We received the news of the loss of Sir David Cox on 18 January 2022 with great sadness. For many in the Mathematical Institute and Department of Statistics (of which he was a member), the loss is personal as well as professional.
David (for he very much preferred that ‘Sir’ was not used) made many contributions of great importance to the discipline of statistics as well as, in his view more importantly, of great importance to other areas of sciences. The Cox proportional hazards model, which being David he never called it, is widely used to identify risk factors that increase or decrease the risk of ‘survival’ in many settings well beyond the field of medicine. Later this year it will be 50 years since his landmark paper introducing the proportional hazards model. David had actively contributed to plans to mark this occasion. His presence will be sorely missed.
His gentle kindness was as much one of his superpowers as his great intellect. David has collaborated with and mentored generations of statisticians, in many cases for decades. At the same time he wrote dozens of books and he continued to supervise research students.
David moved to Oxford in 1988 when he served as Warden of Nuffield College until 1994. He will be greatly missed by people around the world, not least in Oxford. Information about a memorial service will be provided in due course.
Last week saw the beginning of the new term (or Hilary as it is called in Oxford). And with it, came the return to normality, or at least the return to full in-person lectures for students, especially first and second years whose lectures were nearly all online last term. Masks had still to be worn but we were back to the model of a fixed-time, a lecturer, a whiteboard and lots of pens (marker and biro).
But are they preferable to the online version? It's a big question and here is not the place to give an answer (even if we had an answer just yet, or one with which everyone agreed). Instead here are some thoughts from first-year Oxford Mathematics and Christ Church College student Lucy Wang as part of her short film about her first day of term. Linear Algebra, coffee, companionship and comfort food; and some interesting thoughts about the online-offline conundrum. She'll be back with more.
P. S. All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
The Andrew Wiles Building, home to Oxford Mathematics, is very much a public venue and a space for creativity, mathematical and beyond. Over the last eight years we have hosted art exhibitions, music and drama and that spirit continues with two performances in the next month.
First, on 2 February, as part of our partnership with the Faculty of Music in Oxford, we are delighted to welcome the Castalian String Quartet. The Quartet holds the Hans Keller String Quartet Residency at the Faculty of Music for the academic years 2021-24. And later, on February 17-19, we are excited to be hosting the premiere of a new play by Marcus du Sautoy.
The Castalian String Quartet
Mozart - String Quartet No. 15 in D minor, K. 421
Fanny Mendelssohn - String Quartet in E flat major
Interval
Felix Mendelssohn – String Quartet No. 6 in F minor, Op. 80
The Castalian String Quartet presents a programme of three string quartets from Viennese composers. Starting with one of Mozart's quartet tributes to Haydn, his String Quartet No. 15 in D minor; this is followed by one of the earliest known string quartets written by a woman composer, Fanny Mendelssohn's String Quartet in E flat major; and ending with Felix Mendelssohn’s final String Quartet, his last major work, powerful and tempestuous.
The concert will be preceded by a talk by Dr Sebastian Wedler at 6.30pm. The concert will start at 7.30pm.
Mathematical Institute, Woodstock Road, Oxford OX2 6GG.
From the Simonyi Professor for the Public Understanding of Science at Oxford University comes a ground-breaking new play: The Axiom of Choice.
Join eminent mathematician Andre Weil and his fictional creation Bourbaki, on their journey from zero via France, India and Finland to the edge of infinity, as they try to make sense of whether we really have free will or if our choices are pre-determined.
Imprisoned in Rouen during the Second World War, our hero, Weil, faces a choice that will determine his fate. And yet his final decision just doesn’t make sense. Bourbaki are here to solve this equation, recreate their creator and offer a proof to the problem. Life, they believe, is like a mathematical theorem made up of interconnected logical strands. But does a life always add up?
Written & Directed by Marcus du Sautoy
Co-Directed by Lu Curtis
Produced by Claire Gilbert Ltd.
Supported by Dangor Education, Stage One Bursary Scheme for New Producers & Charles and Lisa Simonyi Fund for Arts and Sciences
Thursday 17 February 7.30pm
Friday 18 February 7.30pm + Post Show discussion
Saturday 19 February 2pm & 7.30pm
Tickets: £10
Concessions: £5
Mathematical Institute, Woodstock Road, Oxford OX2 6GG
What do you need to join the Oxford Online Maths Club?
Nothing, except a little curiosity. We're live at 5pm UK time every Thursday. Today we will be featuring Vicky Neale investigating square numbers, plus lots of your live chat (& curiosity).
Network Science provides generic tools to model and analyse systems in a broad range of disciplines, including biology, computer science and sociology. Renaud Lambiotte (pictured) teaches a 4th year undergraduate course on Networks and we are making the whole course available via our YouTube Channel. The first lecture is below with seven more to follow over the next few weeks.
The course aims to provide an introduction to this interdisciplinary field of research, by integrating tools from graph theory, statistics and dynamical systems. Most of the topics to be considered are active modern research areas. This is a mathematical course, where we emphasise the inner working of the methods, but with real-world applications in mind. As a leitmotiv, we will explore the two-way relations between network structure and dynamics: how does network structure affect spreading dynamics, for instance epidemic spreading? And how can we use dynamical processes to uncover salient structures in a large network?
You can also read about Renaud and Michael T. Schaub's research into Modularity and Dynamics on Complex Networks (part of the Cambridge Elements series and available free until 4 January).
There is no doubt about it, Santa is a mathematician. He must be, having every year to calculate the best way to get presents to so many homes in such a short space of time.
So in homage to such genius, we have two Santa themed puzzles for you to solve. You can find the answers at the bottom of the page (but try not to look too quickly).
Puzzle the First
Every year the elves mark Santa's birthday by baking a cake, and adding a candle in the shape of each digit of Santa's age. Being rather mathematical, these elves like to add up the values of the candles, and call the answer a Santa number. For example, the Santa number of 723 is 7 + 2 + 3 = 12.
What is the sum of the first 99 Santa numbers (the Santa numbers of 1, 2, 3, ..., 99)?
(a) 746 (b) 862 (c) 900 (d) 924
---
Puzzle the Second
One of Santa's elves has a tricky parcel to pack. Its shape is a hexagon, with all sides of equal length. The elf has placed the parcel inside a square of side length 1, as shown in the diagram. What is the length of one of the hexagon sides?
Puzzle the First - Solution
Imagine the candles in a pile. 1 to 9 occur 10 times each as units digits, for example 1 is the last digit of 1, 11, 21, …, 91. And they occur 10 times each as tens digits, for example 1 is the first digit of 10, 11, 12, …, 19. So the total is \((1+2+\dotsb+9) \times 20 = 45 \times 20 = 900\).
So the answer is (c).
Puzzle the Second - Solution
Say the hexagon has side length \( h \) (so certainly \( h < 1 \)). The right-angled triangle in the top right of the diagram has short sides both of length \( 1-h \), and hypotenuse of length \( h \) (it's a side of the hexagon), so, by Pythagoras's theorem, \( h^2 = (1-h)^2 + (1-h)^2 = 2 - 4h + 2h^2 \), so \( h^2 - 4h + 2 = 0 \). We can solve that using the quadratic formula, which shows that \( h = 2 \pm \sqrt{2} \). But we know that \( h < 1 \), so \( h = 2 - \sqrt{2} \).
So the answer is (b).
If you enjoyed these puzzles you will find many more like them on our Mathematics Admissions Test pages from where these two puzzles were taken and festively adapted by our very own Vicky Neale.
Sally, PA to the Head of Department, has the hardest of mathematical tasks in Oxford Mathematics, namely the herding of mathematicians. She also asks the toughest question of the year:
"Are we doing a Christmas card this year?"
Because, of course, Sally doesn't mean "are we"; no, she means "what are we", as in "what are we going to do for a Christmas card this year?"
The External Relations Manager, recipient of the emailed question, sighs. The 50th email of the day, hot on the heels of diary invites to committees a year in advance and emails from people claiming to have found a simpler proof of Fermat's Last Theorem. Another unwanted task surely? Or at least a difficult one to fulfil?
Actually, no. Not unwanted at all, and certainly not hard for one simple reason: mathematicians.
Mathematicians are often portrayed as inward-looking, communicating in a forbidden language, far removed from imagination and creativity. But of course such clichés are not just untrue but misunderstand the nature of mathematics and mathematicians. It is an intensely creative subject, requiring imagination and conjecture allied to descriptive precision; and all imbued with an instinctive desire to find not only the best but the most elegant answer. This was no tricky task because there was a whole department of creativity to draw on.
So we launched our annual competition. A small prize was offered in return for a mathematically themed card. November is a busy month (well, everyone says every month is busy but November seems to really take its toll), but nonetheless the answers came pouring in. Jane suggested Farey diagrams would make lovely baubles; Damon proposed beautiful patterns formed by colour coded plots of the absolute values of polynomials with all coefficients +/- 1 evaluated over C; Joo-Hyun went for an animation of the generation of a Christmas tree with a few parameterised surfaces; while Elle, a member of our student support team, went for a Penrose triangle Christmas tree. And there were many more.
But in the end, with the advice of our inestimable designers at William Joseph, we went for Marina Simonian's suggestion, a Fourier transform Christmas tree, feeling it would best lend itself to animation. And so began a volley of email exchanges between Marina and Stéphane at William Joseph as they worked up the idea. Was it all becoming too much? Marina gave a succinct answer:
"When you love maths, it's fine."
You can see the final version in the video below and below that, a short explanation from Marina. Thank you to everyone involved.
Emmanuel Breuillard, the Sadleirian Professor of Pure Mathematics in Cambridge, has been appointed to the Professorship of Pure Mathematics in Oxford starting on 1 January 2022. Held by Professor Roger Heath-Brown FRS from its inception in 1999 until his retirement in 2016, the Professorship of Pure Mathematics is one of the most prestigious statutory positions in Oxford. Professor Breuillard will be a fellow of Worcester College.
Emmanuel Breuillard is an exceptionally broad mathematician with diverse interests intersecting with those of half a dozen research groups here in the Mathematical Institute in Oxford including Geometry, Number Theory and Combinatorics. His many research accomplishments include uniform versions of the celebrated Tits alternative in group theory, structure theorems for approximate groups in various settings, new results about Bernoulli convolutions, and greater understanding of random polynomials with +/- 1 coefficients.
He won a European Mathematical Society Prize in 2012 and was an invited speaker at the International Congress of Mathematicians in 2014. We very much look forward to his arrival.
PROMYS Europe Connect 2021 saw a group of enthusiastic and high-achieving young mathematicians gather (online) in July and August for a four-week intensive summer programme designed to give them the experience of thinking deeply about mathematics in a community of similarly mathematically excited students and staff. In other circumstances, PROMYS Europe is a six-week residential programme in Oxford, organised by a partnership of PROMYS (Boston), Wadham College and the Mathematical Institute at the University of Oxford, and the Clay Mathematics Institute. Circumstances being what they were, the 2021 programme, PROMYS Europe Connect, was tailored for an online format, in which we sought to capture as much as possible of the essence of the traditional event.
PROMYS Europe Connect 2021 was attended by 28 students, 2 of whom were returning students who first took part in PROMYS Europe in 2019, and 9 undergraduate counsellors. Participants represented Austria, Bulgaria, Czech Republic, Germany, Hungary, Norway, Romania, Serbia, Spain, Sweden, Switzerland, the UK and Ukraine. Places are offered to students on the basis of their academic potential as demonstrated in their application; we waive some or all of the fee (which is already heavily subsidised) for students who would otherwise be unable to participate. The programme is funded and resourced by the PROMYS Europe partnership, and by further financial support from alumni of the University of Oxford and Wadham College, and from the Heilbronn Institute for Mathematical Research.
This year, as usual, the core of the programme was a Number Theory course, taught by Glenn Stevens (Boston University, founding Director of PROMYS) and Henry Cohn (Microsoft Research, MIT). Students are encouraged to discover as much as possible for themselves, through their work on daily problem sets and through careful individual mentoring by their counsellor.
Alongside this was a Group Theory course with a similar philosophy, taught by Vicky Neale (Oxford), primarily aimed at the returning students, but also well attended by the first years. The returning students also worked on a research project on elliptic curves. Alongside their own mathematical seminars on category theory and analytic number theory, the counsellors organised social activities to help the students get to know each other and to build the sense of the community that is so important to the programme. These were complemented by guest lectures, exposing students to a range of current mathematical research. Plans are already under way for summer 2022, when we expect to return to the in-person format.
Here’s what participants said after PROMYS Europe Connect 2021:
Thank you for organizing all this, I feel like I almost cannot grasp the impact that this programme has had on my life in these three years of participation. [Returning student]
The online experience was actually much more engaging than I had expected. [Student]
PROMYS Europe Connect has left me with so many fantastic memories. I have truly felt like I am part of an amazing community of mathematicians who are all so passionate about what they do. [Counsellor]
We can't interview all our undergraduate applicants in the time available, so to help us decide who to shortlist, we set the Oxford Mathematics Admissions Test (MAT) which all applicants for Maths, Computer Science, or joint honours courses must take.
Yesterday, 3 November, 5000 aspiring students from all around the world took the MAT for entrance to Oxford (and other universities). Here, courtesy of our admissions guru, James Munro, are the answers in 10 minutes. And remember, as they say before the football results on TV, if you don't want to know the answers, look away now.
James will also host a longer debrief of MAT 2021 in his weekly online podcast next week (11 November). Everyone is welcome.
