Opinionated History of Mathematics
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History of mathematics research with iconoclastic madcap twists.Read more »
History of mathematics research with iconoclastic madcap twists.
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Historiography of Galileo’s relation to antiquity and middle ages
Dec 3
·
35 minutes
Our picture of Greek antiquity is distorted. Only a fraction of the masterpieces of antiquity have survived. Decisions on what to preserve were made by in ages of vastly inferior intellectual levels. Aristotelian philosophy is more accessible for mediocre minds than advanced mathematics and science. Hence this simpler part of Greek intellectual achievement was eagerly pursued, while technical works were neglected and perished. The alleged predominance of an Aristotelian worldview in antiquity is an illusion created by this distortion of sources. The “continuity thesis” that paints 17th-century science as building on medieval thought is doubly mistaken, as it misconstrues both ancient science and Galileo’s role in the scientific revolution.
Transcript
To praise Galileo is to criticise the Greeks. The contrast class of “Aristotelian” science is constantly invoked to explain Galileo’s alleged greatness, both in Galileo’s own works and in modern scholarship. But this narrative gets it all wrong, in my opinion. It is based on a caricature of Greek science that effectively ignores the Greek mathematical tradition.
Francis Bacon put it well: when “human learning suffered shipwreck” with the death of the classical world, “the systems of Aristotle and Plato, like planks of lighter and less solid material, floated on the waves of time and were preserved,” while treasure troves of much more mathematically advanced works were lost forever.
Aristotelian science is not the pinnacle of Greek scientific thought. Far from it. It is not the best part of Greek science, but the part of Greek science that was most accessible and appealing to the generations of mathematically ignorant people who populated the universities in medieval Europe for hundreds of years. And perhaps some generations who still do.
Mathematicians have always felt differently. “So many great findings of the Ancients lie with the roaches and worms,” said Fermat. They are lost, in other words, these mathematical masterpieces that once existed. That’s how Fermat put it, and all his mathematical colleagues agreed. And they were right.
In the 20th century a few such masterpieces were recovered. So these 17th-century mathematicians were proven right in their intuition that great works were forgotten and hidden away among “roaches and worms” indeed.
In 1906, a work of Archimedes that had been lost since antiquity was rediscovered in a dusty Constantinople library. The valuable parchment on which it was written had been scrubbed and reused for some religious text. But the original could still just about be made out underneath it. As one historian put it: “Our admiration of the genius of the greatest mathematician of antiquity must surely be increased, if that were possible,” by this “astounding” work, which draws creative inspiration from the mechanical law of the lever to solve advanced geometrical problems. If even this brilliant work by antiquity’s greatest ...
Read more »
Our picture of Greek antiquity is distorted. Only a fraction of the masterpieces of antiquity have survived. Decisions on what to preserve were made by in ages of vastly inferior intellectual levels. Aristotelian philosophy is more accessible for mediocre minds than advanced mathematics and science. Hence this simpler part of Greek intellectual achievement was eagerly pursued, while technical works were neglected and perished. The alleged predominance of an Aristotelian worldview in antiquity is an illusion created by this distortion of sources. The “continuity thesis” that paints 17th-century science as building on medieval thought is doubly mistaken, as it misconstrues both ancient science and Galileo’s role in the scientific revolution.
Transcript
To praise Galileo is to criticise the Greeks. The contrast class of “Aristotelian” science is constantly invoked to explain Galileo’s alleged greatness, both in Galileo’s own works and in modern scholarship. But this narrative gets it all wrong, in my opinion. It is based on a caricature of Greek science that effectively ignores the Greek mathematical tradition.
Francis Bacon put it well: when “human learning suffered shipwreck” with the death of the classical world, “the systems of Aristotle and Plato, like planks of lighter and less solid material, floated on the waves of time and were preserved,” while treasure troves of much more mathematically advanced works were lost forever.
Aristotelian science is not the pinnacle of Greek scientific thought. Far from it. It is not the best part of Greek science, but the part of Greek science that was most accessible and appealing to the generations of mathematically ignorant people who populated the universities in medieval Europe for hundreds of years. And perhaps some generations who still do.
Mathematicians have always felt differently. “So many great findings of the Ancients lie with the roaches and worms,” said Fermat. They are lost, in other words, these mathematical masterpieces that once existed. That’s how Fermat put it, and all his mathematical colleagues agreed. And they were right.
In the 20th century a few such masterpieces were recovered. So these 17th-century mathematicians were proven right in their intuition that great works were forgotten and hidden away among “roaches and worms” indeed.
In 1906, a work of Archimedes that had been lost since antiquity was rediscovered in a dusty Constantinople library. The valuable parchment on which it was written had been scrubbed and reused for some religious text. But the original could still just about be made out underneath it. As one historian put it: “Our admiration of the genius of the greatest mathematician of antiquity must surely be increased, if that were possible,” by this “astounding” work, which draws creative inspiration from the mechanical law of the lever to solve advanced geometrical problems. If even this brilliant work by antiquity’s greatest ...
Read less