Fermi's Application To University

[bhobba]

When Fermi applied to a very competitive Italian university to be an undergrad student, he had to, as part of the application process, submit a paper. The admission panel rarely if ever interviews applicants. But they had to interview Fermi. Why? His paper was suitable as a doctoral dissertation and they had to meet this undergrad applicant that could produce such an advanced paper. Of course he was rated first as far as applicants go - but that is truly amazing.

How do you plan out the undergraduate education of such an applicant - the mind boggles. Do you award him a doctorate straight away and make him a post-doctoral fellow? Or like Feynman, who started on graduate courses basically after first year, start him on advanced courses? Just what do you do with students like that?

Thanks
Bill

 

[phinds]

Very cool.

Just what do you do with students like that?

Good question. What did they do in his case?

 

[bhobba]

It was at the very prestigious Scuola Normale Superiore di Pisa which had an excellent reputation in math back then - possibly still has. The paper he submitted was on the theme of "Specific characteristics of Sounds" (I don't know if everyone had to submit a paper on the same topic).

The 17-year-old Fermi chose to use Fourier analysis to derive and solve the partial differential equation for a vibrating rod, and after interviewing Fermi the examiner declared, not only his paper was of doctoral thesis standard, he would become an outstanding scientist. Initially he was going to major in math, but was really at heart a physicist.

During this time Fermi learned tensor calculus at the university to understand general relativity. So basically he attended the courses necessary as background for his self teaching. He soon switched to his true love physics, but still remained a mathematician of the highest caliber. He remained largely self-taught, studying general relativity, quantum mechanics, and atomic physics.

He was allowed to attend the University of Pisa for physics, which had the better physics department. Here Fermi was advised by Luigi Puccianti, director of the physics laboratory, who said there was little he could teach Fermi, and often asked Fermi to teach him something instead. Fermi's knowledge of quantum physics was such that Puccianti asked him to organize seminars on the topic.

Technically how he met the requirements of graduation I have no idea, he may not have even bothered with a formal program. But by third year started publishing high caliber papers. Formally he got his degree in 1922 possibly on the basis of the quality of his published work. But it sure was not the usual education these days - however may have been more common back then.

Added later - I just did a bit of research on education in Italy back then. Basically they just had one higher degree - the Laurea which takes 4-6 years after high school. He may have been like Freeman Dyson and not bothered with a doctorate. Evidently getting the degree is based on a system of credits, but its likely research work can be used to accumulate credits, as well attending formal classes which it seems Fermi didn't do that much of - in fact he seems to have given a few himself.

Thanks
Bill

 

[atyy]

And he did both experiment and theory at the highest levels.

 

[bhobba]

And he did both experiment and theory at the highest levels.

Indeed he did. Plus like Feynman he was an excellent teacher. But Feynman was not known as a great PhD advisor - although he did advise at least 30 students, and some were good such as George Zweig - but none distinguished themselves by being a Nobel Laureate. Fermi however advised many other great physicists, including a number that won the Nobel prize. Feynman could be a bit abrasive - read the story of when Ken Wilson asked him to be his advisor. He then went next door to Murray Gell-Mann and they hit it off straight away:
https://arxiv.org/pdf/1407.1855.pdf

Murray's recollection of Fermi is also very interesting:


Because of that he had the distinction of out 'Feynmaning' Feynman. As everyone knows Feynman was well known as a magician with the uncanny ability to quickly give a clear answer to problems where you go - dah - why didn't I see that. Feynman was working at Los Alamos on a problem and couldn't crack it. Fermi noticed he was deep in concentration and asked can I help. He told Fermi the problem and did what Feynman normally did - solved it in a straightforward clear way. Feynman was shocked - he was beat at his own game. After that you would often see Feynman and Fermi together, along with John Von-Neumann challenging each other to problems - it seems most of the time Fermi won. Fermi really was amazing but for some reason did not have the recognition of say, Feynman.

Thanks
Bill

 

[mathwonk]

Indeed the fact of having only the Laurea degree in Italy seems to have persisted until the 1980's

 

[bhobba]

Indeed the fact of having only the Laurea degree in Italy seems to have persisted until the 1980's

Yes - very strange. The Laurea degree now comes in 3 versions - one equivalent to a bachelors, the next one equivalent to a Masters, and the final one equivalent to a Doctorate so is not an issue now. The old one is considered equivalent to a Masters. This begs the question about the entrance paper he wrote being equivalent to a doctoral theses. I got this from a biography on Fermi so I presumed it correct - you can even find sites on the internet about Fermi listing him with the PhD advisor of Luigi Puccianti - who didn't know as much as Femi - and who Fermi taught, rather than the other way around eg:
https://www.atomicheritage.org/article/manhattan-project-spotlight-enrico-fermi
'In 1922, he received his Ph.D. in Physics from the University of Pisa'

After reading more on the biography I found out how he did the formal subjects. They gave him permission to attend the lectures or not as he saw fit, but had to pass the final exams. A few subjects like freehand drawing and Chemistry he didn't already know, so had to go to the lectures. He got honors in every subject except freehand drawing. Of course based on the quality of his papers, which he wrote from third year, he could apply for a DSc if he wished at some other university, had he wanted the title Doctor.

Another interesting thing is he did a thesis in both Mathematics and Physics. The oral exam for his physics thesis was a breeze, but the one in mathematics was like a torture session. It is not quite known why that was - Fermi's wife always said it was because it went over the head of the examining committee. This seems unlikely, as the Scuola Normale Superiore had some of the finest mathematicians in the world - and certainly among the best in Italy. They had written many of the math textbooks he studied from. They even, as was customary, refused to shake his hand at the end of the oral exam, and, possibly worse, publish his thesis, which was also customary. He still got top marks for it though. All very strange - the current thinking is they were peeved he was going to be a physicist rather than the very talented mathematician he was.

Thanks
Bill

 

[mathwonk]

This odd fact of no available PhD program in Italy, was a blessing for those of us in the US. Students from Italy came to the US for further study, for PhD or just research experience, and those of us here with PhD's were invited to Italy to lecture. This was my introduction to the marvellous country of Italy. I visited as a student in 1977 or so and lectured there in maybe 1980 at a summer school in Perugia (some of the students were absolutely brilliant, far more knowledgeable than the lecturer!), and visited again later in maybe 1981. What an eye opening experience. Sometime later, maybe 1983, I visited again in Rome as a researcher. We will never forget these visits. Our reciprocal visitors from Italy were not likely Fermi's but they greatly uplifted our university by their presence. I can confirm it is somewhat humbling to be asked to advise a PhD student who knows more than one does oneself.

 

[dRic2]

In Italy works more or less like this. You get your knowledge during a 5-year period of studies called "Luarea". Now they split this period to resemble the common undergrad/grad studies, but the structure is essentially the same as it was back then: we don't have internship or stuff like that during your BS and it is also not very common also for MS degrees, you just study on books. In your pHD you don't have courses (yeah, now you do, but they are like 1 month courses per year) and you spent basically 90% of the time on your project. In fact it is pretty strange to me to see all this grad students in the US working as teaching assistant or having lots of extra duties, we just have to study all day :D

Btw I think when Fermi attended the Scuola Normale was probably just for formalities. A friend of his father thought him calculus and linear algebra when he was 15 or something and by the time he got admitted he already knew a big chunk of classical physics. At that time in Italy there was also no expert in atomic/quantum physics so, it is said the he basically self-thought all of that. I can believe that. If you read a book of his you can see how he explained things in his own fashion because he "discovered" them by himself (much like Feynman). I personally consider his explanation of classical entropy ( from "Termodinamica" chapter 5), one of the most mind-blowing chapter I ever read (not because of the concepts, but because of the sinplicity of his explanations).

By the way, if you look up Majorana's Wikipedia page, look at what Fermi said about him... Imagine a guy like Fermi saying something like this...

 

[bhobba]

I personally consider his explanation of classical entropy ( from "Termodinamica" chapter 5), one of the most mind-blowing chapter I ever read (not because of the concepts, but because of the sinplicity of his explanations).

That's not really surprising because evidently his favourite area in math was probability. He used to delight in conundrums of a probabilistic nature. No doubt he would not have been fooled by the Monty-Hall problem - I was though - initially

By the way, if you look up Majorana's Wikipedia page, look at what Fermi said about him... Imagine a guy like Fermi saying something like this...

Yes indeed. And Fermi knew all the first rate physicists, Feynman, Von-Neumann (when he was being a physicist - he was more a polymath IMHO), Heisenberg etc.

For a bit of fun I like to think about what the ideal academic system would be. I think grade 11 and 12 are totally redundant and you should get into university by doing a few university subjects in grade 11 - but start at 5 years of age like they do in the UK. Here in Aus it is offered as an alternative route at a number of universities. We have the university of open learning and often 2 subjects at the credit level is all you need. A number of studies have shown performance at university is the best predictor of performance at university . But the Laurea system to me looks better than here in Aus, USA or UK. I read it was generally 4-6 years. You work at your own pace - Fermi was able to do it in 4 years because he already knew so much. Others likely would not do it that fast, but 6 years is better than 4 years undergrad, then 4 years for your PhD, and if you are good like Fermi - 4 years for the lot. Nowadays, even here in Aus, they are all trying to align with the Bologna process. In Aus it works like this - 2-3 years for a Bachelors depending on if its 2-3 semesters a year. 2 years for a Masters of Research, then 3 years for your PhD. If you did not that well in your Masters of Research you will be required to undertake a Maters of Philosophy first. There are a few variations eg at some places you can do an honours year, then a 4 year Phd, or you can do a 1.5 to 2 year Master of Philosophy, then 3 year PhD. Altogether its still about 8 years which I think is not really necessary for the better students.

Thanks
Bill