Sometimes I get a big surprise about those people who have done very important and significant results for science. There are several examples of these facts, so I will just show very few of them here. Examples that, in my opinion, were the result of a very first step: a strong desire to contribute for the science evolution. More than a motivation, this strong desire can guide you to compile and write all your ideas down in pages and pages, and doing it in a very ordered and logical way.
One of the very first examples is the book Elements from Euclid (Greek mathematician, 300 BC). Actually is not a single book about mathematics and geometry, but a treatise of 13 books: Books 1 to 4 are about plane geometry, books 5 to 10 deal with ratios and proportions, and books 11 to 13 deal with spatial geometry. There one can find a collections of definitions, postulates, theorems, and proofs. The word "element" was used to describe a theorem which helps to proof many other theorems. In the Greek language, the word "element" means the same as "letter". In this way, the theorems in Elements can be seen as "letters" in a language. In the images below see the original fragment of Elements (left) and the first English version in 1570 (center), pages from the first printed edition in 1482 (right).
What do you need to be isolated from the world, for many days, weeks or years, and work until the desperation to build one of the most important scientific books of the history?
Probably, somebody made this question to Sir Isaac Newton (English physicist and mathematician) after publishing his Principia Mathematica, written during 1685 and 1686 (yes, just in two years!!). The Principia states Newton's laws of motion, which form the foundation of classical mechanics. In this book, the Newton's law of universal gravitation and a derivation of Kepler's law of planetary motion are also included. See part of the Principia in the images below:
Probably, somebody made this question to Sir Isaac Newton (English physicist and mathematician) after publishing his Principia Mathematica, written during 1685 and 1686 (yes, just in two years!!). The Principia states Newton's laws of motion, which form the foundation of classical mechanics. In this book, the Newton's law of universal gravitation and a derivation of Kepler's law of planetary motion are also included. See part of the Principia in the images below:
What do you need to change the notion of counting and to create the notion of sizes of infinite in mathematics, and despite getting all kind of bad comments, you keep going into your thoughts and ideas, no matter the opinions, anything!!?
Probably, somebody made that question to Georg Cantor (Russian mathematician). Prior to Cantor, the definition of "the infinite" was a topic discussed more in philosophical than in mathematical conversations. By proving that there are (infinitely) many possible sizes for infinite sets, Cantor realized that set theory was not a trivial issue, and it needed to be studied. Set theory has come to play the role of a fundamenta theory in modern mathematics, in the sense that it interprets propositions about mathematical objects (for example, numbers and functions) from all the traditional areas of mathematics (like algebra, analysis, topology) in a single theory, and provides a standard set of axioms to prove or disprove them.
Talking about infinite, there is a fantastic and pedagogic TED talk explaining an example about dealing with infinite:
"The Hilbert's Paradox of the Grand Hotel":
http://ed.ted.com/lessons/the-infinite-hotel-paradox-jeff-dekofsky
These scientists were guided by a big entusiasm, an enormous energy, a strong motivation. None of these adjectives are easy to describe. There are for sure hundreds of other important and very interesting books in our history. I just mentioned very few examples. Again, there is not space here to include all of them...
See you around,
Jesus
Probably, somebody made that question to Georg Cantor (Russian mathematician). Prior to Cantor, the definition of "the infinite" was a topic discussed more in philosophical than in mathematical conversations. By proving that there are (infinitely) many possible sizes for infinite sets, Cantor realized that set theory was not a trivial issue, and it needed to be studied. Set theory has come to play the role of a fundamenta theory in modern mathematics, in the sense that it interprets propositions about mathematical objects (for example, numbers and functions) from all the traditional areas of mathematics (like algebra, analysis, topology) in a single theory, and provides a standard set of axioms to prove or disprove them.
Talking about infinite, there is a fantastic and pedagogic TED talk explaining an example about dealing with infinite:
"The Hilbert's Paradox of the Grand Hotel":
http://ed.ted.com/lessons/the-infinite-hotel-paradox-jeff-dekofsky
These scientists were guided by a big entusiasm, an enormous energy, a strong motivation. None of these adjectives are easy to describe. There are for sure hundreds of other important and very interesting books in our history. I just mentioned very few examples. Again, there is not space here to include all of them...
See you around,
Jesus