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Number-Theory Prodigy Among Winners of Coveted Maths Prize Fields Medals Awarded to Researchers in Number Theory, Geometry and Differential Equations

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Number-Theory Prodigy Among Winners of Coveted Maths Prize Fields Medals Awarded to Researchers in Number Theory, Geometry and Differential Equations NEWS IN FOCUS nature means these states are resistant to topological states. But in 2017, Andrei Bernevig, Bernevig and his colleagues also used their change, and thus stable to temperature fluctua- a physicist at Princeton University in New Jersey, method to create a new topological catalogue. tions and physical distortion — features that and Ashvin Vishwanath, at Harvard University His team used the Inorganic Crystal Structure could make them useful in devices. in Cambridge, Massachusetts, separately pio- Database, filtering its 184,270 materials to find Physicists have been investigating one class, neered approaches6,7 that speed up the process. 5,797 “high-quality” topological materials. The known as topological insulators, since the prop- The techniques use algorithms to sort materi- researchers plan to add the ability to check a erty was first seen experimentally in 2D in a thin als automatically into material’s topology, and certain related fea- sheet of mercury telluride4 in 2007 and in 3D in “It’s up to databases on the basis tures, to the popular Bilbao Crystallographic bismuth antimony a year later5. Topological insu- experimentalists of their chemistry and Server. A third group — including Vishwa- lators consist mostly of insulating material, yet to uncover properties that result nath — also found hundreds of topological their surfaces are great conductors. And because new exciting from symmetries in materials. currents on the surface can be controlled using physical their structure. The Experimentalists have their work cut out. magnetic fields, physicists think the materials phenomena.” symmetries can be Researchers will be able to comb the databases could find uses in energy-efficient ‘spintronic’ used to predict how to find new topological materials to explore. “We devices, which encode information in a kind of electrons will behave, and so whether a material now have a large database of candidate materials, intrinsic magnetism of particles known as spin. is likely to host topological states. and it’s up to experimentalists to uncover new But despite a decade of study, physicists have yet Applying Bernevig’s principles, a team led by exciting physical phenomena,” Yazyev says. ■ to find a topological insulator that has proper- researchers at the Beijing National Laboratory 1. Zhang, T. et al. Preprint at https://arxiv.org/ ties suitable for use in devices — for example, a for Condensed Matter Physics scanned 39,519 abs/1807.08756 (2018). material that is easy to grow, non-toxic and with materials and found more than 8,000 that are 2. Vergniory, M. G., Elcoro, L., Felser, C., Bernevig, tunable electronic states at room temperature. likely to have topological states. This includes B. A. & Wang, Z. Preprint at https://arxiv.org/ abs/1807.10271 (2018). The newly released catalogues classify all both topological insulators and topological 3. Tang, F., Po, H. C., Vishwanath, A. & Wan, X. Preprint non-magnetic materials with known crystal semimetals, which allow the study of new at https://arxiv.org/abs/1807.09744 (2018). structures by their topology, using methods pub- quantum phenomena and are being explored 4. König, M. et al. Science 318, 766–770 (2007). 5. Hsieh, D. et al. Nature 452, 970–974 (2008). lished last year. Until now, physicists had largely for use as catalysts. The team’s database is avail- 6. Bradlyn, B. et al. Nature 547, 298–305 (2017). relied on complex theoretical calculations to pre- able for anyone to access and can be search 7. Po, H. C., Vishwanath, A. & Watanabe, H. Nature dict whether a specific material should harbour using a range of variables. Commun. 8, 50 (2017). AWARDS Number-theory prodigy among winners of coveted maths prize Fields Medals awarded to researchers in number theory, geometry and differential equations. BY DAVIDE CASTELVECCHI umber theorist Peter Scholze, who became Germany’s youngest ever full professor at the age of 24, and geom- Netrician Caucher Birkar — a Kurdish refugee COSTA/ICM2018 PABLO — are among the winners of this year’s Fields Medals, the most coveted awards in mathemat- ics. The medals, which are given out every four years, were presented on 1 August; the other recipients were Alessio Figalli, whose research involves differential equations, and Akshay Venkatesh, who also works on number theory. The winners’ names were announced in Rio de Janeiro, Brazil, at the opening of the Interna- tional Congress of Mathematicians. The Fields Medals, given out by the Inter- national Mathematical Union, are awarded to up to four mathematicians aged 40 or younger. For the first time in the medals’ 82-year his- tory, none of the awardees are citizens of the Fields medallists (left to right) Akshay Venkatesh, Peter Scholze, Alessio Figalli and Caucher Birkar. United States or France — two countries that together have netted nearly half of the medals Few observers doubted that Peter Scholze a book-length proof in arithmetic geometry. so far. Maryam Mirzakhani, a winner in 2014, deserved a Fields Medal, or that he would win Scholze is now a professor at the Univer- remains the only woman ever to receive the one this year. The 30-year-old became famous sity of Bonn in Germany, and a director at the prize. (Mirzakhani died of cancer in 2017.) at 22 for finding a way to drastically shorten Max Planck Institute for Mathematics in the 152 | NATURE | VOL 560 | 9 AUGUST 2018 | CORRECTED©2018 Spri nger N a17tur eAUGUSTLi mited. All r2018i ghts reserved. ©2018 Spri nger Nature Li mited. All ri ghts reserved. IN FOCUS NEWS same city. Most of his work has connec- POLICY tions to ‘p-adic fields’, exotic extensions of the ordinary number system that are use- ful tools for studying prime numbers. On the p-adics, he has built fractal-like struc- German science goes tures called perfectoid spaces, which have helped to solve problems across several fields of mathematics, including geometry under a microscope and topology. In recent months, Scholze has been checking a gigantic proof of the abc conjecture, one of the biggest unsolved Gigantic review of Helmholtz centres finds lack of diversity. problems in number theory. In 2012, the enigmatic Japanese mathematician Shinichi BY QUIRIN SCHIERMEIER materials sciences — Helmholtz centres rank Mochizuki posted a proof online, but no one among the world’s top institutes by quality has yet been able to say definitively whether ermany’s largest research organiza- of basic science and research infrastruc- it checks out. Now, Scholze and a colleague, tion is funding top-notch science, tures, reviewers concluded. Energy research Jacob Stix, are said to have found a signifi- but it needs to employ more foreign and Earth and environmental sciences also cant gap in the proof. Gand female researchers — and it is failing to received high marks. Caucher Birkar, 40, has made break- leverage ‘big data’, such as electronic medical In biomedical research, reviewers endorsed throughs in the classification of algebraic records. the organization’s current focus on infec- varieties — geometric objects that arise These are the conclusions emerging from a tious diseases, dia- from polynomial equations, such as y = x2. first-of-its-kind evaluation of the Helmholtz “Like almost betes, dementia and He was born in 1978 in a region of west- Association of German Research Centres, everywhere in cancer. But special- ern Iran dominated by the Kurdish ethnic which employs some 30,000 scientists and science, real ized health-research group. Birkar recalls his childhood in video technicians at 18 centres and has an annual equity may still centres in Munich, profiles of the Fields medallists: “My parents budget of €4.5 billion (US$5.3 billion). be generations Braunschweig, Bonn are farmers, so I spent a huge amount of time Helmholtz showed Nature the results of the away.” and Heidelberg must actually doing farming,” he says. “In many review, which individual centres will release make better use ways, it was not the ideal place for a kid to get over the next few weeks. of patient data to develop diagnostic tools interested in something like mathematics.” The results will serve as the basis for a and therapies, the review concludes. It also In 2000, after studying at the University strategic evaluation next year, which will be recommends that the centres establish more of Tehran, Birkar moved to the United used to allocate research funding from 2021 designated clinical-trial units, in collabora- Kingdom, where he got refugee status and, to 2027. Other leading science organizations tion with hospitals, to take discoveries from eventually, UK citizenship. He is now a rarely, if ever, conduct such sweeping reviews, the bench to practice. researcher at the University of Cambridge. says neuroscientist Otmar Wiestler, president “Reviewers have clearly seen that Ger- Birkar said that he hopes that his Fields of the association. many is lagging behind in digital medicine,” Medal will put “just a little smile on the lips” says Wiestler. “It is absolutely vital for health of the world’s estimated 40 million Kurds. DISCIPLINED ANALYSIS research and health care in this country that His win made headlines for more than “We were very impressed by the quality of we catch up.” just his research: before the award cer- the science,” says Andrew Harrison, chief emony was over, his briefcase was stolen, executive of the Diamond Light Source at A CHALLENGE TO DO BETTER with his medal in it. The organizing com- the Harwell Science and Innovation Cam- Reviewers also urged the organization mittee of the congress presented him with pus in Didcot, UK. He was one of more than to boost diversity. Efforts to that effect a replacement medal in a special ceremony 600 independent scientists from 27 countries are already under way, says Wiestler. A on 4 August. who, between October 2017 and April 2018, €5.4-million initiative to recruit more female Akshay Venkatesh, who is 36, works on, spent up to a full week in Germany assessing scientists was launched last year.
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