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Authors: Mario Livio
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almost unmatched reputation and authority as a scholar. After all, this was the man who laid out the foundations for much of Western intellectual culture. Whether it was the investigation of all natural phenomena or the bedrock of ethics, metaphysics, politics, or art, Aristotle literally wrote the book. And that was not all. Aristotle in some sense even taught us how to think, by introducing the first formal studies of logic. Today, almost every child at school recognizes Aristotle’s pioneering, virtually complete system of logical inference, known as a syllogism:
Every Greek is a person.
Every person is mortal.
Therefore every Greek is mortal.
The third reason for the incredible durability of Aristotle’s incorrect theory was the fact that the Christian church adopted this theory as a part of its own official orthodoxy. This acted as a deterrent against most attempts to question Aristotle’s assertions.
In spite of his impressive contributions to the systemization of deductive logic, Aristotle is not noted for his mathematics. Somewhat surprisingly perhaps, the man who essentially established science as an organized enterprise did not care as much (and certainly not as much as Plato) for mathematics and was rather weak in physics. Eventhough Aristotle recognized the importance of numerical and geometrical relationships in the sciences, he still regarded mathematics as an abstract discipline, divorced from physical reality. Consequently, while there is no doubt that he was an intellectual powerhouse, Aristotle does not make my list of mathematical “magicians.”
I am using the term “magicians” here for those individuals who could pull rabbits out of literally empty hats; those who discovered never-before-thought-of connections between mathematics and nature; those who were able to observe complex natural phenomena and to distill from them crystal-clear mathematical laws. In some cases, these superior thinkers even used their experiments and observations to advance their mathematics. The question of the unreasonable effectiveness of mathematics in explaining nature would never have arisen were it not for these magicians. This enigma was born directly out of the miraculous insights of these researchers.
No single book can do justice to all the superb scientists and mathematicians who have contributed to our understanding of the universe. In this chapter and the following one I intend to concentrate on only four of those giants of past centuries, about whose status as magicians there can be no doubt—some of the crème de la crème of the scientific world. The first magician on my list is best remembered for a rather unusual event—for dashing stark naked through the streets of his hometown.
Give Me a Place to Stand and I Will Move the Earth
When the historian of mathematics Eric Temple Bell had to decide whom to name as his top three mathematicians, he concluded:
Any list of the three “greatest” mathematicians of all history would include the name of Archimedes. The other two usually associated with him are Newton (1642–1727) and Gauss (1777–1855). Some, considering the relative wealth—or poverty—of mathematics and physical science in the respective ages in which these giants lived, and estimating their achievements against the background of their times, would put Archimedes first.
Archimedes (287–212 BC; figure 10 shows a bust claimed to represent Archimedes, but which may in fact be that of a Spartan king) was indeed the Newton or Gauss of his day; a man of such brilliance, imagination, and insight that both his contemporaries and the generations that followed him uttered his name in awe and reverence. Even though he is better known for his ingenious inventions in engineering, Archimedes was primarily a mathematician, and in his mathematics he was centuries ahead of his time. Unfortunately, little is known about Archimedes’ early life or his family. His first biography, written by one
Every Greek is a person.
Every person is mortal.
Therefore every Greek is mortal.
The third reason for the incredible durability of Aristotle’s incorrect theory was the fact that the Christian church adopted this theory as a part of its own official orthodoxy. This acted as a deterrent against most attempts to question Aristotle’s assertions.
In spite of his impressive contributions to the systemization of deductive logic, Aristotle is not noted for his mathematics. Somewhat surprisingly perhaps, the man who essentially established science as an organized enterprise did not care as much (and certainly not as much as Plato) for mathematics and was rather weak in physics. Eventhough Aristotle recognized the importance of numerical and geometrical relationships in the sciences, he still regarded mathematics as an abstract discipline, divorced from physical reality. Consequently, while there is no doubt that he was an intellectual powerhouse, Aristotle does not make my list of mathematical “magicians.”
I am using the term “magicians” here for those individuals who could pull rabbits out of literally empty hats; those who discovered never-before-thought-of connections between mathematics and nature; those who were able to observe complex natural phenomena and to distill from them crystal-clear mathematical laws. In some cases, these superior thinkers even used their experiments and observations to advance their mathematics. The question of the unreasonable effectiveness of mathematics in explaining nature would never have arisen were it not for these magicians. This enigma was born directly out of the miraculous insights of these researchers.
No single book can do justice to all the superb scientists and mathematicians who have contributed to our understanding of the universe. In this chapter and the following one I intend to concentrate on only four of those giants of past centuries, about whose status as magicians there can be no doubt—some of the crème de la crème of the scientific world. The first magician on my list is best remembered for a rather unusual event—for dashing stark naked through the streets of his hometown.
Give Me a Place to Stand and I Will Move the Earth
When the historian of mathematics Eric Temple Bell had to decide whom to name as his top three mathematicians, he concluded:
Any list of the three “greatest” mathematicians of all history would include the name of Archimedes. The other two usually associated with him are Newton (1642–1727) and Gauss (1777–1855). Some, considering the relative wealth—or poverty—of mathematics and physical science in the respective ages in which these giants lived, and estimating their achievements against the background of their times, would put Archimedes first.
Archimedes (287–212 BC; figure 10 shows a bust claimed to represent Archimedes, but which may in fact be that of a Spartan king) was indeed the Newton or Gauss of his day; a man of such brilliance, imagination, and insight that both his contemporaries and the generations that followed him uttered his name in awe and reverence. Even though he is better known for his ingenious inventions in engineering, Archimedes was primarily a mathematician, and in his mathematics he was centuries ahead of his time. Unfortunately, little is known about Archimedes’ early life or his family. His first biography, written by one
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