Can we become mathematicians by way of self-study? (Part 1)

In the early 19th century, mathematical genius Évariste Galois, who gave birth to abstract algebra, the foundations of many modern sciences such as computer science, cryptography and self-learning to 12 years old came to school.

Now, in the modern context: the internet explodes, the models of home and online schools are becoming more and more popular, whether we can self-study math as those who went first, or have to go through formal training. is it possible to discover new mathematical horizons?

Please read the following series summarizing the relevant comments on Quora.com, one of the largest question and answer websites in the world.

Part 1: Famous self-taught mathematicians in history

People who open the road without a school

There are mathematicians who can't go to university because the university doesn't exist in their time.(Illustration).

According to math teacher Ally Zmijeski, there are too many people to list in the list of people who gave birth to mathematical building blocks.

These were the great mathematicians and thinkers of ancient times like Archimedes, Pythagoras. And they are the creators of math taught in today's universities. Ally didn't mean to say that all the people of the past didn't go to school, just that they worked with a more narrow mathematical perspective than today.

There are mathematicians who can't go to university because the university doesn't exist in their time. Before having a systematic education, mathematicians made important contributions to pure mathematics by observing and trying to understand the patterns in their world.

Leonardo Fibonacci (1170-1250) - many people are honored as the best Western mathematician in the medieval times - a long time ago from a university. At that time, even without a printer, his books were all manuscripts.

Fibonacci is the person who defines the infinite Fibonacci number but the next number is equal to the previous two numbers. The Fibonacci sequence helps us create many different size squares. And by connecting different points inside the square, we will have spiral rings that simulate many natural phenomena like human ears, flower buds in flower pots, bodies of insects walking around. Your backyard . Fibonacci numbers have become a very useful pattern in understanding the natural world.

A spiral represents the Fibonacci number sequence: 2,3,5,8,12,21,34 . (5 = 2 + 3, 8 = 5 + 3 .).

A sample of Fibonacci numbers in natural rose petals.(Photo: Odyssey).

400 years after Fibonacci is Pierre de Fermat (1607-1665), there was a university but Fermat studied civil law, acting as a lawyer and a government official. Although Fermat was an amateur mathematician, Fermat excelled in this field, being one of the two largest mathematicians in the first half of the 17th century. He was well known for Fermat's last theorem that caused mathematicians to headache over 400 years, until Andrew Wiles found a complete proof of this theorem in 1995.

Fermat was the one who gave birth to the theory of probability (along with Pascal), number theory, found extremely small quantities, equations and rules describing the number of elements and works that are very useful today. in the field of online data encryption, a complex field (for example, how your credit card information is not stolen every time you make an online shopping transaction). Fermat's theories also expanded into differential and geometrical calculations clearly in the construction of tangles and orbits, and latent in the way his theories supported Gauss's later works. and Newton.

Pierre de Fermat (1607-1665).

Geniuses don't come to school

When higher education is more popular, the list of self-taught mathematicians continues to grow. According to a former teacher, thinkers, scientists or mathematicians become self-learners for many different reasons and experience many different situations. It can be said that some famous mathematicians are mainly self-taught, not going to formal schools as below.

Mathematician, British physicist George Green (1793-1841) only went to school one year at 8 years old, the rest were completely self-taught.

It is not until the age of 40, 5 years after the publication of the Essay on the Application of electricity analysis and electricityism (Essay on the application of mathematical calculus in electric and magnetic theories) in 1828, Green. decided to go to Cambridge University to study mathematics on the advice of Sir Edward Bromhead. Green's essay is the basis for the fundamental mathematical theory of electricity in the 20th century. Green is the contributor to the expansion of electrical and magnetic calculations by Siméon-Denis Poisson, setting out Green's theorem and art. language, voltage (potential), a useful tool in developing electric and magnetic laws.

French mathematician and physicist Siméon-Denis Poisson lived at the same time as Green, who had many contributions to the application of mathematics to physics and mechanics such as magnetic and static theory.

Indian mathematician Srinivasa Ramanujan (1887 - 1920) twice dropped out of college the first year. Because he was too focused on math, his other subjects were too poor.

Ramanujan's mathematical aptitude revealed from a young age: 13 years old discovered his own complex theorems after mastering a 16-year-old advanced trigonometric book, thoroughly studied 5000 theorems in a math book. summarizing the basic content of printed mathematics in 1886. With nearly 3900 research results mainly on equations and identities, he is considered one of the few mathematical geniuses in centuries. His contributions are extremely important and very valuable in mathematics. Ramanujan was pictured on the stamp of the Indian government in 1996, 2011, 2012 and 2016.

A very famous discovery of Ramanujan, the number 1729 called Hardy-Ramanujan, is the smallest number that can represent the sum of two cubes in two different ways. Hardy-Ramanujan is a compound name between Ramanujan and Godfrey Herald Hardy, a famous English mathematician. Hardy helped Ramanujan gain a bachelor's degree in research from Cambridge University (equivalent to his doctorate today) in 1916 and introduce Ramanujan's works to international experts.

Indian math genius Srinivasa Ramanujan on this country's stamp.

Blaise Pascal (1623-1662), often known by students in high school as the first to invent mechanical computers and applications of Pascal's triangle when developing the coefficient of powers of binomial a + b.

Although Pascal had only studied himself under the guidance of his father, not to school, Pascal was famous as a prodigy from a young age: 16 years old proved a difficult geometry problem (Pascal's theorem) and built a computer to give his father at the age of 19, then was recognized as a capable physicist at the age of 20. With mathematics, apart from mechanical computers, he also made a significant contribution in two fields: projection geometry (projective geometry) and probability theory. Along with Pierre de Fermat, Pascal was the one who gave birth to the theory of probability, a theory that had a great influence on the development of modern economics and social sciences.

Pascal's Triangle.

The list of famous self-taught mathematicians also has names like:

• Évariste Galois (1811-1832), a French math genius, came up with a group theory, the father of abstract algebra is the basis for many modern sciences such as computer science, cryptographic theory and coding. .
• Hua LuoGeng or Hua La Canh (1910-1985), a famous Chinese mathematician for theory, math education, wrote many classic books on mathematics.
• Zhang YiTang or Zhang Ich Tang (born 1956), a Chinese-American mathematician, world famous since 2013 after being the first to prove the biggest distance between two consecutive prime numbers is 70 million.

Galois educated himself with the help of his father from the age of eleven to 11 years old to attend high school, Hua Lougeng was unfinished to attend high school because of poverty, and Zhang YiTang to 23 years old entered university.

Two famous Chinese mathematicians Hua LuoGeng (left) and Zhang YiTang (right).

The secret formula of all mathematicians learning in their own lesson is "reading the masters" (Read from the Masters) . All of them are always obsessed with mathematical beauty, have a strong curiosity in finding the mystery of truth, often read, think and solve problems.

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