True history
is surprising.
I investigate historical mysteries. Some were unsolved for decades, others for hundreds of years. Why?
History can be scientific. I dislike the common practice of inventing the past, so I work to make permanent discoveries. I analyze the evolution of historical claims, subtracting fictions from evidence, to find true explanations.
Here are my best findings:
1
Coulomb’s famous experiment of 1785
Charles Coulomb did one of the most famous experiments in the history of physics. In 1785, his experiment showed that the force of repulsion between electrified bodies is an inverse-square law, similar to Newton’s law of gravity. But strangely, for two hundred years, physicists failed to reproduce Coulomb’s results. In 1992, Peter Heering argued that no physicist ever reported results similar to Coulomb’s. And Heering too did the experiment, but with negative results, apparently showing that Coulomb’s numbers were partly fictitious. Heering's work was praised as one of the best papers of the year in American Journal of Physics.
However, thirteen years later, I successfully replicated the experiment. Working at Caltech, I reproduced Coulomb's procedures and results, thus proving that his numbers were true, not socially constructed.
2
First explanation of
Euler’s rules on imaginary numbers
Leonhard Euler is one of the most brilliant mathematicians ever. However, after he published his Algebra of 1770, mathematicians said that he failed to multiply and divide imaginary numbers correctly. They criticized Euler’s alleged errors for more than two hundred years. Such critics include mathematicians such as Étienne Bézout, Jean Garnier, Tristan Needham, as well as top historians of mathematics, such as Florian Cajori, Morris Kline, and Ivor Grattan-Guinness, plus, the engineer and successful writer Paul Nahin.
I discovered that Euler made no such mistakes. His procedures are logically consistent but were misunderstood. I discovered that Euler’s algebra avoids contradictions in our conventional algebra. In American Mathematical Monthly.
3
First correct explanation of
Einstein’s first derivation
of the Lorentz transformations
Albert Einstein’s 1905 relativity paper is the most famous work in the history of physics. In it, he derived relativistic transformation equations, instead of positing them like Woldemar Voigt, H.A. Lorentz, and Henri Poincaré. Yet readers were confused by Einstein’s derivation. Even decades later, experts who analyzed it didn’t understand it either, such as G.H. Keswani, Karl Stiegler, Arthur I. Miller, Roberto Torretti, John Stachel. They mistakenly claimed that Einstein used four coordinate systems, that some were pseudo-Galilean, that his equation, x' = x – vt, was a transformation, and that his derivation involved variations in the speed of light. Such claims were mistaken and confused.
For years, Einstein’s first derivation puzzled me too. And so, 99 years after the 1905 paper, I published the first correct explanation of Einstein’s original derivation, in American Journal of Physics.
4
Discovery:
In 1600, the famous philosopher Giordano Bruno was burned alive after the Roman Inquisition judged him guilty of heresy. His death became a longstanding mystery. What were his crimes, his heresies? The Inquisitorial proceedings were secret, and so, for more than 400 years, writers speculated. Increasingly, they claimed that the cause was not his Copernican cosmology. Many authorities denied it, including The Catholic Encyclopedia, Frances Yates, Steven J. Dick, Michael J. Crowe, Leen Spruit, and the Stanford Encyclopedia of Philosophy. The denial that Bruno was killed for his semi-Copernican cosmological statements was a recurrent part of writers’ denial that there was a conflict between science and religion.
To the contrary, I discovered that the main reason why the Roman Inquisition condemned Bruno was because of his cosmology: his statements about many worlds, that the stars are suns, innumerably many, surrounded by planetary worlds, possibly like the Earth, even inhabited by alien beings.
5
Discovery:
Galileo’s religious crimes
In 1633, the Roman Inquisition condemned Galileo. Since then, historians have speculated: what were Galileo’s alleged religious crimes, his heresies? For example, Pietro Redondi conjectured that maybe Catholic theologians were annoyed by Galileo’s atomism. Other historians disagreed. In my book of 2011, I asked: Did theologians condemn Galileo for defending pagan beliefs?
Seven years later, my book of 2018 confirmed it. In Rome, I found that Galileo’s strongest critic of 1633, a Consultor for the Inquisition, blamed the pagan cult leader Pythagoras as the first to assert “the heresy of the Earth’s motion,” and he denounced Galileo as a “New Pythagorean.” Allegedly Galileo supported the pagan “heresies” of the animated Earth, many worlds, and beings living on the Moon. The unpublished manuscript also identifies the authorities who had condemned such “Pythagorean” heresies: Saint Jerome, Saint Philaster, Saint Augustine, Saint Isidore, Pope Zacharias, Pope Dionysus, Pope Gelasius, the Fifth Ecumenical Council, and the Roman Inquisition in 1616, 1619, and 1633.
6
Discovery:
Negative times negative
can be negative
For hundreds of years, math teachers have taught that minus times minus is plus. Mathematicians have described this rule not as an assumption but as a necessary logical consequence of the fundamental properties of the laws of algebra, such as the commutative law of multiplication. In the Ars Magna, in 1545, Girolamo Cardano affirmed the rule that minus times minus is plus. But years later, in a little-known work, Cardano changed his mind and argued that it should be minus. Similarly, some other mathematicians rejected the rule, including Thomas Harriot and Francis Maseres, but they failed to formulate a coherent alternative.
In my book Negative Math (Princeton University Press, 2005), I analyzed the history of negative numbers and I formulated a coherent algebra in which minus times minus is minus. In this new algebra, multiplication of numbers with different signs is non-commutative, which introduces symmetries that are missing in traditional numerical algebra.
7
Discovery:
Invariant simultaneity
in Newton’s mechanics
In 1905, Einstein defined a procedure that entailed that the simultaneity of distant events varies among observers moving relative to one another. Still, the question remained: could Newton’s classical mechanics, without imaginary factors (such as signals of infinite speed), articulate a procedure to measure invariant distant simultaneity?
In 1992 I found that within classical physics it is possible to produce invariant measurements of distant simultaneity. In this procedure, observers ascertain simultaneity by using mechanical projectiles, with speeds that depend on their source, that is, projectiles emitted mechanically from sources attached to each reference frame.
8
Discovery:
Measuring light speed
in one direction
Most physicists remain unaware of the fundamental distinction between measuring the speed of light in one direction, and measuring the average round-trip speed of light. Physicists who did distinguish between one-way and round-trip measurements include: Henri Poincaré, Albert Einstein, Edwin Taylor, and John Wheeler. Round-trip speeds of light rays have been measured experimentally many times, with slightly varying results. But the one-way speed of any light ray has never been measured experimentally. It’s because of a procedural circularity. For this reason, in special relativity Einstein posited the constancy of the one-way speed of light as a fundamental assumption, “a postulate,” — not an experimental finding.
Nevertheless, I formulated a way to synchronize clocks such that pairs of clocks will be deemed as synchronized both in Einstein’s relativity and in Newton’s mechanics. Since both theories agree on the setup, it becomes possible to use two pairs of such clocks to measure the one-way speed of light. It would constitute a test of Einstein’s postulate of the constancy of the speed of light.
9
Explanation:
The Pythagorean theorem
was misattributed to Pythagoras
Countless teachers claim that Pythagoras proved the hypotenuse theorem. This claim became widespread because Galileo said it in his famous book of 1632. Yet 340 years later, historian Walter Burkert raised questions about whether ancient sources show that Pythagoras contributed to geometry. Regardless, most writers, such as Eli Maor and Leonid Zhumd, continued to credit Pythagoras.
In 2012, I proved that Pythagoras did not contribute to geometry. Ancient Greek commentators on mathematics, such as Socrates, Plato, Aristotle, Archimedes, and Apollonius, did not attribute anything in geometry to Pythagoras. Writers in antiquity did not link the hypotenuse theorem to Pythagoras until half a millennium after he died. The earliest instance I found of anyone claiming that Pythagoras “proved” it is from 1557, two thousand years after he died.
10
Explanation:
Myth: that the discoverer
of irrational numbers was murdered
At least since the 1890s, writers and math teachers claim that the ancient Pythagoreans murdered their fellow cult member Hippasus for discovering irrationality in mathematics: that certain lines are incommensurable. Versions of this story have been echoed by historians of mathematics, such as Morris Kline and Amir Alexander, and by bestselling writers such as Stephen Hawking and Mario Livio.
However, I found that it didn’t happen: ancient sources do not claim that the Pythagoreans murdered Hippasus. Instead, seven centuries after Hippasus lived, Iamblichus commented that some people claimed that the person who revealed incommensurability was hated and banished, while others claimed that he died at sea. Thus, a vague story about a guy dying at sea became a story about a murdering cult.
11
Explanation:
Galileo didn’t drop things
from the Leaning Tower of Pisa
For centuries, since the 1650s, many writers have claimed that Galileo dropped objects from the Leaning Tower of Pisa, publicly proving that Aristotle’s theory of falling bodies was false. This story was started by Galileo’s first biographer, Vincenzio Viviani, and it has been echoed by countless many physicists, such as Leon Lederman, and by authoritative historians, such as Antonio Favaro, Stillman Drake, and Domenico Bertoloni Meli.
Yet, in 1935 the story was critiqued by Lane Cooper, who wasn’t a historian or a physicist, but just a professor of English. In 2011, I proved that Galileo didn’t do it. His writings do not claim that he dropped anything from the Leaning Tower. Nobody claimed to have seen Galileo do it either. Viviani’s claim that Galileo wrote it in The Two New Sciences is false, and objects dropped from the Leaning Tower do not land at the same instant, contrary to Viviani’s mistaken claim.
12
Explanation:
The myth about Einstein
and the Swiss clock towers
For half a century, since 1973, multiple writers claim that Einstein’s relativity of time originated because of thoughts he allegedly had about clock towers in Switzerland. Such stories have been voiced by prominent Harvard professors, such as Steven Pinker and Peter Galison, well-known physicists such as Michio Kaku and Hans Ohanian, and bestselling biographers such as Walter Isaacson.
When I sought and analyzed the many primary sources I found that all such stories are false. In his writings, Einstein never claimed that clock towers inspired him to think of the relativity of time. None of his friends, relatives, coworkers, or acquaintances claimed that he was inspired by Swiss clocks or towers either.
13
Since the 1960s, a dramatic story has arisen: that Mileva Maric was Einstein’s secret collaborator, and especially, that she helped him create the theory of relativity. Such claims gained popularity after 1989, when letters between Einstein and Maric were published. In those surprising letters, Einstein himself wrote to Maric about “our work,” and remarkably, “our work on the relative motion.” And so, many writers tried to credit or discredit Mileva Maric, with interpretations and guesswork.
Instead, I analyzed the mystery by identifying what the sentences meant. For example, I found that when Einstein wrote “our work on the relative motion,” it didn't refer to his theory of relativity. Because, back then he believed in the existence of the ether and was trying to detect its motion relative to the Earth, like other physicists. Thus I proved that he shared that early aspiration with Mileva Maric, in 1901, but that years later, after he formulated relativity, Maric herself gave him the credit for his physics papers.
14
Discovery:
True origins of The Eyes of Texas
In 1903, John Lang Sinclair wrote “The Eyes of Texas” song. Decades later, it became the song of the University of Texas, one of the most beloved songs in the state. However, for 95 years, since 1929, there have been conflicts and questions about how the song originated. In 2020, an official UT Report claimed that the song was not written for the 1903 minstrel show in which UT students mocked Black people by painting their faces black. And allegedly, its origin was not linked to words by Confederate General Robert E. Lee.
However, by inspecting the primary sources I proved that the song was written for the blackface minstrel show, based on words about General Lee. The author himself, John Lang Sinclair, and other witnesses admitted that the song was written for the minstrel show of 1903. And, I proved that the song’s title and chorus were based on words by and about General Lee in the Civil War. Sinclair stated that the song was not meant to be a university hymn, contrary to the whitewash of a fellow alumnus who he wanted to sue for lying about it.
15
Proof:
Fiction in political news
In their 1988 book, Manufacturing Consent, Edward Herman and Noam Chomsky argued that mass media in the U.S. distorts the news into political propaganda. Having analyzed the evolution of historical myths, I decided to likewise analyze “the first draft of history.” How much fiction is intermixed in political news? I examined news stories that millions of persons accepted as true. During the U.S. Presidential election of 2016, did the news misrepresent the statements of the contentious candidate Donald Trump?
It was controversial: countless Americans were convinced that Trump was a reckless individual and that his statements were evidently malicious and deranged. I meticulously analyzed twenty news stories from 2015 to 2016, all involving Trump and the media. I found that in every single one of those twenty controversies many prominent reporters, columnists, and television pundits grossly misrepresented the news. No other book has analyzed news stories in any presidential campaign with such thoroughness. It clearly shows that American corporate media grossly distorts political news.
16
Discovery:
How many people died in Puerto Rico
because of Hurricane Maria?
In early 2018, researchers at Harvard estimated that Hurricane Maria caused the deaths of roughly 4,645 persons in Puerto Rico. They also wrote that the deaths might exceed eight thousand. Later, researchers at George Washington University claimed instead that Hurricane Maria caused the deaths of roughly 2,975 persons in Puerto Rico.
But there were serious errors in both of those studies. When obtaining official mortality data, I found that the Harvard team had not requested or used mortality data from Puerto Rico’s Demographic Registry. They confected excessive estimates based on random interviews. Plus, I found that the GWU group based their estimate on a miscalculation of how many people “would have died” if the hurricane had not struck. By analyzing annual and monthly mortality rates, migrations, and certified deaths, I calculated excess deaths, thus showing that the researchers at Harvard and GWU published grossly high estimates.
BOOKS
REVIEWS
"Martínez shows that it’s possible to construct a fully consistent system of arithmetic in which minus times minus makes minus. It’s a wonderful vindication...”
JAKE RANDELL
AMERICAN SCIENTIST
"Martínez can certainly take credit for having produced by far the best and most detailed account of this important strand in Einstein's early work.”
JÜRGEN RENN
MAX PLANCK INSTITUTE
“An essential text for any future research on Bruno, Galileo and The Inquisition. ...possibly the most important book of the year for the history of astronomy.”
CLIFFORD CUNNINGHAM
ASTRONOMICAL HISTORY
BIO
Alberto Martinez is originally from San Juan, Puerto Rico. As a professor at UT Austin, he investigates the history of science, especially Einstein and relativity theory, history of math, historical myths, and Giordano Bruno and Galileo. He is a Fellow of the American Physical Society.
He also researches myths in political news media, The Eyes of Texas, and episodes in the history of money and corruption.
Now, he's finishing writing a novel about Albert Einstein.