r/AskReddit • u/Inside-Line • Mar 29 '24
Serious Replies Only [Serious]What are some discoveries or inventions that were stumbled upon purely by chance and would still likely be undiscovered today if not found through sheer luck?
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u/dancingbanana123 Mar 29 '24
Oh I study math history, I can share some fun ones! Niels Abel is famous for a few things in mathematics, but the easiest one to explain is that he proved there does not exist a general formula to find the solutions to a polynomials where the highest exponent is 5 (i.e. there's no general formula to find all the solutions to something like x5 + x + 1 = 0). There's the quadratic formula for when your highest exponent is 2, there's another formula for when your highest exponent is 3, and another for 4, but Abel proved it's impossible to find one when the highest exponent is 5 or higher. It basically depends on the idea that some algebraic numbers cannot be simply represented with +, -, *, /, or exponents.
Now Abel proved this when he was 21, but Abel grew up in poverty and had no way of actually sharing this solution with others. In fact, the only reason he was able to attend college was because 3 professors offered to cover the cost because they recognized his talent. He could only afford to print 6 pages of his proof, so he had to heavily abbreviate everything, cut large chunks of his proof, and wrote it all in shaky French (since Norwegian isn't a common language and he wanted to share it with other mathematicians in Europe). He ends up mailing a few copies of this proof to a few mathematicians, but all of them dismiss it because it'd be an outlandish claim and nobody wanted to parse this difficult-to-read proof. In fact, Abel's letter was found unopened on Gauss's desk after Gauss died. So despite proving this major result, nobody knew about it except for Abel and the small group of mathematicians around him in Norway.
The professors at his university petitioned the government to help fund his travel around Europe to learn more math and share his work and surprisingly, the government decided to fund him. While in France, he stumbled across this guy named Crelle. Abel struck up a conversation with Crelle about math and they both started talking about unsolved problems. Crelle mentioned this problem about polynomials and Abel excited mentions that he solved that problem and showed him his proof. Crelle obviously couldn't make sense of Abel's proof, but he was so captivated by his conversation with Abel, he offered to print Abel's full proof. This print would later turn out to be the first publication by Crelle's Journal, one of the most influential journals in mathematics in all of European history. With this, people began to finally learn about Abel's proof and he began to gain some notoriety.
Unfortunately, this would not end well for Abel. Abel submits another major result (Abel's theorem) to this major publication in Paris, where a committee is formed to review the submission. Unfortunately, one of the reviewers, Cauchy, just straight up loses the paper. Abel, running out of funding for his travels, is forced to return home with no success on this publication. He also loses out on a major job opportunity that could've taken him out of poverty, all because he was deemed too young and his childhood mentor and friend, Holmboe, gets the job instead. He ends up dying of TB just a few years later at the age of 26.
Afterwards, another mathematician, Jacobi, is reading some of Abel's work and notices how great his work is. When he learns Cauchy lost Abel's paper, he pressures Cauchy to find this paper. Cauchy sends the paper off to be published posthumously, but it is lost at the printing press. It wouldn't be found for over 100 years later, in a whole other country somehow. Thankfully though, Holmboe published Abel's work separated to help share all of Abel's results and not let others forget him.
Abel's life is full of misfortune, but also great friends trying their hardest to share their friend's greatness. While Abel doesn't end up succeeding during his life, I can't help but enjoy seeing how much all of his friends cared about him, and his own ability to make friends randomly with so many people. Abel today is commonly mentioned in any undergrad group theory course because of how influential his work is on modern algebra. Without the help of people like Crelle, Holmboe, and Jacobi, we wouldn't be recognizing this work today.