Mathematical View.

An extremely interesting comment of professional Swiss (I believe) mathematician Paul Schmutz Schaller on my two books at Saker's blog. Paul starts with this intro: 

In some sense, this article is a comment on some aspects of Andrei Martyanov’s two books „Losing Military Supremacy: the Myopia of American Strategic Planning“ (2018) and „The (Real) Revolution in Military Affairs“ (2019). I am not aiming at discussing these excellent books...My interest here is the content of these books which is related to mathematics. In this regard, here is a try to condense some of Martyanov’s writing into simple theses:

1) The power of a nation very much depends on its military strength.

2) Military strength is a complex thing, depending on the strength of the whole society: its economy, its culture, its scientific level, its historical experiences.

3) Mathematics are crucial for the military strength, not only for the production of sophisticated weapons and military technology, but also for strategic planning and for warfare.

4) Western societies in general and the USA in particular suffer from a lack of education in mathematics and this is an important reason for their decline.

5) Without understanding mathematics in relation to military, one cannot understand military strength, nor geopolitical developments.

I agree with Paul's distillation, so to speak, of what I am writing about.  But Paul disagrees with me on the 5th point and, I agree, it is at least a debatable one--in a sense of being worthy of a separate discussion. But it is what Paul writes after this which is of a particular and great interest. He makes some extremely important observations, while giving a short retrospective of mathematics development throughout human history: 

Mathematics in the West are declining. This is may-be not yet visible when regarding some top Western universities; they still are quite attractive for mathematicians from other countries due to their prestige and their money. The decline concerns above all the Western societies as a whole. They have become quite hostile towards mathematics. Increasingly, mathematics are just seen as a necessary evil. Typically, in the film „Salt“ (USA, 2010), starring Angelina Jolie, the latter says: „I hate math.“ Could you imagine this in a Chinese, Iranian, Indian, or Russian film?

And Paul observes shift of mathematics to Asia. I agree--this, indeed, is taking place. Very little doubt that mathematics made the West, with Western society exploding with mathematics genius in the last few centuries, with the West, later, changing the whole world, but today balance changes. Oswald Spengler's famous The Decline of The West  takes a very close look at the mathematical thinking of civilizations and, in the words of one academic observer, defines Spengler's claim in the next words:

that similarities may be discerned in the style of mathematics, art and music developed by a particular High Culture – looking first at his discussions of the Ancient Greeks and how their thought-processes differed from that of Western Europeans,as well as from the Persians and Arabs. An attempt is then made to extend Spengler's theory to the Ancient Egyptians (referring to their Rhind Papyrus)and to the Sino-Japanese (by appealing to their 'Sangaku' mathematical art-forms). Finally, it is suggested that we may already be able to identify certain distinctive features and characteristics of the recently born Russian Culture.

Speaking of Russia. Already in Spengler's times (and that is almost a century ago), some feature of Russian high culture started to emerge, as David L. McNaughton continues, and I quote him in full:

Spengler (1922, pp. 192-196, and 1934) believes that a new High Culture has recently crystallized in Russia. He even attempted to discern and analyse the nature and character of its 'soul'. For example, he maintained that the Russian death-impulse "is an expressing and expanding of self (Sichentäussern) till 'it' in the man becomes identical with the boundless plain itself... That 'All are responsible for all' ... is the metaphysical fundament of all Dostoyevski's creation. Mystical Russian love is the love of brothers under equal pressure all along the earth., ever along and along" (Spengler, 1922, p.295 note 1). Spengler may not be completely correct in asserting that the 'prime symbol' of the new Russian Culture is the infinite plain. If so, he can perhaps be forgiven – because he made that assessment one hundred years ago. But if he is right that another 'Cultural organism' has indeed been born, then new discoveries and developments in mathematics, art and music will blossom there. On that assumption, can we try and guess what sort of mathematics might emerge?Without doubt, Russian mathematicians have already made prominent contributions in that field. In particular, Grigori Perelman should be highlighted for demonstrating the truth of the Poincaré Conjecture. In 2006, the world-renowned journal “Science” recognized his achievement as the scientific ‘Breakthrough of the Year’ – the first time such a tribute had ever been accorded in mathematics (Mackenzie, 2006). For his work, Perelman was also awarded the highly prestigious Fields Medal – but refused it. After interviewing him, John Ball (outgoing president of the International Mathematical Union) remarked: "He has a different psychological make-up, which causes him to see life differently" (BBC News, 2006). Earlier, Perelman had confirmed the Soul Conjecture with (what Wikipedia describes as) "an astonishingly concise proof". His two discoveries are important insights and landmarks in the development of mathematical topology (which may be defined as the study of spaces and their connectivity). So perhaps the new Russian mathematics will specialise in this topic? For example, eventually it might produce a comparatively simple proof of the Four Colour Theorem (explained by Appel and Haken, 1977). If the Spenglerian 'timetable' is correct, Russian art, music and mathematics will attain their zenith (after a few more centuries) during what he calls their 'summertime' – so it is probably too soon to know how exactly they will manifest themselves. Despite that, it is worth asking whether the Russian ability and love for the game of Chess is evidence that a new cultural soul is unfolding in that landscape. Each piece on the chessboard commands or controls only certain squares, i.e. a 'subspace' of the whole. And game-strategy assesses how the power or potential of each piece can best coordinate and interact with the others. In a different field, there might be grounds for arguing that it was no coincidence that the Periodic Table of the Elements was first conceived in a Russian mind – that of Dmitri Mendeleyev – rather than a Western one.

It is a very loaded but not incorrect conclusion. The article by McNaughton was written in 2016. You all know what happened in March, 2018. Since then, this is what has been dictating the logic of geopolitical shift on unprecedented scale and what is effectively keeps the world from sinking into one huge global conflict. Math had everything to do with it, math and physics, with physics being, in effect, a mathematical description of the natural world. Does math define a high culture? Absolutely: music is very mathematical, so is architecture and, of course, so is technology. But that is my main point--only nations with high culture can produce what Russia produces today. Far from military technology alone, breakthroughs in such field as aerospace, nuclear energy, new types of propulsion, new materials, among many, have already happened or are about to happen. This happened because of the way the world is viewed by Russians--in a very mathematical way. In the end, Russia awards degrees in Military Science which is same higher math projected at the stochastic world of the warfare.     

As Paul Schaller concludes:

Coming back to the question of the power of a nation, we have to refine. This power is not only related to the present level of mathematics, but also to the attitude with respect to mathematics. In this regard, two items are obvious for everybody. First: The Western empire(s) are fading away. Second: Asia in general and East Asia in particular have already a huge advantage over Western countries.  

Difficult to disagree: both in Russia and China mathematics is a secular religion of sorts, because there is clear understanding that mathematics and future are inseparable. Empirical evidence supporting this is overwhelming. But I wrote on this issue not for once myself, it is pleasant to read similar thoughts from a professional mathematician. 

In other news, meanwhile, Russian government is buying back all shares held by Russia's Central bank in Russia's main consumer bank SberBank (in Russian). Do you smell that smell(c)? Ahh, poor-poor dear German Gref, the CEO of SberBank, the boy always complained that Russia is a nation-downshifter  and, in general, is very backward. Well, I am sure Gref's "expertise" will be in demand among people attending Davos forums. But as Russian government stated--Russia's Central Bank having shares of SberBank is a, and I quote, conflict of interests. Take this news any way you want, but paraphrasing Mr. Samuel Clemens (aka Mark Twain)--the reports of death of Russia's financial sovereignty have been greatly exaggerated.