Dr Leslie Lamport commenced his plenary lecture with an elegant exposition about Euclid’s Algorithm, noting that it computes the greatest common divisor (GCD) of two positive integers.

Giving several examples of how this algorithm and others can be used, Dr Lamport observed that in order to execute an algorithm efficiently on a computer, one must implement it in code. 

Yet programming languages are much more complicated and less expressive than math, so “you don’t want to debug an algorithm in the code”. 

He said that most programmers do not think about the algorithm their program implements. “They design the algorithm as they code. They think about algorithms in terms of code. They should think about them in terms of math.”

Dr Lamport added that it is very expensive to fix fundamental design flaws after the code is written because it requires extensive recoding, and often these flaws are not found until the code has been released to users.

Stating there is drama in mathematics, Professor Efim Zelmanov noted that mathematicians want understanding and hence are sceptical of proofs to mathematical problems solved by machines.

Talking about some of the great mathematicians and their seminal contributions, he noted that Évariste Galois, while still in his teens, was able to solve a 350-year-old mathematical problem.

Galois, in a letter to his friend the night before he died in a gun duel, provided a solution to the long-standing question of determining when an algebraic equation can be solved using radicals, which are solutions containing square roots, cube roots and others (but no trigonometric or other non-algebraic functions). Galois’ solution contributed immensely to Group Theory in algebra. 

Professor Zelmanov noted that Hermann Weyl, another great mathematician, stated that Galois’ solution was the most influential paper in the history of mathematics. He also dwelt on the contributions of other famous mathematicians like Émile Léonard Mathieu.

Obliquely referring to the debate over the use of axioms in mathematics, Professor Zelmanov concluded his plenary by observing that mathematicians formulate the most important properties of an object that are relevant to their study, and then take these properties as axioms and study all objects that satisfy these axioms.

“Since the time of Emmy Noether, mathematics speaks the language of axioms. Even the critics of axiomatics write their papers in this way. It is like complaining about the exceeding predominance of English… in English,” he concluded.

Nuclear magnetic resonance (NMR) will continue to play a crucial role in drug development, declared Professor Kurt Wüthrich in his plenary lecture outlining the history and modern applications of the observation technique which he helped to advance significantly. 

The first NMR machines were created in the 1940s using radar technology developed during World War Two to detect enemy planes. “Today, it is used in many ways, including in structural biology,” said Professor Wüthrich. “We use it to study the structure of molecules in solution, which means that we can look at the molecules of life in an environment very close to their natural environment.” The brain, for instance, is surrounded by cerebrospinal fluid. 

By mapping molecules’ structure, scientists can identify targets for drugs. “When a chemist makes a new compound, you can use NMR in experiments to see if it is effective,” Professor Wüthrich added. He said that he is studying G protein-coupled receptors, which support major human physiological functions and are therefore important drug targets. The receptors are also linked to how pain-relieving opioids work, so better understanding of them could lead to new chemical compounds that are as effective but have fewer or no side effects. He summarised: “NMR can provide the basis for drug development, which is very exciting.”

2020 is the first year for the new international system of measurement units, observed Dr Klaus von Klitzing at the start of his plenary lecture, which was the final one of the Global Young Scientists Summit 2020. 

On 20 May 2019, the world adopted new definitions for the seven units used to express all measurements: the second for time, metre for length, kilogram for mass, kelvin for temperature, ampere for electric current, candela for luminous intensity and mole for the amount of substance. The latest definitions are based on constant fundamentals of nature, such as the speed of light in vacuum. In his lecture, Dr von Klitzing summarised how the definitions had changed over centuries. 

The kilogram, for example, was originally defined in 1799 as the mass of a decimetre cube of water at the temperature of melting ice, before nations agreed in 1875 to use a physical cylinder, subsequently stored in France, and its copies worldwide as the reference. Dr von Klitzing said that the latest definitions for the seven units are better because they are based on the laws of nature, and not physical objects, and thus will not change from country to country or over time: “The constants of nature are the most stable basis for a universal system of units, for all time, and for all people.”