A list of Eureka or other related illumination moments

A list of Eureka and other discovery moments


Below is a list of ‘Eureka!’ or ‘Ah ha!’ moments that mark the illumination step leading to a breakthrough discovery by the savant. They often reveal the crossing of a logical gap with a sudden change of vision. Eureka story can either be a careful recollection of a key moment in the road toward a discovery or (more often) an imaginary recollection mystifying the discovery. Whatever their link with reality, they are part of the mythology of science putting on stage the scientist rather than his science with a strong impact on the public. They participated to the idealization of scientists viewed as a pure and self-absorbed individual driven by his passion and far from the bass struggle for power. I have speculated that these Eureka reflects the ‘self-serving bias’ dimension associated with the narcissism of the scientist (Lemaitre 2016). Indeed, these discovery moments obey to a certain logic: i) they first take place at an unexpected moment revealing the obsessive nature of the discoverer, ii) they do not acknowledge any filiation with other scientists, and iii)  are far from the bench. To my knowledge, they affect mostly male scientists. At the opposite, we could mention the impostor syndrom, that affect scientists that acknowledge too much the role of the community when relating their contribution (and are likely closer to the truth).   Below is a list a short Eureka texts with references as well as few comments on the reality of the discovery. If you are aware of any other Eureka moments, please send me the information

Archimedes “Eureka” in the bath: the father of all the Eureka (about 230-260 BC)

« The exclamation ‘Eureka!’ is famously attributed to the ancient Greek scholar Archimedes. He reportedly proclaimed “Eureka! Eureka!” (i.e. twice) after he had stepped into a bath and noticed that the water level rose whereupon he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. He then realized that the volume of irregular objects could be measured with precision, a previously intractable problem. He is said to have been so eager to share his discovery that he leapt out of his bathtub and ran through the streets of Syracuse naked. Archimedes’ insight led to the solution of a problem posed by Hiero of Syracuse, on how to assess the purity of an irregular golden votive crown; he had given his goldsmith the pure gold to be used, and correctly suspected he had been cheated, by the goldsmith removing gold and adding the same weight of silver. Equipment for weighing objects already existed, and now that Archimedes could also measure volume, their ratio would give the object’s density, an important indicator of purity ».(Source Wikipedia 2015).

Comments: Written more than two centuries after it supposedly took place, there is a consensus among experts to assume that this eureka is a legend. The first trace of the story appeared in a book entitled “De architectura” from the roman civil engineer Vitruvius. According to Mireille Courrent, the infatuation for Archimedes originates from the Romans and notably Cicerone, who was involved in the transfer of Greek knowledge to Romans. This Eureka suggested that Greek philosophers in contrast to Romans were not just interested by useful and concrete applications but were driven by a pure passion for truth. Plutarch will continue the idealization of Archimedes viewed as a man grasping long-lasting truths that are difficult to grasp by the lay public. Three other quotes of Archimedes are also well-known, contributing to his myth: «Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.»; «The shortest distance between two points is a straight line»; “Do not disturb my circles”

Source: Courrent M., Eurêka, eurêka. Archimède et la naissance de la mythologie de la science. Pallas, 2008 pp 169-183

Newtown Apple fall (about 230-260 BC)

«It was 1666, and the plague had closed many public buildings and meetings. Newton had to abandon Cambridge for Woolsthorpe Manor, near Grantham in Lincolnshire, the modest house where he was born, to contemplate the stellar problems he had been pursuing at the university. He was particularly obsessed by the orbit of the Moon around the Earth, and eventually reasoned that the influence of gravity must extend over vast distances. After seeing how apples always fall straight to the ground, he spent several years working on the mathematics showing that the force of gravity decreased as the inverse square of the distance.» (Source: Steve Connor. The Independent 2010).

Comments: It is the second most famous Eureka. In an article in the Independent, Steve Connor relates that Newton  left no written text suggesting this, although there are documents suggesting that he had spoken to others about it when he was an old man, much later after the discovery. One of them is William Stukeley, who also wrote the first biography of Newton. Stukeley spent some time discussing with Newton and mentions ‘”After dinner, the weather being warm, we went into the garden and drank tea under the shade of some apple tree; only he and myself…Amid other discourse, he told me, he was just in the same situation, as when formerly the notion of gravitation came into his mind. Why should that apple always descend perpendicularly to the ground, thought he to himself; occasion’d by the fall of an apple, as he sat in contemplative mood….Why should it not go sideways, or upwards? But constantly to the Earth’s centre? Assuredly the reason is, that the Earth draws it. There must be a drawing power in matter. And the sum of the drawing power in the matter of the Earth must be in the Earth’s centre, not in any side of the Earth…..Therefore does this apple fall perpendicularly or towards the centre? If matter thus draws matter; it must be proportion of its quantity. Therefore the apple draws the Earth, as well as the Earth draws the apple.”

Steve Connor notes that “Both accounts of the apple incident were recalled by Newton some 50 years later. Did it really happen, or was it a story that Newton embellished or even invented?

Source: Steve Connor, The core of truth behind Sir Isaac Newton’s apple. The Independent 2010

The discovery of quaternions by Sir William Rowan Hamilton when he was walking with his wife along the Royal Canal near Dubllin (1843)

On October 16, 1843, the Irish William Rowan  Hamilton discovered the quaternions when he was walking with his wife along the Royal Canal near Dublin. He found them, wrote them in his notebook while walking, scratched the formula on the bridge, and then he went by car to Dublin still writing in his notebook (his wife did not go to the meeting). Having arrived at the meeting of the RIA (he then was president of the Royal Irish Academy) he showed it to two people.He had been searching ‘on and off’ for an extension of the complex numbers to three dimensions, and this time he had been searching for about three weeks.. The next day he wrote a letter to John T Graves in England, to ensure his priority. The notebook and that letter are still extant. And from that moment on it occupied him until the end of his life.

Hamilton described the moment of discovery to his second son, Archibald,

The eureka moment is immortalized in his notebook, and for instance in the photo of this sandsculpture (Photo Daniel Doyle 2012). It is commemorated every year since 1990.



courtesy of Anne van Weerden

The discovery of the periodic table of chemical elements by Dmitri Mendeleev in a dream after three days of effort (1869)

« Mendeleev was said to have been inspired by the card game known as solitaire in North America, and “patience” elsewhere. In the game, cards are arranged both by suit, horizontally, and by number, vertically. To put some order into his study of chemical elements, Mendeleev made up a set of cards, one for each of the 63 elements known at the time. Mendeleev wrote the atomic weight and the properties of each element on a card. He took the cards everywhere he went. On February 17, 1869, right after breakfast, and with a train to catch later that morning, Mendeleev set to work organizing the elements with his cards. He carried on for three days and nights, forgetting the train and continually arranging and rearranging the cards in various sequences until he noticed some gaps in the order of atomic mass.  As one story has it, Mendeleev, exhausted from his three-day effort, fell asleep. He later recalled, “I saw in a dream, a table, where all the elements fell into place as required. Awakening, I immediately wrote it down on a piece of paper.” (Strathern, 2000) He named his discovery the “periodic table of the elements” ».

Source: http://www.famousscientists.org/dmitri-mendeleev/

Comments: While Dmitri Mendeleev is often referred to as the Father of the Periodic Table, other scientists (Lothar Meyer, John Newlands) came to the same conclusion around the same time. As with many discoveries in science, there is a time when a concept becomes ripe for discovery, and this was the case with the periodic table in 1869. Another popular myth also credits Dmitri Mendeleev for the invention of the 40% standard strength of vodka in 1894, maybe to promote the quality of the beverages (but this is definitely a myth, See Wikipedia).

Kekulé’s “Eureka” of Benzene structure while dreaming of a snake seizing its own tail (around 1862)

Kekulé describes his vision of the structure of Benzene as follows:
« During my residence in Ghent in Belgium, I lived in an elegant bachelor apartment on the main street. However, my study was situated along a narrow alley and had no light during the day but for a chemist who spends the day in the laboratory this was not a disadvantage. [one evening] I was sitting, working on my textbook, but it was not going well; my mind was on other matters. I turned my chair toward the fireplace and sank into half sleep [Halbschlaf]. Again the atoms fluttered before my eyes, this time smaller groups remained modestly in the background. My mind’s eye, sharpened by repeated visions of a similar kind, now distinguished larger forms in a variety of combinations. Long lines often fitted together more densely; everything in motion, twisting and turning like snakes. But look, what was that? One of the snakes had seized its own tail, and the figure whirled mockingly before my eyes. I awoke as by a stroke of lightning, and this time, too, I spent the rest of the night working out the consequences of the hypothesis ».

August Kekulé, Benzolfest, written in1890 (probably took place in 1862)

Comments: This story relates the discovery of the cyclic structure of the aromatic compound Benzene, a marking event in organic chemistry. Kekulé told the benzene story many times to friends and family before its publication near the end of his life. The historian of science, Alan Rocke positions this eureka moment around 1862. He wrote: “Kekulé’s theory has often been depicted as one of those anomalous cases where a sudden inspiration, even perhaps as the result of a dream or hallucination, dramatically transformed a scientific field. […] Contrary to most accounts, and to the implication of the dream anecdote told out of context, it is now clear that the benzene theory did not fall into Kekulé’s half-awake mind fully formed-or even partially formed. It was at most the ring concept that arrived by this semi-conscious or unconscious process, a concept which, as we have seen, was not without precedent. The theory was developed only slowly, one might even say painfully, over the course of several years, before its first codification in 1866”. Alan Rocke suggests that it was Kekulé‘s full confidence in the validity of the principles of his structure theory that provided the psychological and conceptual prerequisites for the creation of the benzene theory.
Kekulé is also famous for another “eureka” with a vision of dancing atoms and molecules that led him to his theory of structure. This happened, he claimed, while he was riding on the upper deck of a horse-drawn omnibus in London. This probably occurred in the late summer of 1855 (Source Wikipedia).

Reference: Rocke, A.J. (1985) Hypothesis and experiment in the early development of Kekulé’s Benzene theory. Annals of Science, 42, 4, p 355-381 1985. Web: http://www.tandfonline.com/doi/abs/10.1080/00033798500200411

The discovery of Natural selection by Alfred Russel Wallace in his bed with a fever (between 1858 and 1861)

Wallace describes how he discovered natural selection as follows: « It then occurred to me that these causes or their equivalents are continually acting in the case of animals also; and as animals usually breed much more quickly than does mankind, the destruction every year from these causes must be enormous in order to keep down the numbers of each species, since evidently they do not increase regularly from year to year, as otherwise the world would long ago have been crowded with those that breed most quickly. Vaguely thinking over the enormous and constant destruction which this implied, it occurred to me to ask the question, why do some die and some live? And the answer was clearly, on the whole the best fitted live … and considering the amount of individual variation that my experience as a collector had shown me to exist, then it followed that all the changes necessary for the adaptation of the species to the changing conditions would be brought about … In this way every part of an animals organization could be modified exactly as required, and in the very process of this modification the unmodified would die out, and thus the definite characters and the clear isolation of each new species would be explained ».

Source Wallace, A.F. My Life pp. 361–62. Wikipedia 2016

Comments: According to his autobiography, it was while he was in bed with a fever that Wallace thought about Thomas Malthus’s idea of positive checks on human population growth and came up with the idea of natural selection. Wallace said in his autobiography that he was on the island of Ternate at the time; but historians have questioned this, saying that on the basis of the journal he kept, he was actually on the island of Gilolo. Wikipedia 2016.

The ‘miraculous discovery’ of phagocytosis by Elie Metchnikoff on the seaside in Italy (around 1878)

« One day, as the whole family had gone to the circus to see some exceptional trained monkeys, while I had remained alone at my microscope and was following the life of motile cells in a transparent starfish larva, I was struck by a novel idea. I began to imagine that similar cells could serve the defence of an organism against dangerous intruders. Sensing that I was on to something highly interesting, I got so excited that I started pacing around, and even walked to the shore to gather my thoughts. I hypothesized that if my presumption was correct, a thorn introduced into the body of a starfish larva, devoid of blood vessels and nervous system, would have to be rapidly encircled by the motile cells, similarly to what happens to a human finger with a splinter. No sooner said than done. In the shrubbery of our home, the same shrubbery where we had just a few days before assembled a ‘Christmas tree’ for the children on a mandarin bush, I picked up some rose thorns to introduce them right away under the skin of the superb starfish larva, as transparent as water. I was so excited I couldn’t fall asleep all night in trepidation of the result of my experiment, and the next morning, at a very early hour, I observed with immense joy that the experiment was a perfect success! This experiment formed the basis for the theory of phagocytosis, to whose elaboration I devoted the next 25 years of my life. Thus, it was in Messina that the turning point in my scientific life took place ».

Comments: This story is described by Metchnikoff in « My stay in Messina (Memories of the past) » in 1908). This text was written 30 years after the event. In fact, description of phagocytosis was not new according to S.T. Stossel, but we must acknowledge Metchnikoff for having based a scientific program on this phenomenon. While hesitating about the reality of the myth, Simon Gordon notes “It is not uncommon for scientists to dramatize and telescope the presentation of their discoveries. This can provide a vivid, memorable and synoptic anecdote to interest and enthuse students and other investigators. Should we object to legends of this kind? They can perhaps be misleading, for the lay-reader and even professional investigators, by not conveying the true nature of the scientific discovery process. It can also elevate the excitement and genius of the discoverer, at the expense of the slow, prolonged graft that is often required to make a ‘scientific breakthrough’ ».

Source : Gordon, S. (2016) Elie Metchnikoff, the Man and the Myth. J Innate Immunity DOI: 10.1159/000443331

The sudden illumination by Henri Poincaré on Fuchsians groups and discrète group theory when he was stepping down from on omnibus Summer 1880

I wanted to represent these functions by the quotient of two series; this idea was perfectly conscious and deliberate; the analogy with elliptic functions guided me. I asked myself what properties these series must have if they existed, and succeeded without difficulty in forming the series I have called thetafuchsian.

Just at this time, I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidian geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’ sake, I verified the result at my leisure.

Source: website, see also this article

Discovery of the relativity theory by Albert Einstein on a streetcar in Bern aroung May 1905

«Although Einstein was depressed, his thoughts were still churning in his mind when he returned home that night. In particular, he remembered riding in a streetcar in Bern and looking back at the famous clock tower that dominated the city. He then imagined what would happen if his streetcar raced away from the clock tower at the speed of light. He quickly realized that the clock would appear stopped, since light could not catch up to the streetcar, but his own clock in the streetcar would beat normally. Then it suddenly hit him, the key to the entire problem. Einstein recalled, “A storm broke loose in my mind.” The answer was simple and elegant: time can beat at different rates throughout the universe, depending on how fast you moved. Imagine clocks scattered at different points in space, each one announcing a different time, each one ticking at a different rate. One second on Earth was not the same length as one second on the moon or one second on Jupiter. In fact, the faster you moved, the more time slowed down. (Einstein once joked that in relativity theory, he placed a clock at every point in the universe, each one running at a different rate, but in real life he didn’t have enough money to buy even one.) This meant that events that were simultaneous in one frame were not necessarily simultaneous in another frame, as Newton thought. He had finally tapped into “God’s thoughts.” He would recall excitedly, “The solution came to me suddenly with the thought that our concepts and laws of space and time can only claim validity insofar as they stand in a clear relation to our experiences…. By a revision of the concept of simultaneity into a more malleable form, I thus arrived at the theory of relativity.”

Source: http://www.pbs.org/wgbh/nova/physics/theory-behind-equation.html

Leó Szilárd discovery of nuclear chain reaction (and nuclear bomb) waiting at a red light on Southampton Row in Bloomsbury on September 12, 1933

Richard Rhodes described Szilard’s moment of inspiration:

“In London, where Southampton Row passes Russell Square, across from the British Museum in Bloomsbury, Leo Szilard waited irritably one gray Depression morning for the stoplight to change. A trace of rain had fallen during the night; Tuesday, September 12, 1933, dawned cool, humid and dull. Drizzling rain would begin again in early afternoon. When Szilard told the story later he never mentioned his destination that morning. He may have had none; he often walked to think. In any case another destination intervened. The stoplight changed to green. Szilard stepped off the curb. As he crossed the street time cracked open before him and he saw a way to the future, death into the world and all our woes, the shape of things to come”…

Comments: Leó Szilárd is probably the first scientist to think seriously about the atomic bomb. The possibility of a nuclear chain reaction appeared to him on September 12, 1933 while he was waiting at a red light on Southampton Row in Bloomsbury. The idea would have occurred to him in reaction to an article in The Times summarizing a speech given by Lord Rutherford in which Rutherford rejected the feasibility of using atomic energy for practical purposes. Szilard was so annoyed at Rutherford’s dismissal that, on the same day, he conceived of the idea of nuclear chain reaction (analogous to a chemical chain reaction), using recently discovered neutrons. Richard Rhodes described Szilard’s moment of inspiration:


Rhodes, Richard: The Making of the Atomic Bomb (1986), Simon and Schuster.

Other texts derived from Wikipedia pages on Leó Szilárd


Discovery of the immune selection theory by Niels Jerne on a bridge in March 1954

« I do not know whether reverberations of Kierkegaard contributed to the idea of a selective mechanism of antibody formation that occurred to me one evening in March, 1954, as I was walking home in Copenhagen from the Danish State Serum Institute to Amaliegade. The train of thought went like this: the only property that all antigens share is that they can attach to the combining site of appropriate antibody molecules; this attachment must, therefore be a crucial step in the sequences of events by which the introduction of an antigen into an animal leads to antibody formation; a million structurally different antibody-combining sites would suffice to explain serological specificity; if all 1017 gamma-globulin molecules per ml of blood are antibodies, they must include a vast number of different combining sites, because otherwise normal serum would show a high titer against all usual antigens; three mechanisms must be assumed: (1) a random mechanism for ensuring the limited synthesis of antibody molecules possessing all possible combining sites in the absence of antigens, (2) a purging mechanism for repressing the synthesis of such antibody molecules that happen to fit to auto[or anti-self-] antigens, and (3) a selective mechanism for promoting the synthesis of those antibody molecules that make the best fit to any antigen entering the animal. … [and] a selective mechanism for promoting the synthesis of those antibody molecules that make the best fit to any antigen entering the animal. The framework of the theory was complete before I had crossed the Knippel Bridge ».

Comments: An analysis from his biographer Tomas Soderqvist suggests that Niels Jerne antedated his discovery to appear as the sole and independent discover of the theory. This suggests that this discovery story is rather mythic.

Source: Söderqvist, T. (2003). Science as Autobiography – The Troubled Life of Niels Jerne. Yale University Press.

Discovery of cancer genes by Bob Weinberg on a bridge in Boston in February 1978

« One February morning in 1978, Bob Weinberg had no choice. He had to walk from his home, then on Beacon Hill, to his lab at the Cancer Center, a mile away. The night before, a record blizzard had muffled the entire Boston area…. Perhaps subliminally aware, as he trudged across the Longfellow walkway, of the symbolic significance of bridges, Bob Weinberg had an idea. “It was an idea of numerology”, he said. “I thought about the sensitivity of the transfection technique and about the fact that we could detect the presence of one sarcoma virus amidst roughly a million fold excess of unrelated DNA sequence. The DNA of a single sarcoma virus was all what we needed to produce of focus of transformed cells ».

Source: Angier, N. (1988). Natural Obsessions, Houghton Mifflin (p73-74)

Comment: I have no information on the veracity and context of this narrative.

Discovery of gene regulation by François Jacob in a cinema in Paris

« Jacob later recalled that the decisive moment came on a Sunday afternoon late in July 1958. All his colleagues were on holiday while he remained in Paris with his wife, Lise, preparing for a lecture he had to give in New York on how phage virus hijack the genetic apparatus of their host. Unable to work, Jacob went to the cinema with his wife. He could not concentrate on the film, so he closed his eyes and suddenly in “a flash”, he realized that the two experiments he had been thinking about – the PaJaMo experiment and his own work with Elie Wollman on phage reproduction-were in fact fundamentally identical. He then understood that they both involved the modulation of gene activity by directly affecting the DNA. Jacob later describes his almost mystical experience as he realized the connection between his two problematic experiments: “Same situation. Same result. Same conclusion. In both cases, a gene governs the formation of a cytoplasmic product, of a repressor blocking the expression of other genes and so preventing either the synthesis of the galactosidase or the multiplication of the virus….. These hypotheses, still rough, still vaguely outlined, poorly formulated, stir within me. Barely have they emerged than I feel invaded by an intense joy, a savage pleasure. A sense of strength as well, of power. As if I had climbed a mountain, attained a summit from which I saw in the distance a vast panorama. I no longer feel mediocre or even mortal. I need air. I need to walk ».

Source: Cobb, M. (2015). Life’s Greatest Secret: The Race to Crack the Genetic Code. Profile Book LTD. London (p 158). See also Zimmer, C. (2013). I Think I’ve Just Thought Up Something Important–Francois. Jacob (1920-2013). Phenomena.

Comments: The science historian Michel Morange, who carefully reviewed the career of his former mentor, have doubt in François Jacob’s movie story and suggested a more reasonable scenario for this conclusion.

The discovery of Polymerase chain reaction (PCR) in the car by Kary B. Mullis. (1981)

« They were heady times. Biotechnology was in flower and one spring night while the California buckeyes were also in flower I came across the polymerase chain reaction. I was driving with Jennifer Barnett to a cabin I had been building in northern California. She and I had worked and lived together for two years. She was an inspiration to me during that time as only a woman with brains, in the bloom of her womanhood, can be. That morning she had no idea what had just happened. I had an inkling. It was the first day of the rest of my life ».

Source: Karris Mullins web site. http://www.karymullis.com/

The discovery of the use of worms to fight off autoimmunity by Joel Stock in the plane during a storm (mid 1990s)

« This question was plaguing me as I sat in a plane on the runway of Chicago’s O’Hare airport for five hours one day during the mid-1990s. I was on my way to a grant-review session for the Crohn’s and Colitis Foundation of America when lightning struck the control tower, forcing us to wait until the airport could get up and running again….. That brainstorm in the middle of a lightning storm has turned into an active area of research ».

Source: Stock, J.V. (2012). The Worm Return. Nature 491, 183–5.

Comment: I have no information on the veracity of this narrative and the context this discovery.

The discovery that the mouse lps locus encodes TLR4 by Bruce Beutler in front of the computer (mid 1998)

« The summer of 1998 was, without doubt, the most stressful of the entire project, for hope of finding the gene diminished with every passing day, and there was no hiding the fact that this was so. Mu-Ya soon left the lab, and after her, Xiaolong. I myself was discouraged, given that most of the critical region had been explored. As we approached the limiting markers, B and 83.3, there was simply less and less room for optimism. Nadia Krochin, long ago a student of mine, assured me otherwise. Referring to an account of the ascent of Mount Everest, she drew analogy to the ‘Hillary Step’, an obstacle immediately beneath the summit: one that is not formidable in itself, but formidable to those who have just climbed 98% of Mount Everest. ‘You are at the Hillary Step’, she assured me. But after 5 years, with the vast majority of the contig already analyzed ad nauseam, who could be so certain where the summit lay? The defining moment came at 9:30 pm on September 5, 1998. While working at the computer in my study, reviewing the day’s BLAST results from the BAC I17 (one of the most proximal in the contig, I was stunned to see a powerful match with the human TLR4 sequence. In a few minutes, I saw a second hit (a third was to follow the next day). Tremulous with excitement, I called Alexander. I was, of course, nearly certain that Tlr4 was, after all, Lps. There was no time to be lost in proving that this was the case ».

Source Review: The search for Lps: 1993—1998 Innate Immunity 2000 vol. 6 no. 4 269-293.

Comments: Bruce Beutler (Nobel Prize 2011) describes the discovery of the molecular nature of the LPS receptor (TLR4) with a unique precision where he appears like the captain at the wheel of a ship. An analysis of his long article reveals that he tells the discovery with a winner-takes-all attitude – as a series of struggles against adverse conditions (Beutler and Poltorak, 2000). We can understand his relief because of the intense competition of the moment, with two papers published within months, from Danielle Malo and Shizu Akira research groups, and which reported similar findings.