Plus Blog

September 11, 2020

The mathematician Martin Hairer has been awarded the 2021 Breakthrough Prize for Mathematics which, apart from the accolade, comes with $3 million in prize money.

Hairer received the prize for "transformative contributions to the theory of stochastic analysis, particularly the theory of regularity structures in stochastic partial differential equations". You can find out more about what this means in the following article and podcast, which we produced after interviewing Hairer about receiving the Fields Medal, one of the highest honours in maths, in 2014.

Martin Hairer: At the interface — A brief look at Hairer's groundbreaking work, which involves the maths of change and chance.

Interview with Martin Hairer: The podcast — Listen to Hairer talk about his research in this podcast, recorded a day before he received the Fields Medal in 2014.

Hairer has also written us a series of articles about the maths of randomness. These are based on a lecture he gave at the Heidelberg Laureate Forum 2017, where we also recorded a video of Hairer talking about issue surrounding randomness. The video is shown below.

The maths of randomness — Randomness is surprisingly hard to define. But as Hairer explains in this article, the mathematical language we use to describe it is beautifully succinct.

The maths of randomness: Symmetry — In this article Hairer explains why symmetry is one of the two guiding principles in understanding probabilities.

The maths of randomness: Universality — The second guiding principle of the maths of randomness is universality, which Hairer explains in this article.

The two envelopes problem — Here's a brain teaser Hairer presented at the Heidelberg Laureate Forum 2018. See if you can crack it!

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November 19, 2019

Do you like the number e? Then you might like this curious fact discovered by Aziz Inan of the University of Portland.

Every year on February 7 maths enthusiasts celebrate e day. That's because the first two digits of the number e are 2 and 7, and because February 7, written the American way with the month first, is 2/7.

The year 2018 saw a very special e day: February 7, 2018 is written as 2/7/18, and 2, 7, 1, and 8 represent the first four digits of e. This coincidence occurs only once a century!

But there is more: the calendar date that follows 2/7/18, namely 2/8/18, coincides with the next four digits of e. So 2/7/18 and 2/8/18 put side by side as 27182818 constitute the first eight digits of e. This property makes the once-a-century special e Day 2/7/18 even more special!

To find out more about the number e and some interesting properties of its digits, see this article by Aziz Inan. You may also want to read the following Plus articles.

Maths in a minute: Compound interest and e — Compound interest is the curse of debt and the blessing of saving. Find out how it works and what it has to do with $e$

Maths in a minute: Euler's identity —Here's a quick introduction to the beauty queen amongst mathematical formulas, which involves $e$.

The making of the logarithm —The natural logarithm is intimately related to the number $e$ and that's how we learn about it at school. When it was first invented, though, people hadn't even heard of $e$ and they weren't thinking about exponentiation either. How is that possible?

Have we caught your interest? —This is a longer and more detailed article about compound interest and $e$, complete with some history.

Polar power —Like spirals and flowers? Then you'll love polar coordinates and the pretty pictures they allow you to draw. One of those is intimately related to $e$.

Radioactive decay and exponential laws —Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. This article looks at radioactive decay and exponential laws.

Light attenuation and exponential laws —This is another article that explores the appearance of exponential laws in nature. It explores light attenuation: the way in which light decreases in intensity as it passes through a medium. the a

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September 20, 2019

One of our favourite authors, Wim Hordijk, recently sent us a digital postcard from the beautiful city of Vienna, where he had traced the steps of the eminent mathematician Kurt Gödel. Here is what he discovered.

Portrait of Kurt Gödel

Kurt Gödel.

Kurt Gödel was one of the greatest mathematicians of the 20th century. He made many important contributions to mathematical logic and philosophy, but is best known for his incompleteness theorems. Loosely speaking, the theorem states that the dream of phrasing all of mathematics in terms of a formal system, based on a set of axioms and the rules of logic, is bound to fail: there will always be statements that are true but whose truth cannot be proved within the axiomatic system itself. This abruptly ended a longstanding quest by some mathematicians to construct a set of axioms sufficient for all of mathematics (you can find out more in this Plus article).

Gödel was born in 1906 in Brünn, then part of the Austro-Hungarian empire (now Brno, Czech Republic). At the age of 18 he moved to Vienna, where he studied and worked from 1924 until 1940, and also took part in the famous Vienna Circle. He completed his PhD dissertation at the age of 23, and became a lecturer at the University of Vienna a few years later. In January of 1940, after the start of World War II, Gödel and his wife left Europe for good to start working at the Institute for Advanced Study in Princeton, USA, where he became close friends with Albert Einstein. He died in Princeton from self-imposed starvation in 1978.

The Kurt Gödel Research Center for Mathematical Logic (KGRC) of the University of Vienna was named after and in honor of Gödel, who proved his completeness and incompleteness theorems in Vienna in the years 1929-1931. For a long time the KGRC was housed in a beautiful building called the Josephinum on the Währingerstrasse, close to the main university building, and just a few doors down from one of the buildings where Gödel lived for a while.


The Josephinum on the Währingerstrasse in Vienna, where the KGRC was located. Image: Wim Hordijk.

In fact, Gödel lived in quite a few places in Vienna. During the roughly 15 years that he studied and worked there, he took up residence in seven different places throughout the city. On the KGRC website you can find a list of addresses where he lived (and when), together with a map indicating these locations. Moreover, each building where Gödel lived has a commemorative plaque next to its entrance.


The seven plaques at the buildings in Vienna where Gödel lived. Top row, left to right: Florianigasse, Frankgasse, Währingerstrasse, Lange Gasse. Bottom row, left to right: Josefstädterstrasse, Himmelstrasse, Hegelgasse. Images: Wim Hordijk.

With Vienna's excellent public transportation, it is actually possible to visit all of these places in one day, making Gödel's story come to life. But if you need more time, the building at Währingerstrasse 33 (just a few steps from the Josephinum) is now a hotel. So if you want to make it even more real, it is possible to spend a couple of nights in one of the places where Gödel once lived.

Währingerstrasse 33

The building at Währingerstrasse 33, where Gödel lived as a student, is now a hotel. Image: Wim Hordijk.

The beautiful city of Vienna is already worth a visit in itself, but for mathematics aficionados the visible legacy of Kurt Gödel makes it even more worthwhile. The information presented here will hopefully serve as an inspiration for others to also experience some real maths history first-hand.

About the author

Wim Hordijk

Wim Hordijk is an independent and interdisciplinary scientist and popular science writer. He has worked on many research and computing projects all over the world, mostly focusing on questions related to evolution and the origin of life. More information about his research can be found on his website.

March 28, 2019

Have you ever wondered what the world would be like without mathematics? And who are the people who make new mathematics and how they do it?

Who is your favourite mathematician of all time?

This competition, organised by the British Society for the History of Mathematics, is your chance to explore how mathematics has developed and achieved its status and who were the most important mathematicians in history who contributed to it. This year we would like you to concentrate on choosing one mathematician who has, in your opinion, been the most important person, your favourite, and to make the case for your choice — to explain his/her mathematics and to show their importance or what you think was special about it and them.

The British Society for the History of Mathematics (BSHM) believes that understanding where mathematics comes from and who has contributed to the development of mathematical ideas is an important part of understanding mathematics today. BSHM, working with Plus, invites secondary school students to explore this question and communicate their findings for a wide audience (age 16 upwards).

You could write an article (maximum 1500 words), make a short video (maximum ten minutes) or a multi-media project (maximum ten minutes).

The competition is open to all young people aged 11 to 15 and 16 to 19 who are in secondary education. A number of monetary prizes will be awarded, depending upon the quality and the number of entries. The maximum prize will be £100.

The deadline for entries is Friday, 1st September 2019. All the info about how to submit your entry and where to ask questions is on the BSHM website.

Winners will be notified to collect their prizes in London, at the Society's Gresham College meeting on the 23rd October 2019, and the recording of this will be posted on the BSHM website, with a link given also from Plus.

Good luck!

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December 18, 2018

Caucher Birkar won a Fields Medal at this year's International Congress of Mathematicians. He received the prestigious prize for his contributions to an area of maths called algebraic geometry. In this video he tells us about his work and his unusual mathematical journey.

You can find out more about Birkar's work in this article.

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August 1, 2018

You can see all our coverage from the ICM 2018 here.

The International Congress of Mathematicians opened this morning in a packed amphitheatre, bathed in green light and the sounds of the rain forest. The ceremony celebrated the best of Brazilian talent and creativity and the emphasis of the organising committee on building a legacy for the future of mathematics in Brazil. It was particularly lovely to see the 576 gold medallists from the Brazilian Mathematics Olympiad in the crowd, perhaps some of them will take the stage at some future ICM.

We could feel the excitement in the crowd as we waited for the announcements of the prizes of some of the most prestigious prizes in mathematics. And the winners of the Fields medals are:

Caucher Birkar — Caucher Birkar has been awarded the Fields medal for his contribution to algebraic geometry.

Alessio Figalli — Alessio Figalli has been awarded the Fields medal for his contributions, among other things, to optimal transport theory.

Peter Scholze — Peter Scholze has received the Fields medal 2018 for transforming arithmetic algebraic geometry.

Akshay Venkatesh — Akshay Venkatesh has been awarded the Fields medal 2018 for his work exploring the boundaries of number theory.

You can read about the maths behind these prizes in the articles above. Also announced were:

  • Constantinos Daskalakis – winner of the Rolf Nevanlinna Prize for outstanding contributions on the mathematical aspects of informational sciences.
  • David Donoho – winner of the Carl Friedrich Gauss Prize for scientists whose mathematical research has had an impact outside mathematics.
  • Masaki Kashiwara – winner of the Chern Medal Award, awarded to mathematicians whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics.
  • Ali Nesin – winner of the Leelavati Prize for increasing public awareness of mathematics as an intellectual discipline and the crucial role it plays in diverse human endeavors.
It's been a joyous start to the congress, stay tuned for more stories!