Originally published at 狗和留美者不得入内. You can comment here or there.

To Dr. Scott Locklin,

I’ve learned a fair bit and been inspired much by your writings, in particulars your writings on the history of science and technology. You are few to note the obvious, that since 1960, aside from microelectronics, there have not really been major or revolutionary advancements. Something else that I am very curious about your thoughts on is the matter of Isaac Newton and the relationship of his works with those of Robert Hooke, Leibniz, Huygens.

This American mathematical physicist thinks Newton was the smartest person who ever lived. I read in detail his Wikipedia page and that of Huygens, Hooke, and Leibniz, and I am somewhat inclined to believe that Newton was a nasty person inclined to take credit for the works of others. However, that American mathematical physicist insists that Newton was a league above the rest, even though I might be inclined to suspect that his greatest achievements were ones of explanation in the form of synthesis, which is of course extremely important, but really can only be done once the bits and pieces are already discovered to some degree. That guy thinks that Robert Hooke was mediocre, lacked vision, and how even as a experimentalist, he could not compare with Faraday.

I am inclined to believe that Newton is overrated much because Leibniz created visibly better notation and also came with up with mv^2 as vis viva instead of mv. Moreover, after Newton, English mathematics was visibly a notch lower than mathematics in continental Europe, and one might argue the same to a lesser extent for physics as well, though of course for physics, you had Faraday and Maxwell.

As for calculus, there were lots of hints in terms of concrete examples by John Wallis, James Gregory, Isaac Barrow, and Newton had certainly read Fermat’s work wherein he set the derivative to zero to find local minima/maxima.

All in all, it seems like Isaac Newton’s genius was mostly one of theoretical synthesis and proof. Robert Hooke on the other hand was more of an inventor. Calculus aside, the biggest mathematical achievement I know of Newton is the generalized binomial theorem and power series, in particular reversion of term. It is clear that Isaac Newton was more of a theoretical thinker. As for invention, I don’t know of anything else other than his vastly improved reflecting telescope. Though I know pretty much nothing in detail about those devices, I feel like Huygens was a more significant inventor than Newton, with the pendulum clock’s being much more impactful than Newton’s improvement of the telescope.

I read that Bertrand Russell claimed that what the Islamic world did was mostly preservation of Greek texts as opposed to innovation, but I think in that statement, Russell is full of Eurocentric hubris. The Islamic world advanced pretty far in trigonometry, with law of sines, law of cosines, and trigonometric tables to like 8 decimal places for each degree, not to mention algebra and decimal system (which were first seen in the form of Chinese counting rod arithmetic, with algorithms elaborated in Sunzi Suanjing around 400 AD). In the 13th century, many works were translated after all, and not all of them were ancient Greek texts preserved by the Muslim world. You have Alhazen, Al-Biruni, Al-Khwarizmi, etc. Copernicus was not the first write on heliocentrism; the Muslim scholars had already done so in similar ways, and the Indian Aryabhata in like 5th century already proposed the earth spinning on its axis.

That American mathematical physicist’s argument was simply that Newton was too ahead of his time, too smart, and there was nothing he was not capable of doing himself, but he was often too lazy to write stuff up to explain to the dumb dumbs who he was contemptuous of.

My view is the progression of science seldom starts from a general theory based on first principles. Instead, people solve some isolated problems and concrete example to hint at the general theory. It was the case with calculus. There were lots of hints, with the areas under curves of x^p already figured out in 1630s, setting derivative to zero to find local minima/maxima without an explicit concept of derivative.

I especially disagree with that mathematical physicist I talked with on his view that the continental Europeans by themselves would’ve have done what Newton had done a few decades later. He even said that the British got a major head start because of Newton, but I think it’s apparent that math and physics, especially the former, after Newton advanced more in continental Europe than in Britain. It seems Isaac Newton was too “anti-social” and not all that great of a communicator or cultivator of students who would become top scientists too.

That guy goes on about how even Gauss was intimidated by Newton, and I’ve noticed that both Newton and Gauss were reluctant to publish stuff that they didn’t regard as perfect. Moreover, it is well known that Gauss liked to hide the intuition of his proofs. That guy also said something along the lines of how Isaac Newton was so smart that he didn’t even need good notation to do world class math, and that Leibniz’s understanding of calculus was significantly lesser than that of Newton.

I certainly think that the ability for deep understanding and theoretical synthesis that Newton was genius at is extremely important. However, it is not everything, and especially in Newton’s era, what was more lacking was in some sense advancement, cost-reduction, and proliferation in technology and experimental apparatus. The big game changer that enabled the West to develop modern science in my opinion was actually Gutenberg’s printing press. While some Chinese and Koreans like to say that they invented movable type and metal movable type centuries before, with the first metal movable type book printed in Korea, in effect it doesn’t mean all that much because the logographic writing made it too expensive to scale and proliferate. It was a major reason why Chinese mathematical texts in 13th century with decimal arithmetic, numerical methods for solving polynomials, and solutions of equations for geometric problems were forgotten after a dynasty change, with such research only to be resumed by the Japanese in the 17th and 18th century when they discovered determinants, Bernoulli numbers, series for sin and arcsin, and eventually also definite integrals of polynomials.

Notation is honestly for practical purposes quite important. I read today that the British mathematicians only adopted Leibniz notation around 1820. Sure, a brilliant person can totally get by with worse and cumbersome or inconsistent or redundant notation, but it surely would require more time and cost, sometimes much much more. That Japan and Korea exceeded China in many ways also has to do with their invention of alphabets (Japan before 1000 AD, Korea in 15th century), which made learning, writing, and printing much more efficient.

Again, in those days, the bottleneck, especially in the West, was more material and one of technology. Even then with the printing press, printing and books were not all that cheap, and dissemination of knowledge was still somewhat slow, which only makes communication more important. I say this also because the West already had Euclid’s Elements firmly established within the elite education system. I would also believe that the ideas within Euclid’s Elements were actually initially spun off the need to solve practical problems. I do not think that thinking axiomatically is natural to humans; it has to be developed over a period of time given certain circumstances. The mathematics in the East was algorithmic, computational, and not axiomatic for this reason, and also for the reason that before paper was invented in the 1st or 2nd century I believe, the Chinese could only write on bamboo strips tied together, to which extremely compact hieroglyphs were in some sense more suited, whereas papyrus had been invented in Egypt over 4000 years ago. Once you have these material problems solved, with some aristocrats with free time and curiosity about mathematics, the production of some theoretical geniuses is not all that difficult in my opinion.

I recall you’ve written how it would have been ridiculous to try to build airplanes after Bernoulli’s principle was discovered, with reference to the analogy of quantum computing. This is like how though Vikings explored and had some settlements in North America in like 11th century, it didn’t make much difference because at that time, the economic and social circumstances were not ripe for settlement and colonization at scale. Simply said, some of the more mundane and less sexy stuff has to be achieved before one can deliver the more spectacular results. An important theoretical result in science also takes some time to disseminate and be accepted. Heck, after the Romans took over, it took quite a while before the Greek texts were translated to Latin. Back in those days, the lack of printing meant the fall of a dynasty or empire would mean loss of transmission of knowledge and a consequent backwards step that would take some time to recover. One can imagine even that if not for conquest by the Mongols that caused much destruction, the Muslim world would have gotten the results of Galileo, Kepler, Newton earlier provided that they also invented non water powered mechanical clocks.