By Vasos L Pavlika, on 4 January 2022
Her theorem is considered as important as Einstein’s Theory of Relativity
She had a number of very eminent admirers of her work including A. Einstein (1879-1955) who was very impressed with her work. Her work is concerned with symmetry breaking and conservation laws, well known in the Quantum and Relativistic worlds.
Emmy came to Göttingen University in 1915 having been invited by David Hilbert (of the 23 problems fame, Kurt Godel (1906-1978 solved the second) Paul Cohen (1934-2007 proved the Continuum hypothesis) and Felix Klein (1849-1925 of the bottle fame), who wanted her expertise in invariant theory to help them to understand certain problems in general relativity, Hilbert had observed that the law of conservation of energy appeared to be contradicted in General Relativity. Noether provided the resolution of this paradox, providing a fundamental tool for modern theoretical physics, with Noether’s first theorem, which she proved in 1915 and published in 1918. She not only solved the problem for General Relativity, but also determined the conserved quantities for every system of physical laws that possesses some continuous symmetry. After looking at her work, Einstein wrote to Hilbert:
“Yesterday I received from Miss Noether a very interesting paper on invariants. I’m impressed that such things can be understood in such a general way. The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff“.
Like many of the great Jewish scientists in Germany at the beginning of twentieth century she was expelled from Germany due to the emergence of the Nazi movement along with “Giants” including Max Born (1882-1970), and Richard Courant (1888-1972) who wrote the now-famous books that I have in my office at UCL, “Mathematical Methods for Physicists” by Courant and Hilbert. Staying with books a great book to read to delve into the workings of Max Born’s mind is “My life, Recollections of a Nobel Laureate” by Max Born.
Miss Noether is certainly an unsung “Giant” of Mathematics and Physics.
By Vasos L Pavlika, on 15 November 2021
I have read this book by Ian Stewart and it is wonderful. It is strange that Newton’s second law of motion is omitted but as the Navier-Stokes equation (which is just this law) is included I will not object. Of course, there are some misnomers here namely Pythagoras’ theorem as the result was known numerically to the Babylonians computing triples in sexagesimal (base 60, which we still have remnants of in the measurement of time), furthermore Euler was not the first to be led to the square root of -1, this was first done by the great Italian algebraist Cardano (1501-1576) in solving cubic and quartic equations. I am not sure which one of these beautiful equations is my favourite but the one that caused the most fascination was Euler’s polyhedral formula which amazed me as I suppose on looking at geometric figures (normal Mathematicians) do not notice that V+F=E+2, where V=the number of vertices (nodes), F=the number of faces, E=the number of edges (lines) and from here he spawned the geometric discipline now known as topology (named after the Greek for place). We all know of a topological map (most train networks are topologically accurate but not geometrically accurate) i.e. the position of a node relative to another is important but not its distance or angular orientation.
By Vasos L Pavlika, on 20 October 2021
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!!
By Samir Nuseibeh, on 20 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!
By Kim Morgan, on 20 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
By Vasos L Pavlika, on 20 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!!
By Vasos L Pavlika, on 15 September 2021
Bertrand Russell is such an inspirational figure I hardly know where to begin. Russell was at Trinity College, Cambridge alongside G.H.Hardy FRS (1877-1947) who wrote the wonderful book “A Mathematicians apology” claiming in it that everything he had done was worthless, rather a strange statement. Hardy worked with the great Indian Mathematician S. Ramanujan FRS (1887-1920) (yes the man who knew infinity) and J.E. Littlewood FRS (1885-1977) creating fruitful collaborations. Bertrand (if I may) wrote his Principia masterpiece and named it in the spirit of I.Newton (1643-1727) who also wrote a Principia, this naming was actually quite common with Charles Lylle FRS (1797-1875) the father of Geology similarly writing his masterpiece with the title Principles of Geology (which I have in my office at home).
Bertrand’s work was in logic and included ideas of Kurt Godel (1906-1978) who worked on two of Hilbert’s (1862-1943) famed 23 problems in which the eighth is the legendary Riemann hypothesis and which is still unresolved (as stated on 8th September 2021) today. Godel developed his incompleteness theorem, and it is well known that Kurt took up a job at Princeton’s Institute of advanced study so that he could talk to Einstein and take long walks with him, I would have loved to have been a fly on the wall during these talks, but I recall reading that Kurt stated that he loved hearing Albert’s laugh as it made the whole room shake (awesome).
Returning to Bertrand (who won the Nobel Prize in literature in 1950, what an intellect) developed in 1901 what has become known as Russell’s Paradox and which overturned the life work of Gottlob Frege in a single swoop, however Russell states that Frege acted with incredible integrity and fortitude even though his entire life’s pursuits had been shown to be incomplete, thus:
As I think about acts of integrity and grace, I realise that there is nothing in my knowledge to compare with Frege’s dedication to truth. His entire life’s work was on the verge of completion, much of his work had been ignored to the benefit of men infinitely less capable, his second volume was about to be published, and upon finding that his fundamental assumption was in error, he responded with intellectual pleasure clearly submerging any feelings of personal disappointment. It was almost superhuman and a telling indication of that of which men are capable if their dedication is to creative work and knowledge instead of cruder efforts to dominate and be known. (Quoted in van Heijenoort (1967), 127).
Russell’s so-called Barber problem paradox is a misnomer as it was known to Frege and was not stated by Russell, the paradox can be stated as:
“The barber is the “one who shaves all those, and those only, who do not shave themselves”. The question is, does the barber shave himself?”
Thinking about this one soon realises that there is a circular contradiction.
Well Bertrand gives us more wise words in this quote: “The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.”
By Samir Nuseibeh, on 15 September 2021
Irrespective of the advances made in gene therapy over the past two decades, it is clear that we still don’t have a full grasp over the safety elements associated with them – particularly when high doses are involved.
This was sad news to arrive in my inbox today regarding the development of “AT132” by Audentes Therapeutics to treat myotubular myopathy (MTM1):
Transduction of muscle tissue is notoriously difficult and requires high viral genome doses in order to achieve sufficient expression of a given transgene. Evidently, the developers selected extremely high doses off the back of this demand and are now suffering the consequences of this choice.
Whilst I admire the developer’s commitment to helping the MTM1 community, it does beg the question – are high viral genome doses really an acceptable rationale for gene therapy development, considering the risks associated with safety? I suppose we’ll let the biopharmaceutical industry dictate that…