British historian of mathematics James Gow (1854-1923) is likely the first to introduce the story of Thales transporting salt with mules in historical works on mathematics. In 1884, Gow published AShort Historyof GreekMathematics, which explored the history of Greek mathematics. When introducing Thales’ anecdotes, Gow cited the works of Plutarch and Aristotle, saying:

“Thales used mules to carry his salt to market; one of them, having slipped in fording a stream, found its load considerably lightened by the melting of the salt; and afterwards several times fell in the water purposely. To cure it of this trick, Thales loaded it one time with rags and sponges.” ([12]: p. 139)

Gow argued that the story of Thales transporting salt with mules originated from Plutarch or Aristotle. However, we did not find the story in Plutarch’s The Lives of the Noble Grecians and Romans [13]. The Chinese version of Plutarch’s work was translated from the English version which was translated by Bernadotte Perrin for The Loeb Classical Library. We also did not find it in The Complete Works of Aristotle [14]. The Chinese edition of The Complete Works of Aristotle was compiled by Miao Litian (1917-2000), a renowned Chinese historian of Greek philosophy, and is mainly based on The Loeb Classical Library. This work is regarded as an authoritative Chinese version, and has won many national book awards in China. However, none of these works mentions the story of Thales transporting salt with mules. Analyzing the reason, it might be due to different versions. The works of Plutarch and Aristotle cited by Gow are significantly different from those in The Loeb Classical Library version. The original text of The Lives of the Noble Grecians and Romans or The Complete Works of Aristotle in The Loeb Classical Library, has already removed this story.

In order to find the source of the story, we investigate the English version of Plutarch and Aristotle’s works, such as Plutarch (1952) [15], Aristotle (1984) [16]. The edition of Plutarch’s Lives translated by John Dryden is a classic and has been widely welcomed by readers. The Oxford Translation of Aristotle is universally recognized as the standard English version of Aristotle’s works. However, these English editions also do not mention the story of Thales using mules to transport salt. These facts indicate that the claim made by Gow that the story of Thales transporting salt with mules originated from Plutarch or Aristotle is highly questionable. The same is true in the works on history of Greek philosophy. The well-known works on the history of Greek philosophy, when introducing Thales, also rarely mention the story of Thales transporting salt with mules. For example, Richard McKirahan’s Philosophybefore Socrates is regarded as the standard sourcebook in presocratic philosophy. However, when introducing the ancient Greek philosopher and mathematician Thales, McKirahan (2010) [2] mentioned many anecdotes about Thales except for the story of Thales transporting salt with mules.

In 1888, British historian of mathematics Walter Ball (1850-1925) recounted the story of Thales transporting salt with mules while introducing the ancient Greek mathematician Thales in his work AShort Accountof theHistoryofMathematics. He wrote:

“It is said that once when transporting some salt; which was loaded on mules, one of the animals slipping in a stream got its load wet and so caused some of the salt to be dissolved; finding its burden thus lightened it rolled over at the next ford to which it came to break it of this trick Thales loaded it with rags and sponges, which by absorbing the water made the load heavier and soon effectually cured it of its troublesome habit.” ([17]: p. 13)

Although Ball introduced the story of Thales transporting salt with mules, he did not provide the source of the story in his book, even in the sixth edition in 1915. Yet by comparing with Gow’s story of Thales using mules to transport salt, it can be found that Ball’s tale is highly similar to that told by Gow, and both narratives mention Thales using “rags and sponges” to discipline the mule. Gow and Ball are all British historians of mathematics who lived in the same era, and their books on the history of mathematics were published only four years apart. Based on these facts, it is reasonable to infer that the story of Thales transporting salt with mules introduced by Ball very likely refers to Gow’s work. And it is true, we did find Gow’s work cited in the references of Ball’s book, although Ball disagrees with Gow’s account of the origin of Thales’ story regarding the transportation of salt using mules.

In contrast to Ball’s views, it was found that more scholars introduced anecdotes of Thales, even though they referenced Gow’s work, but ignored the story of Thales transporting salt with mules. For example, the American historian of science and mathematics Florian Cajori (1859-1930) published A History of Mathematics in 1893. Cajori was the first professor of the history of mathematics in history. He referenced Gow’s AShort Historyof GreekMathematics, but ignored the story of Thales transporting salt with mules [18]. This fact indicates that Cajori did not accept the authenticity of the story told by Gow. Sir Thomas Little Heath (1861-1940), a British classicist and authority on the history of Greek mathematics, also holds a similar view. In 1921, Heath introduced numerous anecdotes about Thales in his book A History of Greek Mathematics: From Thales to Euclid. He referenced the work of Gow, but also did not mention the story of Thales transporting salt with mules [7]. Like Cajori and Heath, the renowned American mathematical historian David Eugene Smith (1860-1944) cited Gow’s work in his book History of Mathematics which was published in 1923, yet he also did not accept Gow’s story of Thales transporting salt with mules [19]. In the mid-to-late 20th century, the most important and prominent Western historians of mathematics, including Sarton (1952) [20], Scott (1958) [21], Kline (1972) [22], Neugebauer (1975) [23], and Katz (1992) [24]et al. shared a similar perspective while recounting the anecdotes about Thales. None of them ever mentioned the story of Thales transporting salt with mules in their works on the history of mathematics or science.

Conclusively speaking, although British historian of mathematics Gow referenced the works of Plutarch and Aristotle in his publication AShort Historyof GreekMathematics(1884) to introduce the anecdote about Thales transporting salt with mules, this origin has not been accepted by the leading Western historians of mathematics. When the renowned Western historians of mathematics such as Cajori, Heath, Sarton et al. discussed Thales’ scientific contributions and biographical anecdotes, they did not mention this particular story. This absence suggests that the narrative concerning Thales transporting salt with mules, which Gow traced back to Plutarch or Aristotle, has not gained recognition within the academic community of Western mathematical history. In fact, the world-famous Dictionary of Scientific Biography made no mention whatsoever of Thales’ story about transporting salt with mules when introducing the biography of Thales [25].

The origin of the story of ancient Greek mathematician Thales transporting salt with mules is not unique. Besides the one mentioned by Gow (1884) [12] which is attributed to Plutarch or Aristotle, Niu (2026) [8] pointed out in a recently study that the story of Thales transporting salt with mules originated from Aesop. In 1953, American mathematician Howard Eves (1911-2004) told a story about Thales who used mules to transport salt in An Introduction to the History of Mathematics. He said:

“And there is the story of the recalcitrant mule which, when transporting salt, found that by rolling over in the stream he could dissolve the contents of his load and thus travel more lightly. Thales broke him of the troublesome habit by loading him with sponges.” ([26]: p. 52)

Although Eves referenced Gow’s work when introducing Thales, he did not concur with Gow’s perspective on the origin of the story regarding Thales transporting salt with mules. In fact, Eves did not provide the source of the story. In 1969, Eves recounted the story once more in his book In Mathematical Circles, and offered more detailed storylines, yet still failing to provide any origin [27]. However, in the sixth edition of 1990, Eves proposed that the story originated from Aesop, though he provided no evidence [28]. Eves even commented that: “which [tale of Thales], if not true, are at least apposite.” ([26]: p. 52) Apparently, Eves tends to believe that the story of Thales transporting salt with mules is a historical fact, though it actually originated from Aesop’s fables. As we all know, Aesop’s Fables, which we read today, are the result of many centuries of collection, collation and compilation. They are essentially a collection of literary stories, and have no historical reference value. Taking the edition edited by Stade (2003) [29] as an example, the investigation reveals that Aesop told a story of a peddler using an ass or donkey carrying salt, not that of a mule. Despite some similarities in plot, the storyline of Aesop’s tale differs considerably from the story of Thales transporting salt with mules. For example, the protagonist in the story of “The Ass and His Burdens” in Aesop’s Fables is an anonymous peddler, not the famous philosopher and mathematician Thales.

American mathematician David Burton (1930-2016) was one of the earlier scholars to clearly state that the story of Thales transporting salt with mules originated from Aesop. In 1985, Burton told the story of Thales using mules to transport salt in The History of Mathematics:An Introduction:

“Another favorite story is related by Aesop. It appears that once one of Thales’ mules, loaded with salt for trade, accidentally discovered that if it rolled over in a stream, the contents of its load would dissolve; on every trip thereafter, the beast deliberately repeated the same stunt. Thales discouraged this habit by the expedient of filling the mule’s saddlebags with sponges instead of salt.” ([30]: p. 93)

Burton explicitly stated that the story of Thales transporting salt with mules was related to Aesop, and this view was maintained even in the 2011 seventh edition. However, he did not provide any evidence. Furthermore, we discovered that Burton cited Gow’s work but did not agree with the view that the story originated from Plutarch or Aristotle. Burton even commented that: “This [the tale of Thales transporting salt with mules], if not true, is certainly well invented and more in character than the amusing tale Plato tells.” ([30]: p. 93) It can be seen that Burton argued the story of Thales transporting salt with mules was “well invented”, and even more in line with the character of Thales, also more believable than Plato’s story of Thales falling into a well while looking up at the stars. Obviously, Burton’s viewpoint is hasty, lacks supporting evidence, and is therefore unpersuasive. In fact, in the eyes of historians, history is not an “invention” but a “record”. The essence of history is a record of what really happened according to calendars. Even if a story is well invented, it remains fiction, a form of fictional literature, and can never be classified as history.

With the development of time, the story of ancient Greek mathematician Thales using mules to transport salt in the works on history of mathematics presented more and more detailed information. Taking Mathematicians are People, Too: Storiesfrom theLivesofGreat Mathematicians as an example, Luetta Reimer and Wilbert Reimer presented the story of Thales and salt in this mathematical popular science book in 1990, which enriches the narrative with additional plot elements, especially adding a lot of fictional dialogues [31]. For instance, they stated that the workers of Thales dug salt out of the salt mine, put it in bags and placed it on the backs of donkeys, which carried it down the mountain and sold it in the market, and also mentioned that the foreman had reported to Thales about a strange incident where a donkey always fell when crossing the river.

It can be seen clearly that in their story, the salt carrier has changed from mule to donkey. In addition, these detailed storylines have never been presented in the works of history of mathematics by scholars of the past, such as Gow (1884) [12], Ball (1888) [17], Eves (1953) [26]etal. There is no doubt that these storylines were created by later scholars, and it is probable that Luetta Reimer and Wilbert Reimer invented them themselves. Obviously, these details could not be real history. When introducing the anecdotes of Thales, Luetta Reimer and Wilbert Reimer claim that the tales of Thales were recorded by Aesop and Plato. These facts suggest that the Reimers contributed to the fabrication of a fictional account surrounding Thales, and indicate that they firmly believe that the story of Thales and salt originated from Aesop.

In short, though Eves, Burton and Reimers argued that the tale of Thales transporting salt with mules or donkeys originated from Aesop, none of them provided any reliable evidence. There is no doubt that their conclusion is not entirely plausible. In fact, Aesop’s Fables is a collection of fictional tales, and thus lacks historical authority. The story of “The Ass and His Burdens” found in Aesop’s Fables significantly differs from the account of Thales transporting salt with mules, and there is even no evidence to suggest any connection between the two. Furthermore, no historians of mathematics prior to the mid-20th century had proposed such a view. At that time, the most influential scholars in history of mathematics, such as, Cantor, Cajori, Heath et al. all have not mentioned the story of Thales transporting salt with mules or donkeys in their mathematical history works when introducing the anecdotes of Thales. These facts indicate that none of them agree with the authenticity of Thales’ tale of transporting salt with mules or donkeys. Contemporary serious works on history of mathematics rarely reference the views proposed by them, which traced the origin of the story to Aesop.

Regarding the origin of Thales’ anecdote of using mules to transport salt, the British historian of mathematics Gow (1884) [12] believes it originated from Plutarch or Aristotle, while the American mathematician Eves (1990) [28] holds that it originated from Aesop. In addition to these two viewpoints, some scholars mentioned the tale in the works on history of mathematics, but did not provide any source of the story.

In 1929, British mathematician Herbert Turnbull (1885-1961) published a work on the history of mathematics titled The Great Mathematicians. When introducing the ancient Greek mathematician Thales, Turnbull presented a story of Thales transporting salt with mules:

“It is said that Thales was once in charge of some mules, which were burdened with sacks of salt. Whilst crossing a river one of the animals slipped; and the salt consequently dissolving in the water, its load became instantly lighter. Naturally, the sagacious beast deliberately submerged itself at the next ford, and continued this trick until Thales hit upon the happy expedient of filling the sack with sponges! This proved an effectual cure.” ([32]: p. 4)

Turnbull does not provide the source of the story, and there is no source of the story even in the fourth edition in 1951. In this tale, Turnbull said that Thales had the mule transport “sponges”, but his British compatriots Gow and Ball said Thales had the mule transport “rags and sponges”. The comparison shows that the storylines are not exactly the same. Turnbull was a British mathematician, and was born more than thirty years later than his British compatriots Gow and Ball. It is highly probable that he referenced their works. Indeed, Turnbull explicitly recommends Ball’s work for further reading in his book. The story of Thales transporting salt with mules, introduced by Turnbull, may stem from Ball, but the storyline of the tale has already been refined. For instance, the plot of the story where Thales punished the sly mule by having it carry rags was removed. In fact, whether in the East or the West in ancient times, the cloth used to make clothes was a precious commodity, and usually expensive, the scraps of cloth or rags could not be obtained and disposed of at will.

American mathematics educator Vera Sanford (1891-1971) was likely the forerunner to introduce the story of Thales using mules to transport salt to United States. She published a book on the history of mathematics in 1930, in which she recounted the story of Thales transporting salt with mules:

“It is also reported that he [Thales] had a pack-mule that had discovered that rolling over in the stream which it crossed lightened its usual burden of salt. Thales determined to break the mule of this bad habit, so he ordered a load of sponges to be substituted for the salt. Apparently, the cure was effective.” ([33]: p. 6)

Unfortunately, Sanford did not provide the source of the story. Upon comparison, however, it is evident that the story Sanford recounts closely mirror the version presented by Turnbull. Sanford had referenced Ball’s work, yet the narrative she stated did not include mention of “rags” either. The story of Thales transporting salt with mules, introduced by American mathematician George Simmons (1925-2019) in Calculus Gems:Brief Lives and Memorable Mathematics, bears striking similarity to the narrative presented in Turnbull’s edition, though he provided no reference [34]. But William Dunham, an American historian of mathematics, presents an alternative account of the story about Thales and donkey transporting salt. In 1990, Dunham published Journey Through Genius:TheGreat Theorems of Mathematics, and recounted the story of Thales in this book:

“A similar impression emerges from the story of a farmer who routinely tied heavy bags of salt on the back of his donkey when driving the beast to market. The clever animal quickly learned to roll over while fording a particular stream, thereby dissolving much of the salt and making his burden far lighter. Exasperated, the farmer went to Thales for advice, and Thales recommended that on the next trip to market the farmer load the donkey with sponges.” ([35]: pp. 6-7)

In the story told by Dunham, it was not a mule but a donkey that transported salt, and it was not Thales but a farmer who transported salt using a donkey. Dunham tells of a farmer driving a donkey to the market to sell salt, not Thales driving a donkey to the market to sell salt. This story is not about the anecdotes of Thales’ business dealings, but rather a tale related to Thales. It is clear that Dunham’s story of Thales and salt is completely different from that of previous scholars. It could neither directly come from Plutarch or Aristotle, nor from Aesop. Dunham referenced the works of Burton and Eves but did not concur with their assertion regarding the origin of the story of Thales. Of course, it is entirely possible that Dunham adapted his account of Thales and salt from their versions of the story.

American mathematician Michael Bradley introduced a similar story of Thales and salt in his work The Birth of Mathematics:Ancient Times-1300 in 2006, which embellishing with numerous fabricated details, such as workers digging salt out of the salt mine, mules carrying sacks of salt several miles to the seashore, workers asking doctors to examine the donkey, etc. [36]. Moreover, what Bradley told was not the story of Thales transporting salt with mules or donkeys, but rather a story of Thales helping workers who transported salt with donkeys punish a cunning donkey. This differs from the account of Thales transporting salt with mules mentioned in early works on the history of mathematics. These facts demonstrate that the fictional elements within the narrative of Thales transporting salt with mules have become increasingly pronounced with the passing of time.

After introducing the achievements and anecdotes of Thales, Bradley provided some further readings. These readings include the aforementioned writings of Turnbull and Reimers. Without a doubt, the story of Thales and salt in Bradley’s work stems from these writings, especially from Mathematicians are People,Too: Storiesfrom theLivesofGreat Mathematicians, despite the two story is not exactly the same. In fact, Bradley was well aware that the story of Thales and salt told by Reimers involved a great deal of fictional storylines. However, he still introduced this anecdote of Thales in his works on the history of mathematics. Bradley wrote clearly that some of these stories about Thales may not be true, but he didn’t care whether the tale was true or not, let alone clarify the origin of the story. These findings deserve special vigilance from the academic and educational communities in the process of writing and popularizing Thales’ scientific contributions and anecdotes.

In 2009, German historian and philosopher Georg Wöhrle published a book in German titled Die Milesier: Thales, which is alleged to present all the known testimonies on Thales in the original languages, including Greek, Latin, Arabic and Persian [37]. Later, Richard McKirahan translated it into English in 2014, and supplemented additional testimonies. There is no doubt that Wöhrle’s work is the most complete collection of testimonies on Thales. In this work, Wöhrle (2014) recounted the story of Thales and salt, yet what he described was not the story of Thales but rather that of others transporting salt using mules, and said that when Thales heard the story, Thales told the men to use “wool and sponges” instead of salt to discipline the crafty mule [37]. Although Wöhrle claimed to provide the original literature of Thales’ story on using mules to transport salt in his book, he neither mentioned that the story originated from Plutarch or Aristotle nor from Aesop. This means that none of the above views about the origin of the story of Thales transporting salt with mules are convincing. Furthermore, the authenticity of the original documents Wöhrle refers to is likely questionable. The reason is that previous distinguished scholars on history of Greek mathematics and science, such as Heath, Sarton, Neugebauer et al., never mentioned this story or these original documents, and not even historians of mathematics once mentioned Thales using “wool” to discipline the cunning mule.

In fact, little is known about the lives of Thales in academic communities. The renowned American historian of mathematics Carl Boyer (1906-1976) admitted publicly that Thales left no reliable historical documents, and stated that Thales was once a salt merchant, but didn’t give a detailed account of the story of Thales transporting salt with mules in his mathematical history works [38]. However, this view was removed in the 3rd edition when Uta Merzbach (1933-2017) revised it in 2011. Obviously, Merzbach is a more rigorous historian of mathematics than Boyer, and he completely disbelieved the truth of the story about Thales transporting salt with mules. As for the authenticity of the stories about Thales, distinguished American historian of mathematics Victor Katz wrote clearly that: “Whether this [the tale of Thales’ monopoly of oil presses] or any of the other stories is literally true is not known.” ([24]: p. 44) He didn’t provide any information about the story of Thales and salt in his work, even in the 3rd edition in 2009. Monographs focused on Thales, such as Rossetti (2022) [39] and O’Grady (2016) [40], provide an in-depth account of his achievements and anecdotes. However, they also did not mention the story of Thales and salt at all. These facts demonstrate that rigorous historians of mathematics hardly cite the story in their works, and the reason for this is the absence of reliable evidence supporting the story of Thales transporting salt with mules.