If Newton was a genius, Leibniz, who was a contemporary of Newton and had a lot of grudges, must also be a genius.
Born in Germany in 1646, Leibniz was three years younger than Newton, but the family economy was much better than Newton's. Therefore, Leibniz's enlightenment education is still quite complete, when he was 8 years old, he read two Latin works, and then taught himself a lot of knowledge, among children of the same age, it is definitely the most outstanding one.
Newton PK Leibniz
At this time, a friend who had a good relationship with Leibniz's parents discovered Leibniz's talent and suggested to Leibniz's family that he be allowed to go to his father's library to read. Leibniz was nowhere to be found, and in just a few years he had read almost every field of knowledge.
The age of 15 was a dividing point in Leibniz's reading. Before the age of 15, in his own later words, his interest was completely captured by the "ancients", that is, before the age of 15, he read books by ancient Greek and Roman writers; after the age of 15 he began to read "contemporary" works, that is, the more popular philosophical and theological works of the time.
Why is 15 a bookish for Leibniz? This is because at the age of 15, he officially entered the university. Newton was 19 when he was in college, two years older than the average age, and Leibniz, on the contrary, was two years younger than the average age.
In 1661, at the age of 15, Leibniz entered the University of Leipzig to study philosophy, and later took a course in law, after which he continued his studies at the University of Leipzig, and by the time he was 20 years old, he had completed his juris doctorate.
Leibniz
However, the leaders of the University of Leipzig are more unenlightened, they think that this little child named Leibniz is too young, others have almost thirty doctorates, you are only twenty years old, what kind of system is this?
Therefore, the University of Leipzig refused to give him a doctorate in law. An indignant Leibniz then transferred to the University of Altdorf for further studies, where he received his Juris Doctor degree the following year.
Therefore, from the perspective of our modern people, Leibniz is undoubtedly a thorough prodigy, much stronger than the "junior class" in many universities in our country.
Why do we dare to be so sure? In fact, there are very good reasons: leibniz, as an adult, has achieved great achievements in mathematics, physics, political science, law, ethics, theology, philosophy, history, linguistics, mining, etc., and is a rare generalist in history, and even many people call him Aristotle in the seventeenth century.
In the era we are now living in, such talents are really very few, not to mention prodigies with generalist qualities.
Of course, I would like to introduce you to his contribution to mathematics.
Leibniz's first contribution to mathematics was the creation of calculus.
Regarding the definition of calculus, in fact, we also made some introductions in the previous lesson, in simple terms, calculus is actually a mathematical method for calculating the slope and area of the curve, and we will use calculus knowledge when calculating the speed, acceleration, length, volume, area, maximum and minimum values and other related functions.
As we have already said, in 1687, when Newton published his book, The Mathematical Principles of Natural Philosophy, in which Newton systematically expounded his own calculus ideas. Unfortunately, however, leibniz had published the theory of calculus as early as 1684.
At this point, of course, Newton was unwilling, so he said that Leibniz was plagiarized. Why? First, Newton had developed the theory of calculus twenty years earlier, but for various reasons it had not been published; secondly, Leibniz had also been to London in 1673, and had maintained good contact with the Royal Society since then, and had exchanged letters with Newton himself for some time.
Therefore, There is a certain reason why Newton and British scholars insist that Leibniz plagiarized Newton's academic achievements.
Newton
However, as a genius and great man of Newton's contemporaries, Leibniz was also qualified to create calculus in terms of talent. And his calculus theory is a little more "advanced" than Newton's theory. This is mainly reflected in the use of symbols: leibniz's use of the differential symbols dx, dy, and the integral symbol ∫ he used in his 1686 paper, are very simple to express and easy to use, so they have been used by us until now.
For example, the current indefinite integral that we are currently passing, its definition is: if the function f(x) has a primitive function F(x) on an interval I, then F(x)+C (C is an arbitrary constant) is f(x) the indefinite integral on the interval, which is denoted as ∫f(x) dx. The expression we use now is actually Leibniz's contribution.
Newton's calculus theory uses the "flow number symbol", and what this symbol looks like cannot be found on the Internet now, because this expression is a little more complicated and has been deprecated for hundreds of years.
But we cannot say that Newton's theory of calculus was worse than Leibniz's, because Newton's theory of calculus, because it was used by him in physics, did not exist merely as a theory, but showed people many practical values.
Therefore, we now generally believe that Newton's calculus theory was more accomplished, and Leibniz's calculus theory is more acceptable.
calculus
However, the British at that time could not accept that the Germans had also developed a set of calculus theories, so the British generally believed that Leibniz plagiarized Newton's theory, and even the Royal Society of England investigated the matter, believing that Leibniz was suspected of plagiarism.
So after that, some more interesting phenomena occurred: the British scholars and the European continent, especially the German scholars, completely fell out, and the British felt that you Germans liked plagiarism so much, well, then we will go our separate ways in the future, and cut off academic exchanges.
Therefore, while scholars on the European continent are using the simpler and more convenient "Leibniz" calculus, British scholars are still willfully continuing to use "Newton" calculus. This is actually a certain degree of "closed country", so in this way, the United Kingdom originally led the theoretical science and applied science, and gradually was overtaken by continental European countries such as France and Germany.
Neither Newton nor Leibniz may have imagined that their dispute would have had such an impact on the academic development of Europe. But in any case, the creation of calculus heralds the opening of a new world of mathematics in the new century.
In addition to calculus, Leibniz's second contribution to mathematics was the creation of binary.
Binary is to use 0 and 1 as the basic symbols, we are now in daily life to calculate accounts or learn mathematics, using decimal, but in the computer field, generally use binary. Therefore, Leibniz's binary actually had a huge impact on the invention and use of computers.
Leibniz received the article
There is also a theory that Leibniz's binary ideas actually come from the Chinese ideas of "yin" and "yang", because Leibniz himself is actually a lover of Chinese culture, "Zhou Yi" and Bagua theory, he was exposed to. What the specific situation is, it is difficult to verify now, but there is no doubt that binary has affected modern people's lives.
Okay, finally, let's make a brief assessment of Leibniz.
Like Newton, Leibniz was a genius, a generalist, and the two were very good at many interdisciplinary disciplines such as philosophy, mathematics, and physics. Although the two were unhappy because of calculus, at the time, these two people were definitely the "gemini stars" of the scientific theory community, and both of them made great contributions to the subsequent development of science.
The two kings of higher mathematics
After the relationship between Newton and Leibniz broke down, Leibniz still gave Newton a high evaluation: in all mathematics from the beginning of the world to the time of Newton's life, Newton worked more than half. From here, we can also see that Leibniz is still quite open-minded.
Now three hundred years later, our rockets, spaceships, computers and other high-tech are actually supported by the theories of these two people. We can have such a good life, absolutely indispensable to the efforts of these two geniuses three hundred years ago.