of Christ’s College, Cambridge. He received a knighthood for mathematical excellence and service to British mathematics and mathematics education in the 1991 Queen’s Birthday Honours.
Professor Sir Christopher ZeemanIn 2006, the London Mathematical Society and the Institute of Mathematics and its Applications awarded him the David Crighton Medal in recognition of his long and distinguished service to the mathematical community. The medal is awarded triennially, and Sir Christopher became only the second recipient of the award.

On 19 March last year, at Sir Christopher’s 90th birthday celebration at Hertford College, The London Mathematical Society launched the Sir Christopher Zeeman Archive, representing a lifetime of his work, including letters he wrote, papers he published, interviews he gave, and the Royal Institution Christmas Lectures from 1978, which were shown live on BBC2.

Memorial service

There will be a private funeral for the Zeeman family, followed by a service to celebrate his life which will be announced shortly.

There will be an opportunity to donate to a scholarship for young mathematicians via the London Mathematical Society.

Women in Math Club


The Women in Math club has meetings every other week to provide networking opportunities between female math majors and to support women in completing the math major and going on to use that degree in graduate school or industry. Everyone who supports the idea of women being more involved in mathematics is invited to attend.

Questions? Contact

Sir Christopher Zeeman FRS (1925-2016)

Sir Christopher Zeeman, FRS, passed away peacefully in his sleep on Saturday 13th February 2016 at home in Woodstock, Oxfordshire, aged 91. Sir Christopher was the Founding Professor of Mathematics at the University of Warwick. He later served as President of the London Mathematical Society (LMS) from 1986 to 1988 and as Principal of Hertford College, Oxford. He is survived by his wife, Lady Rosemary Zeeman and his six children.

Sir Christopher (born 4th February 1925) was elected to membership of the Society on 21st January 1954. He was LMS Vice-President from 1968-1969 and became the Society’s 63rd President. He was awarded the Senior Whitehead Prize of the Society in 1982, and was the Society’s first Forder lecturer, in 1987. Sir Christopher also presented the LMS Popular Lecture – The Discovery of Perspective in the Renaissance – in 1983

Sir Christopher’s contributions to mathematics range from geometric topology to dynamical systems, with applications across the sciences. He is known among the wider scientific public for his contribution to, and spreading awareness of Catastrophe Theory, and for the 1978 televised Christmas Lectures at the Royal Institution (the first in Mathematics), from which grew the Mathematics Masterclasses for primary and secondary school children that now flourish around the United Kingdom.

Sir Christopher was elected as a Fellow of the Royal Society in 1975, and was awarded the Royal Society Faraday Medal in 1988. In 2006, the London Mathematical Society and the Institute of Mathematics and its Applications jointly awarded the David Crighton Medal to Sir Christopher in recognition of his long and distinguished service to mathematics and the mathematical community.

In 2008 Sir Christopher presented the first Christopher Zeeman Medal for Communication of Mathematics, named in Sir Christopher’s honour and jointly awarded by the London Mathematical Society and the Institute of Mathematics and its Applications. The award aims to honour mathematicians who have excelled in promoting mathematics and engaging with the general public.

A private funeral will be held for the family.  A service to celebrate Sir Christopher’s life will be announced in due course, and there will also be an opportunity to donate to a fund to support young mathematicians, being set up in Sir Christopher’s name, under the auspices of the London Mathematical Society.

A full obituary will appear in a forthcoming issue of the LMS Newsletter.

Sir Andrew Wiles Awarded 2016 Abel Prize


The Norwegian Academy of Science and Letters has awarded the 2016 Abel Prize to Professor Sir Andrew Wiles, University of Oxford, ‘for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semi-stable elliptic curves, opening a new era in number theory’.Wiles will receive his award from His Royal Highness Crown Prince Haakon at the University of Oslo on 24th May 2016.

Wiles is one of very few mathematicians – if not the only one – whose proof of a theorem has made international headline news. In 1994 he solved Fermat’s Last Theorem, which at the time was the most famous, and long-running, unsolved problem in the subject’s history.

His proof was not only the high point of his career but also the culmination of a remarkable personal journey that began three decades earlier. Wiles recalls that he was intrigued by the problem that he as a young boy could understand, and yet it had remained unsolved for three hundred years. ‘I knew from that moment that I would never let it go’, he said. ‘I had to solve it’. The Abel Committee said: ‘Few results have as rich a mathematical history and as dramatic a proof as Fermat’s Last Theorem’.

Sir Andrew was awarded an LMS Whitehead Prize in 1988 and was elected an Honorary Member of the LMS in 2001.

On behalf of the LMS, and the UK mathematical community more broadly, Professor Simon Tavaré FRS, the President of the LMS, congratulates Sir Andrew on his remarkable achievements that have led to the 2016 Abel Prize.

More information is available here

TV covers Women in Mathematics event


The recent LMS Women in Mathematics Day at Microsoft Research in Cambridge was covered by Cambridge TV. The event was aimed at women in mathematics, in particular at postgraduates, final year undergraduates and those at an early stage in their career, to meet together for a day of talks and discussion groups. The talks were given by women mathematicians from a range of disciplines and who are at various stages in their careers, including Apala Majumdar (University of Bath and LMS Anne Bennett Prize winner), Philippa Hiscock (Roke Manor Research) and Nicola Richmond (GlaxoSmithKline), and there were short talks from early career researchers. The poster competition, sponsored by Wiley, was won by Milena Kremakova (University of Warwick) for her posterMathematicians in Love: Are there real solutions to the ‘two-body problem’?

The coverage is available here 

Annual Iranian Algebra Seminar

The annual Iranian Algebra Seminar will be held at Hakim Sabzevari University on Jul. 19-20,2016.
This is the 25th of a series of seminars organized regularly every year by the collaboration of Iranian Mathematical society. The seminar committee cordially invites researchers in the various areas of algebra to take part in this seminar. The registration will be open on June 20th and detailed information about the venue,accommodation,fees and … will be published then in the present web address. Iranian algebra seminar has started with the aim of improving scientific relationships between researchers and students who are interested in algebra. It also aims to exchanging ideas in various areas of algebra.

16-year-old invents new math theory — and doesn't even earn an 'A'

It’s common for some high school kids to need the help of a math tutor. For others, numbers come naturally. And then there’s Tamar Barabi. The Israeli teenager just invented a new geometric theorem. Like most discoveries, the eureka moment happened by accident. Tamar turned in her math homework and the teacher said the theory she used to solve the problem didn’t actually exist. “He said if I could prove it, it could be my theory. So that’s what happened,” Barabi told From The Grapevine. With help from her dad, who is also a math teacher, they sent the theorem to experts around the world.


Famous math problem solved!


Ten days ago, Maryna Viazovska showed how to pack spheres in 8 dimensions as tightly as possible. In this arrangement the spheres occupy about 25.367% of the space. That looks like a strange number – but it’s actually a wonderful number, as shown here.

People had guessed the answer to this problem for a long time. If you try to get as many equal-sized spheres to touch a sphere in 8 dimensions, there’s exactly one way to do it – unlike in 3 dimensions, where there’s a lot of wiggle room! And if you keep doing this, on and on, you’re forced into a unique arrangement, called the E8 lattice. So this pattern is an obvious candidate for the densest sphere packing in 8 dimensions. But none of this proves it’s the best!

In 2001, Henry Cohn and Noam Elkies showed that no sphere packing in 8 dimensions could be more than 1.000001 times as dense than E8. Close… but no cigar.

Now Maryna Viazovska has used the same technique, but pushed it further. Now we know: nothing can beat E8 in 8 dimensions!

Viazovska is an expert on the math of “modular forms”, and that’s what she used to crack this problem. But when she’s not working on modular forms, she writes papers on physics! Serious stuff, like “Symmetry and disorder of the vitreous vortex lattice in an overdoped BaFe_{2-x}Co_x As_2 superconductor.”

After coming up with her new ideas, Viaskovska teamed up with other experts including Henry Cohn and proved that another lattice, the Leech lattice, gives the densest sphere packing in 24 dimensions.

Different dimensions have very different personalities. Dimensions 8 and 24 are special. You may have heard that string theory works best in 10 and 26 dimensions – two more than 8 and 24. That’s not a coincidence.

The densest sphere packings of spheres are only known in dimensions 0, 1, 2, 3, and now 8 and 24. Good candidates are known in many other low dimensions: the problem is proving things – and in particular, ruling out the huge unruly mob of non-lattice packings.

For example, in 3 dimensions there are uncountably many non-periodic packings of spheres that are just as dense as the densest lattice packing!

In fact, the sphere packing problem is harder in 3 dimensions than 8. It was only solved earlier because it was more famous, and one man – Thomas Hales – had the nearly insane persistence required to crack it.

His original proof was 250 pages long, together with 3 gigabytes of computer programs, data and results. He subsequently verified it using a computerized proof assistant, in a project that required 12 years and many people.

By contrast, Viazovska’s proof is extremely elegant. It boils down to finding a function whose Fourier transform has a simple and surprising property! For details on that, try my blog article: