**Michael Atiyah 1929–2019**

**A giant of mathematics **

The eminent mathematician Michael Atiyah died in Edinburgh on 11 January, aged 89. He was one of the giants of mathematics whose work influenced an enormous range of subjects, including theoretical high-energy physics.

Atiyah’s most notable achievement, with Isadore Singer, is the “index theorem”, which occupied him for more than 20 years and generated results in topology, geometry and number theory using the analysis of elliptic differential operators. In mid-life, he learned that theoretical physicists also made use of the theorem and this opened the door to an interaction between the two disciplines, which he pursued energetically until the end of his life. It led him not only to mathematical results on Yang–Mills equations, but also to encouraging the importation of concepts from quantum field theory into pure mathematics.

**Early years**

Born of a Lebanese father and a Scottish mother, his early years were spent in English schools in the Middle East. He then followed the natural course for a budding mathematician in that environment by attending the University of Cambridge, where he ended up writing his thesis under William Hodge and becoming a fellow at Trinity College. As a student he had little interest in physics, but went to hear Dirac lecture largely because of his fame. The opportunity then arose to spend a year at the Institute for Advanced Study in Princeton in the US, where he met his future collaborators and close friends Raoul Bott, Fritz Hirzebruch and Singer.

A visit by Singer to the University of Oxford (where Atiyah had recently moved) in 1962 began the actual work on the index theorem, where the Dirac operator would play a fundamental role. This ultimately led to Atiyah being awarded a Fields Medal in 1966 and, with Singer, the Abel Prize in 2004. Over the years, proofs and refinements of the index theorem evolved. Although topology was at the forefront of the first approaches, in the early 1970s techniques using “heat kernels” became more analytic and closer to the calculations that theoretical physicists were performing, especially in the context of anomalies in quantum field theory. In the 1980s, in a proof by Luis Álvarez-Gaumé (who subsequently became a member of the CERN theoretical physics unit for 30 years), Hirzebruch’s polynomials in the Pontryagin classes – which form the topological expression for the index – emerged as a natural consequence of supersymmetry.

Singer visited Oxford again in 1977, this time bringing mathematical questions concerning Yang-Mills theory. Using quite sophisticated algebraic geometry and the novel work of Roger Penrose, this yielded a precise answer to physicists’ questions about instantons, specifically the so-called ADHM (Atiyah, Drinfeld, Hitchin, Manin) construction. That mathematicians and physicists had common ground in a completely new context made a huge impression on Michael, and he was energetic in facilitating this cooperation thereafter. He frequently engaged in correspondence and discussions with Edward Witten, out of which emerged the current fashion in mathematics of topological quantum field theories – beginning with a formalism that described new invariants of knots. Despite the quantum language of this domain, Michael’s mathematical work with a physical interface was more concerned with classical solutions, and the soliton-like behaviour of monopoles and skyrmions.

**Founding father**

During his life he took on many administrative tasks, including the presidency of the Royal Society and mastership of Trinity College. He was also the founding director of the Isaac Newton Institute for Mathematical Sciences in Cambridge.

With his naturally effervescent personality he possessed, in Singer’s words, “speed, depth, power and energy”. Collaborations were all-important, bouncing ideas around with both mathematicians and physicists. Beauty in mathematics was also a feature he took seriously, as was a respect for the mathematicians and physicists of the past. He even campaigned successfully for a statue of James Maxwell to be erected in Edinburgh, his home city, in later years.

As for the index theorem itself, it is notable that one of the more subtle versions – the “mod 2 index” – played an important role in Kane and Mele’s theoretical prediction of topological insulators. As they wrote in their 2005 paper: “it distinguishes the quantum spin-Hall phase from the simple insulator.” A fitting tribute to an outstanding pure mathematician, whose intuition and technical power revealed so much in so many domains.

*Nigel Hitchin, University of Oxford.*

**Hans-Jürg Gerber 1929–2018**

**A flair for the fundamental **

Swiss physicist Hans-Jürg Gerber passed away on 28 August last year. Born in Langnau/Kanton Bern, he studied and did his PhD from 1949 to 1959 at ETH Zurich on “Scattering and polarization effects of 3.27 MeV neutrons on deuterons”. He then worked at the University of Illinois in the US, before joining CERN from 1962 to 1968. There, he carried out experiments at the 28 GeV Proton Synchrotron (PS). He studied high-energy neutrino interactions using a spark chamber, and performed measurements of lepton universality. He also tested time-reversal invariance in the charged decay mode of the Λ hyperon. He was also PS coordinator from 1965 to 1966.

In 1968, Gerber became head of the research department at the Swiss Institute for Nuclear Physics (SIN). He was elected by the Swiss Federal Council to become associate professor of experimental physics in 1970, and in 1977 promoted to full professor. Gerber initiated basic research at SIN and later at the Paul Scherrer Institute (PSI) with his precision experiments on the decay of charged muons – experiments that continue to this day at PSI (see p45). His flair for the fundamental led to the most general determination of the leptonic four-fermion interaction for the normal and inverse muon decay using experimental data, which brought him international recognition.

In the 1980s and 1990s, Hans-Jürg returned to CERN to help set up and operate experiment PS195 (CPLEAR) for studying CP violation using a tagged neutral-kaon beam. The concept of the experiment, which involved tagging the flavour of the neutral kaon at the point of production, was opposite to already operational kaon experiments based on K-short and K-long beams. As a skilled experimenter, he contributed significantly to the success of CPLEAR with unconventional ideas. For example, during a crisis when the liquid-scintillator started to develop air bubbles due to the heat from nearby electronics, he invented a system to remove the air dissolved in the liquid using ultrasound. CPLEAR’s measurements on the violation of time-reversal invariance (T-invariance) and tests of quantum mechanics were the starting point for significant theoretical work he undertook on T, CP and CPT invariance.

While he retired in the spring of 1997 after a long and extremely successful career, he still continued working on particle physics with various publications on the interpretation of the CPLEAR results regarding testing of quantum mechanics, T- and CPT-violation. He was also a contributor to the review of particle physics in the Particle Data Group.

Experiment, theory and teaching formed a unity for Hans-Jürg. This was particularly evident in his lectures, in which he enthusiastically conveyed the joy of physics to his students. We also remember dinners with Hans-Jürg after long working days setting up experiments, where we talked about all possible physics questions.

He is survived by his wife Hildegard, his three children and grandchildren.

*His friends and colleagues at CERN. *

**Bastiaan De Raad 1931–2018**

**CERN accelerator pioneer **

Bas de Raad arrived at CERN in July 1954 at the tender age of 22 – two months before the Organization was formally established. After graduating from the Technical University of Delft in the Netherlands, he joined the team working on the design of the Proton Synchrotron (PS), based at that time in the École de Physique in Geneva, with special responsibility for the PS main magnets, which are still operating reliably to this day. He moved on to work on magnets for the external beams of the PS.

After a sabbatical year in Stanford in 1963/1964, he returned to the accelerators division at CERN to work on the design of the optics for the Intersecting Storage Rings (ISR), the first hadron collider. Later, he became leader of the ISR beam transfer group with responsibility for the design of the two long transfer lines from the PS to ISR, as well as the injection and beam-dumping systems.

On approval of the construction of the Super Proton Synchrotron (SPS) in 1970, Bas joined the core team of John Adams, where he led a much bigger group working on the design and construction of all the transfer lines to and from the SPS (together with injection), and both resonant and fast-extraction systems and the beam dump. He was deputy division leader of the SPS division from 1977 to 1981 and leader until the end of 1989.

Even with his heavy load as leader of one of the biggest divisions at CERN, he still managed to find time for technical work. In preparing the SPS to accelerate electrons and positrons for the Large Electron Positon collider, he realised the importance of shielding the SPS coils from synchrotron radiation and took on the job himself, spending many hours in the SPS tunnel fitting the shielding masks. From 1990 until his retirement in 1996 he was the leader of CERN’s technical inspection and safety commission.

Bas was a great leader, training a new generation of machine builders during the construction of the ISR and the SPS with the meticulous attention to detail that he demanded of himself.

*His friends and colleagues.*