Pythagoras’ theorem is one of the most ancient, well known and studied mathematical theorems. It has a history longer than three thousand years as well as more than three hundred proofs. Although its first detailed description is in Euclid’s Elements, people often attribute its discovery to Pythagoras and named it after him. It is unknown whether Euclid discovered the theorem alone or he was aware of Pythagoras’ work, but there is one thing that is certain — Pythagoras was not the first discoverer either. In an Egyptian papyrus circa 1800 B.C. there is a record of a mathematical problem whose solution is a Pythagorean Triple, suggesting that the ancient Egyptians already possessed the knowledge of Pythagoras’ theorem. Historical records show that the ancient Babylonians, Chinese, and Indians have all discovered Pythagoras’ theorem independently, and their works were equally as marvelous and ingenious as Pythagoras’. However, nowadays most people only know Pythagoras’ name, and all the contributions of the other mathematicians were either lost in history or not properly acknowledged.

To many people’s surprise, this kind of rediscovery of knowledge is not uncommon throughout the history of science (and of course this blog is not the first one to discuss this either). In the times where communication was highly inefficient and the spread of information difficult, it was easy for scientific knowledge to be discovered, lost, and rediscovered at another time and location. However, although the stories might look similar, the way in which credits are attributed differs drastically. Here I categorize them into roughly three scenarios.

The first one could be called “the dominance of the first mover”, that is, the scientist who first discovered the knowledge became prestigious while the others who came up with a later solution were almost all obscure. A well known example is the independent rediscovery of Mendel’s Laws of genetics by Hugo de Vries and Carl Correns, whose names are largely unknown to people unfamiliar with the history of genetics. You may as well recall the example of the Bayes’ theorem. Although Bayes first proposed the principles of the Bayes’ theorem, it was Laplace who rediscovered the theorem, stated it with high clarity and applied it to celestial mechanics. In this scenario, the first discoverer’s name becomes more and more prominent over time due to the Matthew Effect.

The second scenario is the famous Stigler’s law of eponymy, which states “no scientific discovery is named after its original discoverer.” Contrary to the first case, the first discoverer is almost forgotten, while the one who rediscovered and/or popularized the knowledge becomes celebrated. Consistent with itself, Stigler attributed the discovery of Stigler’s Law to Robert K. Merton. Readers familiar with the history of statistics may immediately recall Gaussian distribution, the discovery of which involves de Moivre and Laplace et al. It is actually quite interesting that in French speaking countries, the normal distribution is sometimes also called the Laplacian distribution. In the field of complex networks, Albert-Laszlo Barabasi and Reka Albert proposed the famous preferential attachment model which explains the generation of a network with power-law degree distribution. However, the idea of linking to nodes proportionally to their degrees first appeared in the independent works of Yule, Simon, and de Solla Price, which remained unknown to the scientific community until recently. You may also think of other examples such as the Benford’s law, Arrhenius’ equation and Alzheimer’s Disease, but the most exemplifying one may be that Arabic numerals were actually invented by the Indians.

The third case is the “unresolved debate or shared glory”, in which several people arrived at the same conclusion but it is hard to attribute the credit to any one of them. Newton and Leibniz both declared to be the first inventor of calculus, and fought to their deaths for it. People now consider both as the father of modern calculus. The case of the Navier-Stokes equation is more complicated. Navier, Cauchy, Poisson and Stokes have all derived the famous equation of motion of viscous fluid, but only two of them had their names attached to it.

You may not agree with my categorization of rediscoveries of knowledge, but we must both agree that it is less and less likely that they will happen. The time when it was nearly impossible to know what has been done is long gone, and the latest information technology allows us to access papers published a second ago. It is highly unlikely for a scientist today to begin a research project without running a literature check. The attribution of scientific credits will also be more accurate, since it is easy to know who first published a paper on a certain topic. In current time, it is common that journals would place papers with the same but independently discovered results together. Sam’s theorem will indeed be first discovered by Sam, and has not been previously discovered by Jack, Peter, or anyone else. Every finding, writing and contribution will be attributed to the true author. Perhaps after a million years when humans are long extinct and aliens in the future found this little blog post, they will know who is its author. For this reason, I hereby sign my name as

Xiaohan Zeng

Written by

## The Science Collective

#### Like the Borg.. but less hivemind. Stories from the intersection of Science and real life. For more info: http://bit.ly/1kwE7zF

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