Not all mathematicians have the chance to be born in a developed county. many are born in underdeveloped countries and never get the chance to participate in math Olympiads, receive special training, have their school work adapted to their needs, entering university at a young age, and participate in research internships. Can mathematicians with no special training compete with the mathematicians that have received special training? Can this disadvantage be surpassed? How much influence to all the factors stated above have?
The highest achievements in mathematics are not related to the country of origin, social standing or any specific education just to recall Galois and Ramanujan
https://mathshistory.st-andrews.ac.uk/Biographies/Galois/
https://mathshistory.st-andrews.ac.uk/Biographies/Ramanujan/
Dear Janusz Pudykiewicz ,
Ramanujan was a genius, however, recall that Ramanujan’s genius as well as his work would have been lost if he did not write a letter to Hardy and if Hardy did not invite him to England to Cambridge. Also before going to England, Ramanujan did not know how to prove any of his theorems and would have never been able to publish any of his work. If Ramanujan stayed in his country of origin, no one would have known who he was and no one would have known anything about his work. Ramanujan spent the first 22-24 years of his life reinventing well know theorems. Also Ramanujan’s death at 32 is somewhat linked to the conditions in his country of origin. Your country of residence has a very begin impact.
Dear Roudy El Haddad
Mathematical genius defies all classifications, although early private lessons can have a colossal impact on the development of talent, particularly if you consider for example
János Bolyai
https://mathshistory.st-andrews.ac.uk/Biographies/Bolyai/
and
Sofia Kovalevskaja
https://mathshistory.st-andrews.ac.uk/Biographies/
Perhaps , Jacobi and Ramanujan provide good examples mathematics need no special training. Because problem solving abilities and intuition can't be systematically teach it to humans.
Meeting the Teacher on time is critical. The teacher should be understood in a broad sense. The infrastructure only increases the likelihood of a meeting.
Michael Faraday
Charles Steinmetz
Nikola Tesla
Just a few of the mathematician/scientists who lacked a higher education.
Mas allá de la formación tradicional o los que tienen una formación especial, eso fue debido a las circunstancias de vida que estuvieron presentes en el momento en que los mismos iniciaron sus estudios matemáticos. Ahora que luego de graduados sigan bajos los esquemas tradicionales va a ser una decisión del matemático, como cualquier otro profesional, a sabiendas que la realidad de la educación hoy por hoy nos exigen a los docentes a salir de nuestros esquemas. Mi formación en pregrado pudiera ubicarse como "especial" pues es en el arte, que suele tomarse como un complemento especial para cualquier otra rama. En estos tiempos me ha tocado hacerme de herramientas tecnológicas para adaptarme a lo que la realidad nos pide.
Siempre resalto lo importante que es el arte en la vida, pero mas allá de ello es lo importante que para un profesional es ser mejor en su rama pero también indagar, buscar y apropiarse de otros conocimientos, nutrirse de otras especialidades para ser mejor en la propia. Ver más allá del borde de la página nos hará mejores en nuestras profesiones, cualquiera que fuera.
Dear Roudy El Haddad and Readers,
In order to fully appreciate all elements of creativity in mathematics I always recommend the analysis presented in a well known book by A. Borovik:
“Mathematics Under the Microscope: Notes on Cognitive Aspects of Mathematical Practice“
Even after a brief encounter with this book we will see that the basic training in mathematics should start early in life, although there are always fantastic and spectacular cases of mathematical contributions that are not easy to explain.
For some additional information about the book please kindly consult:
https://euro-math-soc.eu/review/mathematics-under-microscope-notes-cognitive-aspects-mathematical-practice
As far as the the initial contact of Ramanujan with the western mathematics is concerned please consider that he obtained one of the best possible sources of knowledge to support his studies. According to S. Wolfram:
“While in high school Ramanujan had started studying mathematics on his own—and doing his own research (notably on the numerical evaluation of Euler’s constant, and on properties of the Bernoulli numbers). He was fortunate at age 16 (in those days long before the web!) to get a copy of a remarkably good and comprehensive (at least as of 1886) 1055-page summary of high-end undergraduate mathematics, organized in the form of results numbered up to 6165. The book was written by a tutor for the ultra-competitive Mathematical Triposexams in Cambridge—and its terse “just the facts” format was very similar to the one Ramanujan used in his letter to Hardy”
https://writings.stephenwolfram.com/2016/04/who-was-ramanujan/
I agree with Manoj Sithara mathematics is a living breathing subject that even the well trained seem to fail at capturing. Teachers who have an innate philosophy of interactivity and creativity bring the subject alive in real life situations. All in the process and not the product.
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