You and me both, buddy!
"Oppenheimer obtained his Doctor of Philosophy degree in March 1927 at age 23, supervised by Max Born. After the oral exam, James Franck, the professor administering, reportedly said, "I'm glad that's over. He was on the point of questioning me." "
Franck had won the Nobel two years earlier.
Sources: [Refs] quoted directly from Wikipedia article
 from Wikipedia: https://content.time.com/time/subscriber/article/0,33009,853... --> p.4
Apparently on the way into his viva he said to Bertrand Russel "Don't worry, I know you'll never understand it.". He passed with flying colours.
(Note: I tried to google and didn't find a primary source, but post saying the same thing I remembered, so possible citation needed here)
 True, I didn't understand it but it clearly has had an impact!
Usually Von Neumann is thought to be Hungarian. Born in Budapest, which at the time was part of the Austro-Hungarian Empire.
James Franck, who had emigrated to the US, advocated to not use the Atomic bomb against Japan:
That does make me wonder: why DOES the qualification/position/status name mention only philosophy?
The terms we use to differentiate fields of study are still shifting. Nobody uses the term "naturalist" anymore, at least not to refer to a scholarly field. There's often a huge overlap between math and various other fields. I'm not sure the recent explosion in degree names is any better than using Ph.D. It's tempting to suggest that fields like Art History and English Literature should be differentiated from [modern] Physics, but ideally scholars in all those fields should be (and often are) using many of the same analytical techniques. And realistically, I doubt usage of a shared signifier, Ph.D, is causing any consequential confusion. Arguably, as specialization increases the value of using Ph.D increases--it general implies someone has attained the highest credential in their field of study, whatever the field.
In the centuries since, new kinds of knowledge were discovered, but they generally got squeezed in as sub-categories of philosophy, so when you specialise in them, you get a PhD.
Natural philosophy was the original (and i think better) name for science, especially physics. It was understood to be an important subbranch of philosophy.
I think its better name because it elucidates an important epistemological difference: science is a method, not knowledge. I learn science when I learn about experimental design. Im not learning science when I learn about evolution; rather Im learning a theory, very likely to be true, that is almost impossible to put under scrutiny using the scientific method.
The Pythagorean theorem has no science and is 100% true. In fluids, Bernoulli devised experiments to demonstrate to his calculus illiterate colleagues what he had already mathematically proven.
Science is a bad term.
Maybe I misunderstood you, but I have the feeling you're downplaying the importance of experiments in Physics. Once you mathematically prove something, you proved that a statement is true when given a certain set of axioms. This is enough in Mathematics, like your example of the Pythagorean theorem, but it isn't in Physics. The reason being that proving something Mathematically consistent isn't enough to prove that it reflects what happens in the real world. A famous example in pop science of this is string theory.
I also have some doubts about what you say regarding evolution theory, but I'm not familiar whit how biologists verified it. Maybe every time a new fossil is found we can consider it as an experiment that can add a data point in favor or against the theory?
Im reading Truesdell's (America's greatest 20th century physicist?) book now where he goes through the history of fluid mechanics and the paucity of experiments. If I remember ill send you the reference
"The computer: ruin of science and threat to mankind”
Bloody brilliant. 70 years ago he foresaw the problems of modern science.
Interestingly enough I just realized in Italian there is an old word, "dotto" that literally would mean "someone who has been taught" but concretely is used in the sense of well educated, knowledgeable, wise, cultured.
Bologna, the home of the first university, has the nickname "la Dotta", i.e. the educated one.
the very definition of a "theory" in the scientific sense of the word (e.g. "theory of evolution") includes the ability to test it using the scientific method.
the wikipedia page goes into great detail: https://en.wikipedia.org/wiki/Scientific_theory
and this is a good brief explanation: https://web.archive.org/web/20170709065046/http://science.ke...
Jumping to specifics, Evolution Theory is relatively easy to demonstrate on short time scales of under a year with fruit flies, and can also be demonstrated on longer timescales of five, ten, thirty years given patience .. with ongoing field observations of some two centuries now in various locations.
And yes, I know about little bugs changing color and bacteria becoming resistant to antibiotics.
But, strictly speaking, that isnt what we're taught is "science" in 10th grade, is it? That's really an observation of what we cannot control fitting nicely into our theories.
The embarrassing thing about evolution is that biologists keep having to tweek it in ways that are bewildering if evolution is (I think better) understood as information theory. For example, why did biologists reject horizontal gene transfer?
Anyway the whole field is sitting atop of an ignored quantity-quality emergent behavior which is also the most interesting question.
PhD is the degree you usually get at that level for English, Classics, Economics, Histrory etc..
Some Universities use DPhil (Oxford) for all these but I know of no other degree at that level except for those two (MD is effectively lower and DSc is usually some form of honourary degree and I am not certain what LLD is)
Most early physic had surprisingly little explanatory or experimental connection to the actual physical world.
But it often made up for that with a solid grounding in popular mythology and the produce of some extraordinary imaginations.
You know, like philosophy!
Anyway, those crazies came up with atomistic theory to explain silly myths.... and ended up explaining phase change as an emergent phenomenon.
The ancients were not just the famous Greek, Roman, Babylonian, Indian and Chinese philosophers, who made progress in reasoning.
Human's across every culture have spun creative explanations for natural phenomena, going back as far as we have any records.
- Why does it rain? How can we make it rain?
- What are the planets? What do their cycles and alignments mean?
- What is an illness? How do we avoid it? Cure it?
Even those philosophers were not immune to this kind of thinking.
Non/Pre-scientific answers to unanswerable questions gave satisfied people’s need for order and gave them hope.
Today, many people still take such answers seriously where there is no science (afterlife, cosmic justice, ...), and even where there is (astrology, crystals, etc.)
This implies philosophy and philosophers will disappear once we know everything, which could by some be considered one of the rewards of this quest for truth.
BTW, many institutions today offer the ScD degree, doctor of science; it is generally equivalent to a PhD, though in some places it can be considered "higher"
The basis of all of these branches of the sciences owe their place to the work done by the early thinkers who established the ways of knowing. It is in the method of knowing that the highest degree in academic sciences is a Doctor of Philosophy. By obtaining the degree you have proven you are capable of establishing "knowing". Which is to say, you can reason.
I find this sentence a very concise phrasing for how I appreciate those with a degree vs. those without. I personally do not have a degree, but I far prefer working with people who do - simply because I can trust that they can reason.
> Which is to say, you can reason.
"Doctor of Philosophy" (PhD): a doctorate in just about any subject except law or medicine.
"Doctor of Letters" (D.Lit.): a doctorate in Law.
"Doctor of Medicine" (D.Med.): a doctorate in medicine.
"Actually, it's not called the Sapir–Whorf hypothesis anymore. The preferred term is 'linguistic relativity' now."
... while you keep using titles that have been nonsensical for 200 years. Got it.
Academia is 99% power games. The emperor wears no clothes.
They also had a language requirement, which was often fulfilled by memorizing the 500 most common words in a foreign language as well as 300-500 common math terms in that language; there was a library of prepared crib sheets for these. It was kind of a running joke in that it tested your ability to translate an article from German/Russian/French into English sufficiently well to explain it to a bored examiner, but most of the students kind of looked it as a kind of giant 'Wheel of Fortune' exercise in intelligently guessing between the revealed clues.
Second, some of the other graduate students basically went insane studying for this -- one locked himself in a room with a 30 day supply of microwavable meals, and another locked himself in his dorm and (having read MicroSerfs) only ate 2 dimensional food slipped under the door. A lot of this was immature students trying to out-do each other in commitment and probably didn't markedly improve pass rates.
Tao matured, but mostly because he got older -- there were finally reasonably smart people his age studying with him. He also used to hang out with John Conway a lot, and Conway was going through his own problems; he spent more time with the 'more conventionally normal' faculty and that probably rubbed off.
10 juniors with year of experience don't make it even close to decade of experience
He clearly should have read Bhargava’s generals, where Andrew Wiles asks Bhargava the same question!
What is Brauer's theorem? [I had no idea and they moved on]
Worst case I've seen of this was when I was in 9th grade and our geometry teacher required us to memorize the chapter and section names of theorems in the book when proving. For example, in our proofs about triangles, we had to write "theorem 12.5" or else we wouldn't get credit on the test, and here 12.5 was the chapter and section number in the particular textbook, which is an utterly useless piece of info.
Of course, the name Brauer is not nearly as useless as a chapter name, but still being familiar with math history probably shouldn't be hard requirement for being a professional mathematician.
Interviewer: what do you know about transactions?
Candidate: Transactions can be serializable.
Interviewer: great, tell me the difference between final state serializability and view state serializability and prove that they are the same if neither of them has dead step.
Candidate: yada yada yada.
Interviewer: Can you tell me how to use such concepts in implementing a production database system? Please come with a few short illustrative examples too.
Not something fun to go through, that's for sure!
As far as I understand, in America graduate student can mean both a M.Sc. student and a Ph.D. student.
Jokes aside, Tao also has a nice write-up in AMS Notices on this experience and how it influenced his career:
> this was the first time I had performed poorly on an exam that I was genuinely interested in performing well in. But it served as an important wake-up call and a turning point in my career. I began to take my classes and studying more seriously. I listened more to my fellow students and other faculty, and I cut back on my gaming. I worked particularly hard on all of the problems that my advisor gave me […] In retrospect, nearly failing the generals was probably the best thing that could have happened to me at the time.
See also https://terrytao.wordpress.com/career-advice/ which among other things links to "Work hard": https://terrytao.wordpress.com/career-advice/work-hard/
TT was 21 when he got his PhD, according to wikipedia.
By tradition, they can ask you anything. But in practice, they're not out to kill you. I went to a second tier university, and it was generally believed that the questions at a top school tended to be harder. I have no recollection of mine.
At this time, you also typically present a proposal for your thesis project. Passage of these hurdles makes you a "candidate," i.e., a candidate for a PhD upon defense of your thesis.
— other names I have heard people use for these: prelims, quals, ...
One of the grad schools I attended had both a written "prelim" in year 1 and an oral "qual" in year 2/3. The other just had an oral "general" in year 2.
It's just faculty ensuring he has enough general knowledge of mathematics
At this point in time he would've been a teenager
(And, as listed on his wikipedia page, 27 other awards, medals, and prizes.)
Funny, because he received the Fields medal 1o years later for "his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory". So either his knowledge wasn't that bad or he is a very quick learner. ;)
Turns on super saiyan mode for the first time
I imagine using chatgpt plus these questions would greatly help a grad student study for their comps.
Great mathematicians are said to be exceptional at visualization. I wonder if the modern greats think in TeX or LaTeX on top of that. It is amazing how fast they post fully-formed, meticulously referenced blog articles or upload preprints.
Looking back I wish I had continued practicing typing after the one class I took in it. I should also have learned shorthand.
And I wrote my PhD in TeX. Not LaTeX ... that hadn't been invented.
But, we were 'appy in them days, though we wuz poor.
Brings to mind when I first learned TOPS-20 Emacs in law school (long story), circa 1980-81: A few of the CS grad students tolerantly looked down on Emacs as a crutch for newbies, because any real programmer would use TECO instead ....
(IIRC, that version of Emacs was written as a collection of TECO macros.)
Obligatory XKCD: https://xkcd.com/378/
I think they mean 4n + 3 unless this is a joke I'm missing
I haven't the foggiest idea of what an "elementary explanation" of anything during a math graduate degree committee assessment would even sound like.
I guess the closest equivalent in programming is "implement X without using any external libraries (or perhaps only the standard library)".
serious question. i only know his name for being smart. not anything specific
I am sure no one has ever ever called him “The Tao of Math” before, but they have now! He is in it. Everywhere!
Legacy Achievement: locked in :)