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Archive for October, 2021

If you want to be a physicist, you must do three things

Vasos L Pavlika20 October 2021

“…first, study mathematics, second, study more mathematics, and third, do the same.” Arnold Sommerfeld
So true!! My two final year Physics modules as an undergraduate were Relativity and Quantum Mechanics, these were really just Mathematics modules with the occasional word thrown in from time to time. The other six were Applied Mathematics modules.

Now Arnold was a real “Giant” of Quantum Physics, introducing new quantum numbers into mainstream Physics and mentoring/teaching many future Nobel Laureates (only J.J.Thomson (1856-1949) taught more). Arnold was fortunate to study courses with the “Great” 20th century Mathematician David Hilbert (1862-1943), of the 23 problems fame and who had General Relativity within his grasp after Albert Einstein (1879-1955) inadvertently divulged too much to him when he told him about the problems that he was having with the mathematics in the said theory. Most certainly Hilbert is not the person one would want to discuss Mathematical issues with whilst racing to the Relativity summit. I visited Gottingen in 2011 and viewed where Hilbert and Gauss once worked, this was quite a surreal experience, and we even had our photographs taken under the Gauss-Weber statue only to be looked at rather strangely by the locals who sadly were not aware of who Gauss (1777-1855) was and his status as the Prince of Mathematics. Regarding David Hilbert I would like to relay a real account of almost coming into contact with Greatness of the past. In 2001 I attended an Applied Mathematics and Analysis conference in Romania and I was kindly asked to chair a session, in this capacity I was asked to inform speakers that they had three minutes left of their talk (by raising a card with the number 3 written on it) , well during my session a very elderly professor perhaps in his late 80s who was very shaky on his feet, commenced his talk. I was worried that he would fall over during his talk, well he started his talk using only “chalk and talk” (the best way I might add) discussing a theorem of Euclid (Mid-4th century BCE) from the 13 books of the Elements. After 15 minutes I raised the 3-minute card and he looked at it, well 10 minutes later he was still discussing the theory without any sign of stopping, I looked around at the other professors in the hall for advice on what to do and they just nodded and said “let him carry on, don’t worry yourself”. After he had finished his talk, I asked why had he been permitted to do this, the news I received shook me to the core, they said “He is a very special professor, he did research with David Hilbert so we let him do whatever he wants”.

Returning to Somerfield he continued his career in Konigsberg and no doubt that we have all heard of the seven bridges problem that Euler (1707-1783) solved (negatively) giving rise to the theory of topology and graph theory.

The advice from Arnold is still as true today as it was when I was an undergraduate, I hope my Engineering students see this post!!

UK’s first gene therapy baby celebrates 21st birthday

Samir Nuseibeh20 October 2021

An incredible story really. Despite the ups and downs associated with gene therapy development over the past few decades, it’s moments like this that remind us of just how revolutionary it can be. And good to see that UCL has played a role in such a triumph!

https://www.gosh.nhs.uk/news/uks-first-gene-therapy-baby-celebrates-21st-birthday/

TED talk just published on lab-grown food

Kim Morgan20 October 2021

Following the recent appointment of Petra Hanga here in UCL Biochemical Engineering, the following TED talk describes the importance of cellular agriculture as a new technology. In this TED talk, Isha Datar discusses the challenges and opportunities of a whole new approach to agriculture where you can “grow chicken nuggets” without ever harming an animal. I’m grateful to our Head of Department, Prof. Gary Lye, for sharing this

√(−1) – The Equation That Changed The World

Vasos L Pavlika20 October 2021

This is arguably one of the greatest equations in all of Mathematics, in fact Richard Feynman (1918-1988) as a 13-year-old stated that “it was the most amazing equation in Math” this was just after he stated that when he tried to self-teach himself circular trigonometry functions he was left confused. Of course, the equation introduces the use of the square root of negative one, however the existence of this number was known much earlier in fact it was known to the great Italian algebraists including: Scipione del Ferro (1465-1526), Gerolamo Cardano (1501-1575) and Niccolò Fontana Tartaglia (the stammerer) (1499-1557) who whilst solving the general cubic equation realised that the path of the solution led to numbers of the form a+b* root(-1) . In fact, they had “Mathematical” duals between themselves on who could solve cubic equations posed by the other, however this discussion is for another day. The square root of -1 is unfortunately today called imaginary and this is very inconvenient for Mathematics and the numbers created by using it along with another real number are called complex and we have Rene Descartes (1596-1650) to thank for that. Rene showed (and it is very easy to do so by reduction ad absurdum) that i is not greater than zero, it is not less than zero and it is not equal to zero thus consequently he decided to call it imaginary, and we are stuck with it.
Interest in root(-1) was ignited again by the Prnce of Mathematics J.C.G.Gauss (1777-1855) who at the age of 17 showed that an algebraic equation of order n has n solutions (taking into account repeated roots) so if one looks at x^2+4=0, then either Gauss was wrong (and I find such a statement tantamount to blasphemy) or we need a “larger” set of numbers. Of course, these numbers were not accepted immediately into Mathematics but now their axiomatic foundations are well understood.
Euler’s result which leads nicely to what we call de Moivres (1667-1754) theorem is such a beautiful theorem, I often wonder why it is not called Euler’s theorem as I doubt he would have missed it (even thought he was blind for the last 17 years of his life). Even in his blindness Euler became the most prolific Mathematician in history with Jabobi (1801-1854) of the Jacobian determinant fame being second. Euler also has another amazing formula (his polyhedral formula) which states that for a polyhedron with no holes: V – E + F = 2; where V is the number of vertices, E is the number of edges and F is the number of faces, this formula gave birth to graph theory and network analysis but alas “this page is too narrow to contain it” (for my Mathematical friends that was a reference to Fermat (1607-1665)).
There are descendants of Euler still alive today who decided not to study Mathematics citing that there would be too much pressure on them with the surname Euler if they studied Mathematics (I don’t blame them).

One of Switzerland’s finest sons by a country mile!!