**Creative and innovative challenges in education worldwide amidst the COVID-19 Crisis** were in focus at the **Global Online Conference **organized by the **UNESCO Chairs of the University of Jyväskylä** and **Council for Creative Education, Finland**. The goal of the event was to celebrate the **United Nations’ World Creativity and Innovation Day** on 21 April 2020. The online educational conference attracted 12,220 unique visitors from more than 60 countries, across five continents. **Please find more information on the event here**.

**Reidun Twarock: Virus Structure through a Mathematical Microscope.
**Link: https://youtu.be/kDht2M0_q24

**Andreas Daniel Matt: Celebrating first International UNESCO Day of Mathematics amidst Covid-19 Crisis.**

Link: https://youtu.be/K77ASNsplKw

**Paul Hildebrandt: Viruses and Hyperspace.**

Link: https://youtu.be/QAxaGW1PUpI

**Mike Acerra: Hands-on Modeling and STEAM Learning about viruses, including COVID-19 with LUX BLOX.**

Link: https://youtu.be/hxr1CPqUlxM

**Thierry (Noah) Dana-Picard: E-Teaching of Differential Geometry in a time of COVID-19 crisis.**

Link: https://youtu.be/kHGX-CmeeTQ

**Christopher S. Brownell: STEAM Education Efforts Include Playful Mathematics.**

Link: https://youtu.be/iAZtks57c88

**Zsolt Lavicza: Developing technological and pedagogical innovations in STEAM education.**

Link: https://youtu.be/Q_LCyTyIVls

**Kristof Fenyvesi: Creativity and Innovation: Developing Critical Skills for Critical Times through STEAM Learning.**

Link: https://youtu.be/47KBNN9Cdmw

**Zhao Yuqian: Distance Education of Playful Coding for Children in Hubei Province During the COVID-19 Crisis.**

Link: https://youtu.be/Ms4v0hMhw9I

**Pamela Burnard: Revisioning New Ideas of STEAM, Enacting ‘Art-Science Creativity’, Attending to the Present (and Post) COVID-19 Outbreak.
** Link: https://youtu.be/MvaSiUJeX0Y

**Janika Leoste: Robotics Education During and After the COVID-19 Crisis.** Link: https://youtu.be/uywpF9XZGH0

**Huei Syuan Lin & Ing Ru Chen: STEAM Movement and Developing Critical Skills for Critical Times in Taiwan for the Youth by the Youth.**

Link: https://youtu.be/uTUl7DqFGyI

**Anne M. Harris: Creative Ecologies in the time of COVID-19.**

Link: https://youtu.be/27M6pnJkFpo

**Pekka Neittaanmäki: UN’s Day of Creativity and Innovation: Critical Skills in Critical Times.
**Link: https://youtu.be/wwDHZyUq3kY

**Heikki Lyytinen: UN’s Day of Creativity and Innovation: Critical Skills in Critical Times.
**Link: https://youtu.be/2kbi3y10r98

*Click here to view the embedded video.*

**Ben Sparks: The Coronavirus Curve – Numberphile.**

*Click here to view the embedded video.*

**Michel Rigo: Modèles mathématiques et confinement (in French).**

Sometimes I wish I hadn’t invented that game.

–John Horton Conwayabout theGame of life^{[3]}

The most famous mathematical invention by **John Conway** was undoubtedly the *Game of life*, that was popolirized by **Martin Gardner** on his column published on *Scientific American* ^{[1]}, but today I want to tell you something about the free will theorem.

The theorem was proposed by Conway with **Simon Kochen**, inspired by the question about the interpretation of quantum mechanics. The statement is:

If the choice of directions in which to perform spin 1 experiments is not a function of the information accessible to the experimenters, then the responsesof the particles are equally not functions of the information accessible to them.

^{[2]}

That is, the theorem states that the outcome of the experiment is independent of the choices made by the experimenters. Or if you prefer that the eyes of the experimenters does not influence the outcome of the experiment (and therefore does not change the universe).

In the following the two mathematicians are concerned with showing the consistency of the theorem with quantum mechanics, first of all showing that this is only one of the last arguments against the hidden variables of **David Bohm**, proposed to restore the determinism lost by quantum mechanics.

The other interesting effort of the two mathematicians is to reconcile everything, at least from a logical-philosophical point of view, with relativity. In their judgment, after introducing a series of concepts, such as actual randomness (the universe would appear random from any reference system), Conway and Kochen show a series of errors of interpretation related to the EPR paradox that would push physicists to believe the existence of violations of the principle of randomness (and therefore of relativity). The point is that if in the system of the two connected states A, B the spin A is measured and it is down, it is much more correct to say that if the measurement is performed on B its spin will be up and not the spin of B is instantly up.

The situation is undoubtedly much more complex and detailed than this, but overall the feeling is that the two mathematicians wrote an explicit invitation to physicists to take the question more relaxed. Which seems confirmed by the phrase that I think perfectly summarizes the work of Conway and Kochen:

God lets the world run free.

**Card Colm Mulcahy**, an irish mathematician and Conway’s friend, on 11 april 2020 published on twitter the news of the death of Conway. His source was *a close associate of his* and confirmed by the family.

I written this little post in his honour: good bye, Mr. Conway.

- Gardner, M. (1970). Mathematical games: The fantastic combinations of John Conway’s new solitaire game “life”.
*Scientific American*, 223(4), 120-123. (pdf|html) - Conway, J., & Kochen, S. (2006). The free will theorem.
*Foundations of Physics*, 36(10), 1441-1473. doi:10.1007/s10701-006-9068-6 (arXiv) - Dierk Schleicher (2013). Interview with John Horton Conway.
*Notices of American Mathematica Society*, vol. 60, n. 5, pp.567-575 (pdf)

Infectious diseases are much on everybody’s mind at the moment, as frantic efforts are going into stopping the spread of the coronavirus and developing a vaccine. Medical research is obviously important in this, but so is mathematics. It is used extensively in modelling infectious diseases: finding out how rapidly they can be expected to spread, how many people will be affected, and also what proportion of a population should be vaccinated, if a vaccine exists. Here we republish, by courtesy of the author and the original hosting site Plus Magazine, an article by Marianne Freiberger, where these topics are discussed.

This article is published by courtesy of

A basic mathematical model, developed back in the 1920s but still used today, is called the *SIR model*. To understand how it works, imagine you are playing a computer game. In it there’s a population of people (of a city, country, continent or the world) divided into three classes: those that are not yet sick, but susceptible to the disease (class S), those that are sick and infectious (class I), and those that have been removed from the disease (class R), either because they have recovered and become immune, or because they have died. There also is a set of equations which describes how many people pass from one class to another in a given time step, say in a day, or in a month. You now click “go” and watch the computer simulate the disease developing over time. This, in essence, is how scientists use the SIR model.

Of course, everything depends on the equations that govern the transition from one class into the other. In the basic SIR model, these equations depend crucially on the likelihood that an infected person infects someone else and on the average length of time someone is sick for before they recover or die. When scientists use the SIR model to predict the evolution of a disease, they estimate these parameters by observing how the disease behaves in real life. By figuring out the impact interventions, such as travel restrictions or improvements in hygiene, have on the important parameters, they can also predict how useful those interventions are likely to be.

It turns out that much hinges on one special number, called the *basic reproduction ratio*, usually denoted by *R _{0}*. It measures the number of people an infectious person goes on to infect, on average, in a totally susceptible population. For measles, which is airborne and spreads easily,

The SIR model as we have described it here is of course too simple to apply to all real-life diseases and you may have to modify it to get more accurate predictions. For example, some diseases, such as childhood diseases and AIDS, affect some people more than others, so we may have to subdivide the population into further classes. The infection rate may also vary over time, for example it’s higher among school children during term time than during the holidays, and a more sophisticated model needs to take account of that. And some diseases, like malaria, are transmitted by animals and so the model must include animal as well as human populations. But still, the SIR model is a good starting point for building those more complex models.

To find out more about the SIR model, the basic reproduction number, and the maths of infectious diseases in general, read these *Plus* articles:

- The mathematics of diseases describes the SIR model in detail.
- Protecting the nation explores how scientists decide whether a vaccine and a vaccination strategy are effective and safe.
- Swine flu uncertainty describes how scientists went about getting those vital first estimates on numbers of infected and dead in the case of swine flu.
- Build your own disease is a classroom activity exploring epidemiological models using basic probability theory.

To see all our content on epidemiology, see our infectious disease package.

**Marianne Freiberger**

The International Day of Mathematics (IDM) is a worldwide celebration. Each year on March 14 all countries will be invited to participate through activities for both students and the general public in schools, museums, libraries and other spaces.

On November 26, 2019, the 40th session of the General Conference, UNESCO proclaimed March 14 as the International Day of Mathematics. The first official celebration will be on March 14, 2020.

March 14 is already celebrated in many countries as Pi Day because that date is written as 3/14 in some countries and the mathematical constant Pi is approximately 3.14.

The International Day of Mathematics is a project led by the International Mathematical Union with the support of numerous international and regional organizations.

Please, go to the page of the event to discover all the events which will take place in your region.

Will you organize an event in your city to celebrate the International Day of Mathematics 2020? Tell us more!

We are preparing an interactive map of celebrations of the International Day of Mathematics around March 14 2020 for our official website (https://www.idm314.org/).

Will you organize a celebration, large or small, in a park, museum, school, library or any other public venue? Tell us more about your plans and we will include your city or country in the first version of the map.

Please fill this FORM.

]]>If you are a reader of the *Hitchhiker’s guide to the galaxy*, you probably know that 42 is the answer to the *Ultimate Question of Life, the Universe, and Everything*. The choice of the number by **Douglas Adams** was quite random, excluding the simple fact that the number liked the writer. Yet the 42 was the protagonist of a recent news related to one of the open problems of mathematics:

Is there a number that is not 4 or 5 modulo 9 and that cannot be expressed as a sum of three cubes?

To find an answer to this question, mathematicians used numerical methods. In particular, **Andreas-Stephan Elsenhans** and **Jorg Jahnel** ^{[2]} using a particular vector space ^{[1]}, searched solutions of the following diophantine equation:

for with . This method was later developed by **Sander Husiman** ^{[3]} to . In the end all numbers, except for 33 and 42, below 100 that are not 4 or 5 module 9 have solutions.

The cubic decomposition of these two numbers come in 2019. In both cases, the protagonist was **Andrew Booker** ^{[4]}. In the case of 33 the solution arrives in march:

It’s interesting to observe that Booker, in abstract, write that he was inspired by a *Numperphile*‘s youtube video:

The solution for 42 arrived at the beginning of september:

In this case Booker obtains his result in collaboration with **Andrew Sutherland**: in this way the list of all numbers less than 100 that are not 4 or 5 module 9 is completed.

Now, in the list of numbers between 100 and 1000, the numbers without a cubic decomposition are: 114, 165, 390, 579, 627, 633, 732, 921, e 975.

- Forgive me for the excessive simplification.
- Elsenhans, Andreas-Stephan; Jahnel, Jörg (2009), New sums of three cubes,
*Mathematics of Computation*, 78 (266): 1227–1230, doi:10.1090/S0025-5718-08-02168-6 - Huisman, Sander G. (2016), Newer sums of three cubes, arXiv:1604.07746
- Booker, A.R. Cracking the problem with 33.
*Res. number theory*(2019) 5: 26. doi:10.1007/s40993-019-0162-1 (arXiv)

One of the most popular expressions in Italy for giving strength to numbers is *mathematics is not an opinion*. The expression is exclusively Italian and mathematicians don’t agree with this opinion, since they have fun inventing a large number of different mathematics. For example, a curious mathematics is what today called *lunar arithmetic*. In this kind of arithmetic, the sum between two digits gives the largest digit, while the product between two digits gives the smallest one. A particular consequence of the multiplication rule is the definition of prime numbers: in base 10 a *lunar prime number* is a number divisible only by itself and by 9, because the neutral element of *lunar multiplication* is 9.

There are many interesting consequences that derive from this fact, which can be observed by looking at the list of lunar prime numbers. For example all numbers smaller than 90 that contain 9 as a digit are prime; moreover all numbers from 90 to 99 are primes, extremes included. 109 is a prime number, and we can prove the absence of its factorization by absurdity and hence prove that all the numbers of the form 10…09 are prime. Furthermore, not all numbers containing a 9 are prime.

The fun proposal was advanced in 2011 by **David Applegate**, **Marc LeBrun** and **Neil Sloane** in the *Journal of Integer Sequences* . To explain it clearly and in theme with this month of July, Sloane thinks of himself in this video from the youtube channel *Numberphile* :

Applegate, D., LeBrun, M., & Sloane, N. J. A. (2011). Dismal Arithmetic. Journal of Integer Sequences, 14(2), 3. (arXiv)

]]>Math is everywhere – it’s time to celebrate it! The International Mathematical Union (IMU) plans together with UNESCO to proclaim March 14th, known as Pi-Day, as the annual International Day of Mathematics (IDM). Festivities will be launched on all continents of the world following a joint theme. The topic of the year 2020 will be: “Math is everywhere”.

We invite you to join us!

Do you want to celebrate in your school, university or museum?

Or would you rather organise a small exhibition or event in your region?

Would you like to celebrate in your local math clubs or launch a national activity?

In whichever way you want to celebrate, we will support you on www.idm314.org with ideas, projects, material, software and much more. Every activity will become a part of an interactive map, that collects all projects around the globe.

The website is preliminary for now, providing information about the project plans, partners and the topic “Mathematics is everywhere”. You can also subscribe to the IDM newsletter.

Spread the news, let passionate mathematicians, other math enthusiasts, all your friends (and even people you don’t like that much) know and tell us of your planned activities!

]]>

Dr Tom Crawford, aka the ‘Naked Mathematician’ and the person behind the award-winning website tomrocksmaths.com, has recently launched a new series of online articles explaining his PhD thesis in simple terms. If you’re feeling brave, you can tackle the full beast online here, but for most people we suggest starting with the first article outlining the motivation behind the work with the question ‘where does river water go when it enters the ocean?’

*“It might seem like a simple question, but just think
about it for a second… Water falls from the sky as rain, it flows over and
under the ground and enters into a river. The river flows downstream, maybe
passing through a few lakes along the way, until it reaches the ocean. Now what
happens? The water has to enter the sea and will eventually be evaporated by
heating from the sun and end up back in the atmosphere to form rain again. A
lovely full-circle route called the water cycle – you probably learnt about it
in Geography class. But, what if we could track a raindrop from the sky, into a
river and then into the ocean. What would happen? Does it just flow into the
ocean and then get mixed up and thrown around in the wind and waves? Or do
tides drag it out further to sea? And what about the fact that the Earth is
rotating? Perhaps not so simple after all…”*

The second article ‘how to build a river in the lab’ explains how laboratory experiments can be used to gain invaluable insights into the real-world situation, provided of course that they are suitably well-designed. Article number three, ‘the right ingredients’, moves onto the issue of how to decide which variables are most important in a given problem, touching on the incredibly powerful method of scaling analysis – an applied mathematicians favourite tool.

The fourth article introduces the experimental setup used to collect the data, which will ultimately prove or disprove the mathematical theory used to describe the problem. The title of the article ‘spinning a giant fish tank’ is a surprisingly accurate description of what is in fact a highly sophisticated scientific experiment (though maybe you’ll just have to take my word for it). Finally, ‘let the floodgates open’ features an explanation of an actual experiment in full detail, including a birds-eye view of the river current as it discharges into the rotating ocean.

*“This is a false colour image of an experiment viewed
from above. The freshwater from the river is dyed red with food colouring which
means that we can convert the colour intensity into a depth measurement. The
more intense the red food colouring, i.e. the more of it there is, the deeper
the current must be. The scale starts with black to represent no current (as is
the case for the saltwater ocean), then increases with the current depth
through red, yellow, green and finally blue for the deepest parts of the
current.”*

Tom plans to continue the series in the coming months so if you enjoy the first five articles please do keep your eyes peeled for when the next ones become available. Or better still, follow him on Facebook, Twitter, Instagram and YouTube @tomrocksmaths to be the first to hear when new material is posted!

]]>A Diderot Mathematical Forum dedicated to

**“Mathematics and Architecture”**

will be held on June 8th 2019 in the three cities :

Helsinki (Finland), Porto (Portugal) and Prague (Czech Republic)

The cycle of conferences “Diderot Mathematical Forum” was introduced by the European Mathematical Society (EMS) in 1996.

Each conference takes place simultaneously in three European cities exchanging information by videoconferences, addresses a specific topic, and has both a research and a public component.

——————————————————————————-

Preliminary Programme :

HELSINKI

Organizer : Juliette Kennedy

Speakers:

– Kirsi Peltonen (Aalto University)

IN TRANSITION – Mathematics and Art

– Philip Tidwell (Aalto University)

TBA

– Juhani Pallasmaa (Aalto University)

Man, Measure, Proportion: mathematics and music in architecture

– Axel Kilian (MIT)

Embodied Computation – Architectural Robotics

Location: Metsätalo, conference room 2, Unioninkatu 40 00170 Helsinki

________________________

PORTO

Organizers: João Pedro Xavier and João Nuno Tavares

Speakers:

– Sylvie Duvernoy (Politecnico di Milano. Scuola di Design)

Guarino Guarini, architect and mathematician

– Alexandra Paio (ISCTE-IUL)

Shape grammar

– José Pedro Sousa (FAUP)

Parametric architecture and digital manufacturing

– João Pedro Xavier (FAUP)

Perspective in perspective

Location: University of Porto / Department of Mathematics

_____________________________________

PRAGUE

Organizer : Jiří Rákosník

Speakers:

– Henri H. Achten (Prague, Czech Technical University)

– Robert Aish (London, University College London)

– Daniel Piker (London, Foster and Partners)

– Christopher Williams (Gothenburg, Chalmers University of Technology)

Location: Institute of Mathematics of the Czech Academy of

Sciences, Žitná 609/25, 110 00, Prague

_________________________________________

A publishing of a book in the series of the CIM-Springer collection

http://www.cim.pt/CIM-MS ) is considered

Secretariat and Administration

CIM (Centro Internacional de Matemática, Portugal )http://www.cim.pt/CIM-MS

———

Coordination and Contact

Mireille.Chaleyat-Maurel (University Paris Descartes, Paris, France)

]]>*Gabriella Pinzari started studying the stability of the solar system during her PhD, when she planted the seeds for results that brought her all the way to ICM 2014 in Seoul, where she was an invited speaker. She is now Associated Professor of Mathematical Physics at the University of Padova and Principal Investigator in a prestigious ERC grant funding her research on N-body problems.*

*In this interview, she tells us about her life-long love for mathematics and how a non-standard path can lead to a very successful career. Interview by Anna Maria Cherubini. (from europeanwomeninmaths.org)*

My research deals with the study of the motions of a number of point masses undergoing gravitational attraction. The problem is very old and is known as “many-body problem”. I am particularly interested in the cases with a physical, real-world, interpretation, as the case where one of the masses is much larger than the others (this emulates our solar system); or one large mass, one intermediate, one very small, as in the Sun-Jupiter-Asteroid system.

I am interested in understanding which are the motions that remain stable for very long times, or if there are situations of instability: for example, can it happen that the distance of one body from its sun grows indefinitely?

## “…it would be great to study my whole life”

I have always loved maths since the first classes in my primary school. With time this love grew bigger and bigger. At a certain point, in my 20s, I realised it would be great to study my whole life. At that time I was studying for my physics degree at the University of Rome Sapienza. I liked in particular theoretical and mathematical physics. The cultural environment was fantastic, and I had great mentors: Giovanni Jona Lasinio and Giovanni Gallavotti. Gallavotti was the supervisor of my master thesis.

The untimely death of my father, when I still was a student, put a stop to my dreams for many years. I started working as a teacher and worked for ten years. When I realised I was not happy, I thought I should try to see if I was able to solve a mathematical problem. I asked Gallavotti to give me a problem. He agreed, and that was the starting point of a collaboration with Alessandra Celletti. My second mathematical life started at that point. In the next years, I did a PhD (without salary) in Rome, under the direction of Luigi Chierchia. After my PhD I got a post-doc position in Naples, where I collaborated with of Massimiliano Berti.

During my PhD, I worked on open problems in the theory of stability of planetary motions, as defined by V.I. Arnold in the 60s. The results I found have been highly valued by the scientific community, and in 2014 I had the honour of being invited to the ICM in Seoul. I must also mention that I am very grateful to Massimiliano Berti, for giving me the opportunity to present my results at some important conferences he was organising, while I still was at the beginning of my career.

I have always liked the use of mathematics to understand problems in physics.

My father, my mother, my uncles, my husband, my children, my mentors. I would take this occasion to thank all of them.

## “Scientific research is for me a continuous process of learning and trying new ways.”

Scientific research is for me a continuous process of learning and trying new ways. I truly hope that the work we are doing within the ERC project will be lead to lines of research entirely new, not yet planned. I would also like to explore, in the future, fields which I have not yet touched, such as quantum or statistical mechanics.

What I observe is that, too often, if a paper is co-authored by a man and a woman, it happens that the credit is attributed to the man. This happens especially when the paper is very innovative and the woman is academically junior, compared with the man. People think the credit should be given to the man, but this is not always true.

Speaking of career progression, too often the impact of scientific merit on career progression is very different for a man and a woman. Career progressions for men are still much faster than for women. In certain math departments, even the ones with the highest scientific reputation, the proportion between the number of women and men at the highest career step is unacceptable.

When I was younger I liked painting. Now I have no time. I dedicate all my time to research and academic duties.