Betty Shannon, Unsung Mathematical Genius

I have seen quite a few cases where people with PhD degree in physics or mathematics went to Wall Street and became traders there and totally gave up their original pursuit of physics or mathematics...

also it is not a small number of people who would choose to pursue an academic career not because their research interests them but because it brings them fame and admiration, as well as stability in life -- as once they obtain their tenure, they would go start companies and pursue profits, instead of discovery...

I am not saying that there are not many people still hold their academic ideals pure and high...It is just that in this era when academic positions are highly respected, admired and well-paid, it might give people the incentive to pursue such a career not for its original purpose but for something else....And one of the very reasons why these days academic positions are highly respected, admired and well-paid was because those scientific and engineering giants in those old days had made really prominent and conspicuous contributions that made this world a significantly better place than it was a century ago -- and if we trace further to the reason why they chose science and engineering as their career in the first place and then made great contributions afterwards, it seems that in many cases it was not because science and engineering could bring them material profits, but rather they were genuinely interested and intrigued; and it was extremely fun to them...

But of course, it is a very difficult to say whether there is such a general decline in our pursuit for knowledge in general (such measurement is hard!)...not to mention the complexity in the essence behind some of the declining factors and drives...

Nevertheless, I wish that at the time when I am old and feeble, as I look back at those days in our time, I could say to myself, just as Odysseus might have said to himself, that I have lived in an age of many great ideals and many great heroes...Yet still, I feel that we should be warned that after the heroic Mycenaean period[1] ended, what immediately followed was several hundreds of years of darkness in the ancient Greek civilization[2]...

Note:

[1] https://en.wikipedia.org/wiki/Mycenaean_Greece

[2] https://en.wikipedia.org/wiki/Greek_Dark_Ages

I am not complaining about the giants are dead; I am complaining that the spirit of pursuing something truly great in academia seems to be fading out -- but of course, different people are most likely to see the world differently. Perhaps you still can enjoy that great atmosphere of pursuing truth rather than profits, which I feel really really glad to see and it helps me to restore some faith...It is just that perhaps these days I have seen a lot of dark lunatic side of academia that makes me feel pessimistic...

Sorry...no offense to other fields...actually, I myself really don't think there is a definite separation in many fields that are administratively regarded as different...I personally feel that essentially they are all languages, using their different description systems to rationally describe the world as it is observed by them and then to make predictions...

most of my study background has been in computer science -- although I really do not think there are much difference that makes it so distinguishable from math or physics...and actually, sometimes I could not tell the difference between math and physics...I feel they are merely terms (or identifiers) used to refer certain things; and as I already mentioned that quite often we do not need to manually put boundaries on those certain things, the differentiability of the different terms then does not really matter here...

and if you like, we could call it study (or X) in general,or any other name would do, as long as it does not generate too much ambiguity...

> I would place Brouwer ahead of Hilbert, and I wonder how one can speak of Turing and Gödel but not of Church and Russell.

Yes, I was thinking of Church and Russell (and I really enjoy his non-math writing too) while I was writing those words...but then I felt that I would have to trace back to Georg Cantor -- and then I realized that I just need a few examples to make my points, instead of enumerating all the smart guys that I heard about (and many I even haven't heard about due to my insularity as human)...so I have to find a place to take a break...

> Did not know about about the age of the 25-page PhD thesis containing only 2 references (a slight exaggeration?) though. That is indeed a loss.

I did not know that either...I was looking for a 3-page PhD thesis, but did not find one (-- and also did not want to spend too much time on that)...then I came across John Nash's thesis -- so the act of ranting and complaining turned out to be a good learning experience as well...

There's two things you mentioned I want to touch/speculate on. The first is the idea that there's a loss or shame in the dearth of new papers with few references. I think this is a function of the growth of disciplines: as the network adds neighbouring nodes, it becomes increasingly important to make your usage of terms and suppositions continuous with the rest of the relevant field. This way you avoid saying something important only to talk 'past' the readers. Where it does become a problem is in 'referentialism': the notion that what is being pulled out from a concept can only be described in the original terminology or via quotations. It's a serious problem in the humanities, but not exclusive to it. Ideas really are multiply realizable -- that's the beauty and creativity of analogies. I have a pet theory that this is a tension implicit in paradigm shifts, but one that isn't focused on enough in the process of academic 'meta-cognition'. My guess is that when it comes to 'standing on the shoulders of giants', it's all too tempting to marvel at the giants themselves than look to the expanded horizon. Perhaps that relates to the other posters' point about the Mycenaean age.

When it comes to Romer's paper, though I haven't yet read it all, I think there's an analogy in 'compsci-ness'. I suspect his observations work just as well with other epistemological (knowledge-kind) combinations and their tensions. It seems that what both highly abstracted fields do so well is further what we can do with the perceived objects and kinds in the world and how they relate. This kind of advancement seems it should improve our critical methods, and how we pin down the qualitative questions -- but it seems we are hard-coded to prioritise arrangement, not inspection. Perhaps it's that there is just too much for the potential Socrates archetypes to effectively 'Socratise', or perhaps they've been swallowed by Python.

But, may Betty rest in peace...(she passed away this past May)...

It seems that one implicit assumption made in your question is that there exists such "giant" today...

Well, then that would depend on how you define "giant"...If we consider Isaac Newton as a giant, then perhaps one good description that illustrates his distinction is these two lines written by Alexander Pope:

  NATURE and Nature’s Laws lay hid in Night:
  God said, “Let Newton be!” and all was light.

Due to my ignorance, I don't think that in our time I could identify any living person who has advanced our knowledge as significant as Isaac Newton or other of those "giants" ( -- I just borrowed this term from Newton in my initial post...) -- I am not commenting on the aspect of human well-being, and I am only ranting about our knowledge...but as I am too ignorant, perhaps only with hindsight I could see better...

But still unless proved otherwise, there is a possibility there isn't (or won't be) any living giant in our time...This happened a few times in human history. For instance, 3000 years ago, after Mycenaean civilization ended, the Greek civilization seems to be moving into a state of falling back (which was a period that we refer as Greek Dark Ages): the practice of writing had ceased (i.e. linear B system), and even been forgotten in many places; their buildings were modest, and decorative art unimpressive -- even their favorite pottery was generally painted with less complex patterns ( -- perhaps it's not avant garde intentionally, as in our modern taste) ...bards and poets after the this dark period would only remember the heroes and giants in the Trojan war which happened in the Mycenaean age that preceded the dark age...

Nevertheless, the Greek Dark Age would eventually end, like all other historical periods...but I just feel sad for those people living in the dark days, although they might very likely not share this similar empathy for themselves (or they might factually have lived a very happy life)...

I try to imagine how Einstein got famous. Even now hardly anybody, relatively speaking, understands that stuff. A good story, I guess: a lowly patent clerk changes our conception of space and time. Also entwined in the war - opposition to Germany, pro Zionism, the bomb - patriotism and propaganda. Our hero.

Feynman has a story that sells. Plays bongo drums, picks locks in a top-secret environment. Excellent at explaining things.

Nowadays, who invented CRISPR? They were Chinese. Is that a good story to tell? Maybe not to a western audience. Fusion, worked on by many many people, might be solved by AI. Will the AI become famous? Maybe the giants now are corporations: Facebook, Google, Apple, Microsoft.