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

By Vasos L Pavlika, on 20 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!!

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!!