Category Archives: Genius

Quotes – Ramanujan

Source: WikiQuote, date indeterminate

Paul Erdős has passed on to us Hardy‘s personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100, Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.

  • Bruce C. Berndt in Ramanujan’s Notebooks : Part I (1994), “Introduction”, p. 14

The formulae (1.10) – (1.13) are on a different level and obviously both difficult and deep… (1.10) – (1.12) defeated me completely; I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written by a mathematician of the highest class. They must be true because, if they were not true, no one would have the imagination to invent them.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like Riemann before him.

  • Michio Kaku, Hyperspace : A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), p. 172

The great advances in mathematics have not been made by logic but by creative imagination. The title of mathematician can scarcely be denied to Ramanajan who hardly gave any proofs of the many theorems which he enumerated.

GH Hardy (via Paul Erdos) on Ramanujan

Source: Famous Scientists, date indeterminate

He was told an interesting story by the great Hungarian mathematician Paul Erdős about something G. H. Hardy had once said to him:

“Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100. Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.”

Counterfactual History of Scientific Discoveries

Source: Nautilus, Dec 2016

think about the way science works: how ideas arise out of the context of their time and the contingencies and quirks of individual scientists.

Heliocentrism – Johannes Kepler

There are few great discoveries for which one can’t find precedents, and heliocentrism—the idea that the Earth revolves around the sun and not vice versa—is no exception. It’s such a pivotal concept in the history of science, displacing humanity from the center of what was then considered the universe, that anticipations have been well documented before the German-Polish astronomer Nicolaus Copernicus outlined the theory in his epochal De revolutionibus orbium coelestium, published as he lay on his deathbed in 1543.

Tycho’s protégé and Galileo’s correspondent, the German Johannes Kepler, would have done it first. He had access to Tycho’s excellent observational data, he was mathematically adept, but crucially he also had Copernicus’s dash of (to our eyes) mysticism that saw a sun-centered universe as appropriately harmonious. To dare to put the sun in the middle, you needed not just rational but also aesthetic motives, and that was Kepler all over.

Laws of motion – Christiaan Huygens

A single law of gravitational attraction was all you needed to explain the shapes of planetary and lunar orbits and the trajectories of comets.

All this was laid out in Newton’s Principia, published in 1687 after being instigated to eclipse Hooke’s reckless claim that he could explain the ellipse-shaped planetary orbits. Before he could deal with planets, Newton had to set down his basic laws of motion. The three that he described in Book I are the foundation of classical mechanics. In short: Bodies maintain their state of uniform motion or rest unless forces act on them; force equals mass times acceleration; and for every action there is an equal and opposite reaction.

They are concise, complete, and simply stated, almost heart-breaking in their elegance. Could anyone else have managed that feat in Newton’s day?

at least one genius among the Society’s many continental correspondents who might have risen to the challenge. Dutchman Christiaan Huygens was polymathic even by the
 ample standards of his day: a mathematician, astronomer (he made
 some of the first observations of 
Saturn’s rings), inventor, and expert
 in optics and probability. He was especially good at devising clocks and watches, which occasioned a priority dispute with the irascible Hooke. Huygens’ theorems on mechanics in his book on the pendulum clock in 1673 were taken as a model by Newton for the Principia.

Newton’s first law was scarcely his anyway: Known also as the law of inertia (a moving object keeps moving in the absence of a force), it was essentially stated by Galileo, and Huygens embraced it too. The Dutchman’s studies of collisions hover on the brink of stating the third law, while Huygens actually wrote down a version of the second law independently. He had what it took to initiate what we now call Newtonian mechanics.

Special relativity – James Clerk Maxwell

One reason why it is more than just fun to imagine alternative routes to discovery is that it can help to puncture myths. The story of Einstein imagining his way to special relativity in 1905 by conceptually riding on a light beam captures his playful inventiveness but gives us little sense of his real motives.

awarding that realization to a man who was dead in 1905, namely Maxwell himself. He died in 1879 aged just 48, and was very much active until the end. He had the kind of deep intuition in physics that was needed for the remarkable feat of adding electricity to magnetism and producing light. Given two more decades (and the seeds of doubt sown about the ether) I suspect he would have figured it out. You don’t need to take my word for it: Einstein said it himself. “I stand not on the shoulders of Newton,” he said, “but on the shoulders of Maxwell.”

General relativity – Hermann Minkowski

In 1916 Einstein unveiled a new view of gravity, which superseded the theory of Isaac Newton that had reigned for over two centuries. He argued that the force we call gravity arises from the curvature of space and time (the four-dimensional fabric called spacetime) in the presence of mass. This curvature causes the acceleration of bodies in a gravitational field: the steady speeding up of an object falling to Earth from a great height, say. This was the theory of general relativity, which is still the best theory of gravitation that exists today and explains the orbits of the planets, the collapse of stars into black holes, and the expansion of the universe. It is Einstein’s most remarkable and revered work.

Permit me again to bend the rules of the game here—for once more, Einstein might have been beaten to it if another scientist had not died first.

In 1908 Minkowski explained that the proper way to understand Einstein’s theory of special relativity—which was all about bodies moving at constant speeds, not accelerating—was in terms of a four-dimensional spacetime. Einstein was at first skeptical, but he later drew on the concept to formulate general relativity.

Minkowski was already alert to the implications, however. Crucially, he saw that whereas the path of an object moving at a constant speed in spacetime is a straight line, that of an accelerating object is curved. In three-dimensional space, the path of the moon orbiting the earth under the influence of their gravitational attraction is more or less circular. But the four-dimensional worldline of the orbiting moon is a kind of helix: It goes round and round in space, but returns to the same position in space at a different time.

There’s more to general relativity than that. It is mass itself, Einstein said, that deforms spacetime into this curving, so-called non-Euclidean (not flat) shape. But the idea of a non-Euclidean spacetime was Minkowski’s, and it’s quite conceivable that he would have fleshed out the idea into a full-blown gravitational theory, perhaps working together with the formidable mathematician David Hilbert at the University of Göttingen, where Minkwoski was based starting from 1902.

We do know, from a lecture Minkowski gave at Göttingen in 1907, that he was already thinking about gravitation in the context of relativity and spacetime. But we’ll never know how far he would have taken that, had he not died suddenly at the start of 1909, aged just 44.

Structure of DNA – Rosalind Franklin

I’d love to think that Rosalind Franklin, the English crystallographer whose data were central to the discovery of the double-helical structure of DNA, would have figured it out if James Watson and Francis Crick hadn’t done so first in 1953. It was famously only when Watson saw the pattern of X-rays scattered from DNA and recorded by Franklin and student Raymond Gosling that he became convinced about the double helix. He was shown these data by Maurice Wilkins, with whom Franklin had a prickly working relationship at King’s College London—and Wilkins did not have Franklin’s permission for that, although any impropriety has been overplayed in accounts that make Franklin the wronged heroine. In any event, those data triggered Watson and Crick’s deduction that DNA is a helix of two strands zipped together via weak chemical bonds between the gene-encoding bases spaced regularly along the backbones.

I was worried, though, that Franklin—cautious, careful and conservative by instinct in contrast to the brilliant, intuitive Crick and the brash young Watson—wouldn’t have stuck her neck out on the basis of what by today’s standards is rather flimsy evidence. She knew that a female scientist in those days couldn’t afford to make mistakes.

So I was delighted when Matthew Cobb, a zoologist at the University of Manchester who delved deeply into the DNA story for his 2015 book Life’s Greatest Secret, confidently told me that, yes, Franklin would have done it. “The progress she made on her own, increasingly isolated and without the benefit of anyone to exchange ideas with, was simply remarkable,” Cobb wrote in The Guardian. Just weeks before Watson and Crick invited Franklin and Wilkins to see their model of DNA in March 1953, Franklin’s notebooks—studied in detail by British biochemist Aaron Klug, who won a Nobel Prize for his own work on DNA—show that she had realized DNA has a double-helix structure and that the two strands have complementary chemical structures, enabling one to act as a template for replication of the other in the way Watson and Crick famously alluded to in their discovery paper in Nature that April.

“Crick and I have discussed this several times,” wrote Klug in the Journal of Molecular Biology. “We agree she would have solved the structure, but the results would have come out gradually, not as a thunderbolt, in a short paper in Nature.” At any rate, her contributions to the discovery are undeniable. “It is clear that, had Franklin lived, the Nobel Prize committee ought to have awarded her a Nobel Prize, too,” writes Cobb.

The other contender for the discovery is American chemist Linus Pauling, who was the Cambridge duo’s most feared rival. Pauling had impetuously proposed a triple-helical structure of DNA in early 1953 with the backbones on the inside and the bases facing out. It made no chemical sense, as Watson and Crick quickly appreciated to their great relief. Unperturbed by such gaffes, Pauling would have bounced back. But he didn’t have Franklin’s X-ray data. “Pauling was a man with great insight, but not a magician who could manage without data,” wrote Klug.

Natural selection – ?

Sometimes discoveries or breakthrough ideas occur to different individuals more or less simultaneously. It happened with calculus (Leibniz and Newton), with the chemical element oxygen (Scheele, Priestley, and Lavoisier), and most famously, with evolution by natural selection, announced in 1858 by Charles Darwin and Alfred Russel Wallace.

That tells us something about this entire counterfactual enterprise. Science provides us with theories that are objectively useful in explaining and predicting what we see in the world. But that doesn’t deny the fact that specific theories generally have a particular style in terms of what they express or stress, or of what metaphors they use:

quantum electrodynamics could have been constructed without using the celebrated language of Feynman diagrams devised by Richard Feynman. It seems entirely possible that the way we conceptualize the world bears the imprint of those who first proposed the concepts. Scientists may be less replaceable than we think.

Freeman Dyson on Richard Feynman

Source: Nautilus, Dec 2016

What made Feynman different from other scientists?

He was extremely original. He had his own way of doing science, which was different from everybody else. That’s why he had a hard time communicating. He never wrote down equations. Most people in physics write down an equation and then find the solutions, but that wasn’t the way Feynman did it. Feynman would just write down the solutions without ever writing the equations. It seemed like a sort of magic because he thought in terms of pictures instead of equations. He had these little pictures in his head and he scribbled little pictures on paper and nobody understood what they meant. My job was to translate Feynman into language other people could understand.

Do you need to be willing to risk your reputation and pursue crazy ideas? Is that what leads to great breakthroughs?

First of all, it helps to be ignorant. The time when I did my best work was when I was most ignorant. Knowing too much is a great handicap. Especially if you’ve been teaching for some years, things get so fixed in your mind and it’s impossible to think outside the box. I was in the lucky position of jumping into physics without ever having taken any courses in physics. I’d only been a pure mathematician up to that point.

Is the great scientist also naturally subversive?

Yes, undoubtedly. You’ve got to destroy what exists in order to build something new. You need good taste, of course. If you destroy indiscriminately, it doesn’t help at all. That’s where intuition comes in—what parts of the old building should be taken down.

Great Voices from the Past

Alexander Graham Bell:  Hear My Voice.  Alexander Graham Bell: 

another source:

Albert Einstein:


Feynman anecdotes

Source:, date indeterminate

Feynman on Hawking

Several conversations that Feynman and I had involved the remarkable abilities of other physicists. In one of these conversations, I remarked to Feynman that I was impressed by Steven Hawking’s ability to do path integration in his head. Ahh, that’s not so great, Feynman replied. It’s much more interesting to come up with the technique like I did, rather than to be able to do the mechanics in your head. Feynman wasn’t being immodest, he was quite right. The true secret to genius is in creativity, not in technical mechanics.

Damn it, Murray, you’re right again …

This took place just after the publication of Surely You’re Joking, Mr. Feynman. We were all sitting together at lunch talking about the success of the book, when one of the other graduate students remarked that they had not seen Murray Gell-Mann lately. I thought he had gone and started writing his own book of anecdotes. The other student remarked, Yeah, and I know what he is going to call it too, ‘Damn it Murray, You’re right again!’ At this remark, Feynman lost it, and slid under the table laughing.

Feynman Van

Feynman and I would sometimes go camping together. On these occasions he would drive his van, which had Feynman diagrams painted all over it and a license plate that said Quantum. (Murray Gell-Mann had a license plate that said Quarks.) I asked Feynman if anyone ever recognized the diagrams. Yes. Once we were driving in the midwest and we pulled into a McDonald’s. Someone came up to me and asked me why I have Feynman diagrams all over my van. I replied, ‘Because I AM Feynman! The young man went “Ahhhhh…..

Related Resources:

The Atlantic, Jul 2000

Though Feynman was essentially a loner, Gell-Mann loved the camaraderie of collaboration. And he was terrified of heading solo into the void with an idea that might turn out to be wrong. He and Feynman had been trying to understand a problem involving neutrinos, the evanescent particles that fly through planets almost as easily as through empty space. The puzzle could be explained, they surmised, if there were actually two kinds of neutrinos (they called them red and blue). Gell-Mann wanted to write up the idea, but when Feynman resisted, he didn’t have the nerve to go it alone. The theory, with others’ names on it, later turned out to be correct, and Gell-Mann added Feynman’s obstinacy to his lengthening list of grievances.

Symmetry Magazine, May 2014

“The game I play is a very interesting one,” says Nobel Laureate Richard Feynman in a low-resolution video posted to YouTube. “It’s imagination in a tight straitjacket.”


A Trillion-Dollar Enterprise Requires Major Scientific Advances

Source: The New Yorker, Oct 2016

Altman wanted to create a trillion-dollar conglomerate and to move the world forward. “you couldn’t have a trillion-dollar enterprise without major scientific advances.”

Altman said, “hard things are actually easier than easy things. Because people feel it’s interesting, they want to help. Another mobile app? You get an eye roll. A rocket company? Everyone wants to go to space.”

Altman recognized, he told me, that “there’s absolutely no reason to believe that in about thirteen years we won’t have hardware capable of replicating my brain. Yes, certain things still feel particularly human—creativity, flashes of inspiration from nowhere, the ability to feel happy and sad at the same time—but computers will have their own desires and goal systems. When I realized that intelligence can be simulated, I let the idea of our uniqueness go, and it wasn’t as traumatic as I thought.” He stared off. “There are certain advantages to being a machine. We humans are limited by our input-output rate—we learn only two bits a second, so a ton is lost.

Altman believes that a true general A.I. should do more than deceive; it should create, discovering a property of quantum physics or devising a new art form simply to gratify its own itch to know and to make.

Sam’s program for the world is anchored by ideas, not people,” Peter Thiel said. “And that’s what makes it powerful—because it doesn’t immediately get derailed by questions of popularity.”

I’m on Team Human. I don’t have a good logical reason why I’m sad, except that the class of things that humans are better at continues to narrow.” After a moment, he added, “ ‘Melancholy’ is a better word than ‘sad.’ ”

The merge has begun—and a merge is our best scenario. Any version without a merge will have conflict: we enslave the A.I. or it enslaves us. The full-on-crazy version of the merge is we get our brains uploaded into the cloud. I’d love that,” he said. “We need to level up humans, because our descendants will either conquer the galaxy or extinguish consciousness in the universe forever. What a time to be alive!”

He is thinking about establishing a group to prepare for our eventual successor, whether it be an A.I. or an enhanced version of Homo sapiens. The idea would be to assemble thinkers in robotics, cybernetics, quantum computing, A.I., synthetic biology, genomics, and space travel, as well as philosophers, to discuss the technology and the ethics of human replacement.

In the best case, tech will be so transformative that Altman won’t have to choose between the few and the many. When A.I. reshapes the economy, he told me, “we’re going to have unlimited wealth and a huge amount of job displacement, so basic income really makes sense. Plus, the stipend will free up that one person in a million who can create the next Apple.”

“The missing circuit in my brain, the circuit that would make me care what people think about me, is a real gift. Most people want to be accepted, so they won’t take risks that could make them look crazy—which actually makes them wildly miscalculate risk.