# What are examples of serendipity in the history of the sciences and math?

Cosmic microwave background radiation was discovered after Penzias & Wilson couldn't get rid of the noise generated by their horn. In fact, the noise was their discovery.

The strings in string theory were introduced in the context of the strong interaction to make the back-then newly discovered interaction between quarks visible. The strings turned out to be applicable (in closed form) even to gravity, certainly not what they were intended for.

What are other examples of serendipity in the sciences?

(If someone has a tag suggestion it is welcome)

• Invention of vulcanized rubber? Or is that a myth? Jul 18 at 23:41
• @davidbak No, it is not. Jul 19 at 15:33
• @davidbak One day in 1839, when trying to mix rubber with sulfur, Goodyear accidentally dropped the mixture in a hot frying pan. To his astonishment, instead of melting further or vaporizing, the rubber remained firm and, as he increased the heat, actually became harder. Goodyear quickly worked out a consistent system for this hardening, which he called vulcanization because of the heat involved. Serendipity indeed. Luckily he didnt eat it. Jul 19 at 15:53
• Oh well, I know plenty of sources say that Goodyear discovered vulcanized rubber by accidently dropping some glop in a hot frying pan and observing the results. But, really, doesn't that shout "urban myth" to you? Maybe if any one of these secondary sources had a reference to some writing of Goodyear's where he claims it that would suffice. But, e.g., Wikipedia does not provide such evidence, neither in the article on vulcanized rubber nor in the one on Goodyear himself. Jul 19 at 16:00
• BTW, this book of Goodyear's, though it does not claim he discovered it by accident (or make any claims on how it was discovered at all) is fascinating in that it contains over 300 pages of uses of vulcanized rubber! Jul 19 at 16:01

Teflon (Polytetrafluoroethylene) was discovered by Roy Plunkett while working on new refrigerant. There was a residue at the bottom of the bottle he was using, a bottle which should have been emptied of gas and yet still registered extra weight. He discovered that the milky new substance was stable and extremely slippery and, voila, we can no longer use metal implements on our non-stick pans!

Roy J Plunkett; Science History Institute

Another example is the discovery in 2006 that tarantulas have silk-producing spinnerets on their feet which they use for traction. Adam Summers, a research assistant at University of California, Irvine normally placed tarantulas on a glass plate tilted at an angle to store them temporarily. Tarantulas have a fear of falling and would simply cling to the glass without moving, a fact long-established. One day he noticed that there were trails of web from the tarantulas' feet where the tarantulas had been slowly sliding down the angled glass plate. Prior to this observation, it was not known, apparently, that any spiders possessed spinnerets on their feet, a fact with evolutionary implications. A chance observation led to the discovery.

Tarantulas Produce Silk From Feet, Science Daily

• That tarantula discovery is fascinating. Could it have evolved because of their weight, and smaller spiders wouldn't have needed the extra help? Jul 20 at 20:09
• @GammaGames; The thinking seems almost to be the other way round and that all spinnerets evolved from sensory organs (which they still resemble) into the later development of webbing-specific organs. The size factor might explain why the tarantulas retained the older function. .en.wikipedia.org/wiki/Spinneret Jul 22 at 11:41

One famous example is that of Alexander Fleming. He left a cup of staphylococci on his desk and later discovered that it was contaminated with some fungus. Instead of disposing this cup, he started to investigate and the result was the discovery of penicillin, the first antibiotic. This is how he later described this himself:

One sometimes finds, what one is not looking for. When I woke up just after dawn on September 28, 1928, I certainly didn't plan to revolutionize all medicine by discovering the world's first antibiotic, or bacteria killer. But I suppose that was exactly what I did.

• It helps if you rise just after dawn! Jul 20 at 10:58
• It seems that the antibiotic properties of penicillin were known long before that. See en.wikipedia.org/wiki/… and en.wikipedia.org/wiki/Ernest_Duchesne for example
– user15003
Jul 20 at 15:33
• @Joseph_Jaroslaw: Nevertheless, the article you refer to calls Flemings discovery a "breakthrough", and this is correct. Jul 20 at 16:46
• Indeed it was a breakthrough!
– user15003
Jul 20 at 17:45

In 1961, Edward Lorenz was running a numerical simulation of weather systems.  To restart a run half-way, he copied the initial values from a previous printout — but saw that the simulation began to diverge from the previous run.

This turned out to be the result of the printout showing values that were rounded to 3 decimal places, without the full precision used in the calculations.  He expected the resulting errors to stay small; but instead, they grew exponentially, doubling roughly every four simulated days, until after two simulated months the weather scenario was completely different.

He thus encountered what is now known as the butterfly effect.

One example is radioactivity. In 1896, Henri Becquerel was working on an experiment involving a uranium-enriched crystal. He believed that sunlight was the reason that the crystal would burn its image on a photographic plate. But then, on a day, the weather was bad, with dark clouds blocking the light from the Sun. Becquerel packed up his stuff and decided to continue his research on another sunny day.

Some few days later, he retrieved the crystal from a darkened drawer, but the image burned on the plate was, as he described, “fogged.” The crystal emitted rays that fogged a plate, but were dismissed as weaker rays compared to William Roentgen's X-rays. Becquerel wouldn't go on to put a name to the phenomenon. He left that for a couple of fellow scientists: Pierre and Marie Curie.

• So he discovered radioactivity without knowing that it was radioactivity? What kind of radioactivity was it? Jul 18 at 7:26
• It's the result of uranium decaying. The result is the emission of either $\alpha$ particles (helium nucleus) or $\beta$ particles (fast energetic electrons or positrons). Jul 18 at 8:02
• While he thought it was electromagnetic radiation (X-rays)? Did he think sunlight was refracted by the crystal, and that that burned the plate (like with a looking glass)? Jul 18 at 8:36
• Perhaps that, at first, Becquerel thought that these were X_rays. I don't know the answer to the other question. Jul 18 at 8:42
• The idea was that the crystals were absorbing and re-emitting photons. The discovery was that the crystal itself produced photons without any external input. Jul 19 at 15:25

It was well known that when you iterate $$x\mapsto \lambda x(1-x)$$, the following happens: when $$\lambda$$ is small, $$x=0$$ is an attracting fixed point; as $$\lambda$$ grows, at some moment $$\lambda_1$$ the attracting point becomes repelling, but an attracting $$2$$-cycle is born nearby. ($$2$$-cycle is an fixed point of $$f\circ f$$). As $$\lambda$$ grows further, this attracting cycle becomes repelling at $$\lambda_2>\lambda_1$$, but a new attracting $$4$$-cycle is born nearby, so we have a sequence of "doubling bifurcations" $$\lambda_1<\lambda_2<\ldots$$, and this sequence converges to some $$\lambda_\infty$$.

In 1978, Mitchell Feigenbaum studied this sequence using a hand calculator. He used Newton method to compute $$\lambda_k$$. Newton's method requires a good initial guess. Since the computation was slow, Feigenbaum started to think what the best initial guess will be, that is how to extrapolate the obtained sequence one step further. And he discovered that the ratio $$(\lambda_{n}-\lambda_{n-1})/(\lambda_{n+1}-\lambda_{n})$$ tends to a constant. To his great surprise, when he tried another function, $$x\mapsto \lambda\sin x$$, he found that this ratio tends to the SAME constant!

This great discovery is called the Feigenbaum Universality, and the constant Feigenbaum constant. It is a universal mathematical constant (like $$\pi$$), and it is approximately equal to 4.669201609102990671853203820466...

He said himself once, that the discovery was made because he had no programmable calculator at his disposal.

• Great one! Especially his remark about the calculator. Im not sure which answer to accept. They are all nice examples. But this is the nicest so far. In my eyes that is. Jul 20 at 19:51

The subject of Graph Theory in mathematics, via the Seven Bridges of Königsberg and involving Euler of all people!

"The theory of graphs is one of the few fields of mathematics with a definite birth date." -Oystein Ore, graph theorist & number theorist

Namely, that birthdate is in 1736 when Leonard Euler refers to "geometry of position" that we've come to know and love as Graph Theory.

Quotes below are from Chapter 3 of Graphs & Digraphs, 5th Edition, by Chartrand, Lesniak, and Zhang:

Early in the 18th century, the East Prussian city of Konigsberg (now called Kaliningrad and located in Russia) occupied both banks of the River Pregel and the island of Kneiphof, lying in the river at a point where it branches into two parts. There were seven bridges that spanned various sections of the river. A popular puzzle, called the Konigsberg Bridge Problem, asked whether there was a route that crossed each of these bridges exactly once. Although such a route was long thought to be impossible, the first mathematical verification of this was presented by the famed mathematician Leonhard Euler (1707–1783) at the Petersburg Academy on 26 August 1735. Euler’s proof was contained in a paper that would turn out to be the beginning of graph theory. This paper appeared in the 1736 volume of the proceedings of the Petersburg Academy. Euler’s paper, written in Latin, started as follows (translated into English):

"In addition to that branch of geometry which is concerned with magnitudes, and which has always received the greatest attention, there is another branch, previously almost unknown, which Leibniz first mentioned, calling it the geometry of position. This branch is concerned only with the determination of position and its properties; it does not involve measurements, nor calculations made with them. It has not yet been satisfactorily determined what kind of problems are relevant to this geometry of position, or what methods should be used in solving them. Hence, when a problem was recently mentioned, which seemed geometrical but was so constructed that it did not require the measurement of distances, nor did calculation help at all, I had no doubt that it was concerned with the geometry of position – especially as its solution involved only position, and no calculation was of any use. I have therefore decided to give here the method which I have found for solving this kind of problem, as an example of the geometry of position.

Euler goes on to say (see an excerpt from this amazing lecture on Euler's genius):

"...this solution bears little relationship to mathematics, and I do not understand why to expect a mathematician to produce it, rather than anyone else, for the solution is based on logic alone."

I guess I find this story so serendipitous, because you had to have so many things fall into place:

• the rivers naturally flowing in a unique way
• people to settle and build just the right bridges in just the right places to make the underlying problem unsolvable
• an arbitrary human constraint to want to cross bridges exactly once on a Sunday afternoon walk
• petitioning one of the most prolific and insightful minds of mathematics for all time (Euler)...
• ...who proceeded to solve it despite the fact that he didn't think it had any applications in math, nor did he think a mathematician was needed to solve this problem!

I find it hard to believe Graph Theory would not have been developed eventually by someone else for another of its many applications, but to think that this was the fashion that it was introduced makes me consider it a serendipitous outcome.

There's always Archimedes ''eureka' moment, sitting in a bath tub and realizing that a given volume of a material will displace the same amount of water when fully submerged regardless of the object's shape.

• You can now research whether this is believed to be a true incident. Jul 20 at 21:40

José Carlos Santos' answer mentions X-rays but not their discovery.

From the American Physical Society's This Month in Physics History; November 8, 1895: Roentgen's Discovery of X-Rays:

Roentgen's scientific career was one beset with difficulties. As a student in Holland, he was expelled from the Utrecht Technical School for a prank committed by another student. His lack of a diploma initially prevented him from obtaining a position at the University of Würzburg even after he received his doctorate, although he eventually was accepted.

Wilhelm Roentgen, Professor of Physics in Wurzburg, Bavaria, discovered X-rays in 1895—accidentally—while testing whether cathode rays could pass through glass. His cathode tube was covered in heavy black paper, so he was surprised when an incandescent green light nevertheless escaped and projected onto a nearby fluorescent screen. Through experimentation, he found that the mysterious light would pass through most substances but leave shadows of solid objects. Because he did not know what the rays were, he called them ‘X,’ meaning ‘unknown,’ rays.

On November 8, 1895, German physics professor Wilhelm Röntgen stumbled on X-rays while experimenting with Lenard tubes and Crookes tubes and began studying them. He wrote an initial report "On a new kind of ray: A preliminary communication" and on December 28, 1895 submitted it to Würzburg's Physical-Medical Society journal. This was the first paper written on X-rays. Röntgen referred to the radiation as "X", to indicate that it was an unknown type of radiation. The name stuck, although (over Röntgen's great objections) many of his colleagues suggested calling them Röntgen rays. They are still referred to as such in many languages, including German, Hungarian, Ukrainian, Danish, Polish, Bulgarian, Swedish, Finnish, Estonian, Turkish, Russian, Latvian, Lithuanian, Japanese, Dutch, Georgian, Hebrew and Norwegian. Röntgen received the first Nobel Prize in Physics for his discovery.

The principle of the microwave oven was discovered by accident.

In 1946, the engineer Dr. Percy LeBaron Spencer, who worked for the Raytheon Corporation, was working on magnetrons. One day at work, he had a candy bar in his pocket, and found that it had melted. He realized that the microwaves he was working with had caused it to melt. After experimenting, he realized that microwaves would cook foods quickly - even faster than conventional ovens that cook with heat.

Zoom Inventors and Inventions

• That's a nice story. Unfortunately, it's entirely false: radio heating was known at least as far back as 1930, and a microwave oven was demonstrated at the 1933 World's Fair.
– Mark
Jul 19 at 1:00
• @Mark The 1930 device (operating at wavelengths of 10s of meters) was not microwave oven. The cavity magnetron which is the essential component of all practical microwave ovens was indeed invented during WWII (but not by American engineers) and its heating effect discovered by accident. In fact, the design of the cavity magnetron was given free to the USA by the UK when the USA entered WWII. (Of course without centimeter-band radars using magnetrons, the US Air Force would not have been able contribute much anyway) Jul 19 at 15:17
• @alephzero the Tizard mission actually occurred over a year before the US entered the war Jul 19 at 17:17
• @alephzero, an impractical microwave oven is still a microwave oven.
– Mark
Jul 19 at 20:10
• @Mark I think the distinction being made is between short-wave RF and microwaves. Although it does seems weird that if they knew about short-wave cooking, it took this serendipitous discovery to come up with microwave ovens. Jul 19 at 20:12

Alfred Wilm discovered the age hardening effect of aluminium, after delaying his testing of some freshly annealed samples (I believe to take the weekend off to go sailing). This is now used in the design of aluminum alloys with applications from aircraft to bicycles to keychain bottle openers, with his alloy used in "Duralinium".

https://www.researchgate.net/publication/279898292_Aluminium_Alloys_-_A_Century_of_Age_Hardening

The eponymous Serendipity elements used in the finite element method for solving PDEs fit the bill.

These elements ignore the internal nodes (unlike their Lagrange counterparts), reducing the number of degrees of freedom of the system while (and this is the key) retaining the same element order.

Serendipity elements are therefore less computationally expensive than Lagrange elements but just as accurate and herein lies the "happy chance".