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Edit 1: I have received a lot of great answers. I am not accepting any answer because I think there might be in future that some user want to contribute any new answer, as in my opinion some users might find the answers useful to them to keep their head high in time of despair. Thank you very much to all!

I am a person living in a 3rd world country who has done a master's in mathematics and is preparing for grad school in math. Unfortunately, I fell into depression due to horrible harassment by 2 professors against which no action could be taken due to nepotism and corruption in my country, family issues and had to take a break. I don't get much support from my parents or friends as research in mathematics doesn't yield much money and there are a lot of other high paying jobs. I don't care much about their opinions. I live in a very very capitalistic country and people here respect only money. I like to study mathematics as I am very much interested in it. I am taking therapy and medications. I have realized that I need some motivating instances to help keep me going and so that I can motivate myself when I am low due to my depression.

It is my humble request to you to suggest books, websites, and/or blogs of real life instances of mathematicians overcoming challenges and hardships in life, both mathematical and non-mathematical.

I have been reading Men of Mathematics by E.T. Bell but it is mostly about mathematicians of older centuries, not the 20th and 21st centuries, although it's still very good read.

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    $\begingroup$ Not an answer, but might be useful: hsm.stackexchange.com/q/317/72 $\endgroup$ Dec 19, 2021 at 9:22
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    $\begingroup$ Lu Jiaxi seems to have struggled his whole life: en.wikipedia.org/wiki/Lu_Jiaxi_(mathematician) and probably Yitang Zhang: en.wikipedia.org/wiki/Yitang_Zhang $\endgroup$
    – StefanH
    Dec 19, 2021 at 14:51
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    $\begingroup$ Try to procure marketable math skills alongside with learning/doing pure mathematics. Good mathematicians are so wanted by places like google, meta, banks, etc. Work on your programming skills. Algorithm design is a math heavy branch of compute science which is utterly exciting. Look for companies like Databricks. Parallel computing is full of fancy mathematics and it gives you luxurious jobs. I am talking about 300 K USD per yr salaries. So be broad in your math learning and always remind your critical friends that you are going to make 300 K very soon in future :P $\endgroup$ Dec 19, 2021 at 18:15
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    $\begingroup$ @StefanH while I am glad about having heard about Lu Jiaxi from you, I think this story is the opposite of uplifting. Poor guy. $\endgroup$
    – lalala
    Dec 21, 2021 at 10:50
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    $\begingroup$ To people, who vote to close: gentlemen, I find this to be an important document of our era. In my opinion, it is a sin to destroy it. $\endgroup$ Dec 22, 2021 at 11:10

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The AMS published a book called Living Proof in which a number of mathematicians relate their own experience with overcoming adversity. Some of these are famous although most are ordinary mathematicians. The stories are equally inspiring. The book is available as a free download from the AMS.

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A good overview (including several mathematicians with an unusual background) is compiled by Nassim Nicholas Taleb at Bookauthority. Even without buying the books, the list may give you pointers to role models that could inspire you.

Women Who Count: Honoring African American Women Mathematicians could also be an inspiring read.

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The "Unreal Life of Oscar Zariski" by Carole Parikh is very inspiring.

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    $\begingroup$ I accidentally downvoted you. It won't let me change it. I really don't remember doing that though. Apologies. $\endgroup$ Dec 20, 2021 at 23:25
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Alexander Grothendieck was born the son of Russian anarchist Jew in Nazi Germany, was imprisoned in a concentration camp as a young stateless child, had to hide from the Nazis, lived as a miserable teenager with barely enough to scrape by and who had to support his permanently ill mother and became perhaps the most phenomenal mathematician of the second half of the 20th century. You can read about his life in the following links (whether he actually overcame the hardships of his young life remains unfortunately debatable).

https://mathshistory.st-andrews.ac.uk/Biographies/Grothendieck/

https://www.ams.org/notices/200808/tx080800930p.pdf

or

https://allary-editions.fr/products/alexandre-grothendieck-de-philippe-douroux

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Ramanunjan comes to mind. He produced extraordinary results despite living in absolute poverty. Also, during all of his short life he was sick very often.

Ramanujan failed his Fellow of Arts exam in December 1906 and again a year later. Without an FA degree, he left college and continued to pursue independent research in mathematics, living in extreme poverty and often on the brink of starvation.

Ramanujan was plagued by health problems throughout his life. His health worsened in England; possibly he was also less resilient due to the difficulty of keeping to the strict dietary requirements of his religion there and because of wartime rationing in 1914–18. He was diagnosed with tuberculosis and a severe vitamin deficiency, and confined to a sanatorium. In 1919 he returned to Kumbakonam, Madras Presidency, and in 1920 he died at the age of 32. After his death his brother Tirunarayanan compiled Ramanujan's remaining handwritten notes, consisting of formulae on singular moduli, hypergeometric series and continued fractions.

Ramanunjan - Wikipedia

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Here is an article (published in the proceedings of the Arizona Winter School 2007) written by Vladimir Berkovich. It contains his own account of the discovery of what are nowadays known as `Berkovich Spaces' in non-archimedean analytic geometry. Interspersed between mathematical explanations, Berkovich also tells about the hardships that he had to overcome during his life in the Soviet Union in the 1980s. Quote:

I was very lucky to be accepted to Moscow State University for undergraduate and, especially, for graduate studies in spite of the well-known Soviet policy of that time towards Jewish citizens. I finished studying in 1976, and got a Ph.D. the next year. (My supervisor was Professor Yuri Manin.) Getting an academic position would be too much luck, and the best thing I could hope for was the job of a computer programmer at a factory of agricultural machines and, later, at the institute of information in agriculture. As a result, I practically stopped doing mathematics, did not produce papers, and was considered by my colleagues as an outsider. It took me several years to become an expert in computers and nearby fields, and to learn to control my time. Gradually I started doing mathematics again, and my love for it blazed up with new force and became independent of surrounding circumstances. By the time my story begins, I was hungry for mathematics as never before.

And another quote:

My job occupied me five days per week from 8am till 5pm. It took me several years to learn to devote an hour or two to mathematics during working hours. Time free from my job belonged to my family, and when I was completely hooked on mathematics and an hour or two per day was not enough for it, I discovered an additional source of time. I learned to get up every day very early (often as early as at 2am), and thus extended the time for doing mathematics. At this time of the day, the world around me was quiet and fresh, nobody and nothing disturbed me, my head was clear, and I could plunge into another world to explore and describe it.

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A Beautiful Mind, 2001 film about John Nash

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Niels Abel surely deserves a mention here. Mario Livio gives a detailed account of his and Galois' lives, but unfortunately not of their mathematical results, in The equation that couldn't be solved. Abel came from a very poor background and was always short of money. The Norwegian government gave him money to travel Europe to meet Gauss and other prominent mathematicians of the day, but demanded that he repay it on his return to Norway. He died from tuberculosis at the age of 26, days before Crelle obtained a position for him as a professor in Berlin. (Galois was a hot-head who would inevitably have got himself killed one way or another.)

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    $\begingroup$ Abel's and Galois's Life has been mentioned in Men of Mathematics. $\endgroup$
    – Arnold
    Jan 13 at 8:53
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    $\begingroup$ @Arnold Men of Mathematics is a horrifically poor reference for historical facts. $\endgroup$ Apr 17 at 21:40
  • $\begingroup$ @Carl-FredrikNybergBrodda Are the stories exaggerated in that book? $\endgroup$
    – Arnold
    Apr 18 at 9:30
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    $\begingroup$ @Arnold Very much so. See e.g. the end of the Wikipedia article. Particularly the quote by Clifford Truesdell: "I now find the contents of that still popular book to be little more than rehashes enlivened by nasty gossip and banal or indecent fancy." is quite apt. $\endgroup$ Apr 18 at 11:27
  • $\begingroup$ @Carl-FredrikNybergBrodda Thanks for letting me know! $\endgroup$
    – Arnold
    Apr 18 at 12:44
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Similar to Rubus, Ramanunjan also came to mind when I saw this question.

However I thought I'd mention specifically that it has a film about him named "The Man Who Knew Infinity" (2015).

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  • $\begingroup$ Ramanujan is also mentioned in the answer by @Rubus. The film is (presumably) based on a book of the same title, by Robert Kanigel, originally published by Macmillan. $\endgroup$ Jan 5 at 21:39
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Tartaglia is another name that comes to mind. I do not have a list of books or articles, but I am sure a Google search would turn up some

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    $\begingroup$ Mario Livio's The equation that couldn't be solved, which I mentioned under Abel. also discusses Tartaglia. $\endgroup$ Jan 2 at 16:06

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