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I started developing passion for mathematics back in 2013 when my Visual Basic Programming language tutor asked me and two other students to write a program to compute the factorial of any positive integer. I got home, tried the problem but couldn't get it right. I told him the next day I couldn't solve the problem but the other two students were able to solve it probably because they got help from the internet which I was not aware of at that time. My tutor asked me to have a look at their work and learn from it, which I did and on getting home, I was able to solve the problem in a different way. Then, something popped up on my mind and after solving that problem and that was: "I should be able to write a program to add the first $n$ natural numbers". Again, I wasn't aware that $$\frac{n(n+1)}{2} \tag{1}$$ could treat all that. Fortunately, I was able to write the program successfully using FOR...NEXT statement(more like a recursion in mathematics), but then, another thought popped up and that was: "I should be able to develop a formula to find the addition of these numbers". That was the start of my independent thinking. After days of racking my brain, I was able to come up with (1). I tested it on so many first $n$ natural numbers and I was always getting it right. I was so happy that I was dreaming of writing a maths textbook in the future. One day, I was using the internet and I bumped on (1). I couldn't believe my eyes at first. I became immediately devastated but I came over it days later. That was when I thought "if I could discover what had been discovered before, I could discover something new". That was when I started using the internet frequently from then. I would try to comprehend the ones I could and shun the rest. I was so obsessed with formulas and Identities since I didn't have the training to understand how to prove theorems. Moreover, I was unfamiliar with many of the symbols used in mathematics back then. Looking back now, Some of the Identities I was able to discover independently include: $$2(x⁴+y⁴+(x+y)⁴)=(x²+y²+(x+y)²)² \tag{2}$$ If $F_k$ is the $k$th Fibonacci number, then $$\sum_{j=1}^{n}\left(\sum_{k=1}^{j} {F_k}^2\right)^3 = \left(\sum_{j=1}^{n}F_j \left(\sum_{k=1}^{j} {F_k}^2\right)\right)^2 \tag{3}$$ $$n=\left(\left(\sum_{k=1}^{n+1} k\right)^2+\left(3\sum_{k=1}^{n} \frac{k(k+1)}{2}\right)^2\right) - \left(\left(\sum_{k=1}^{n} k\right)^2+ \left(1+3\sum_{k=1}^{n} \frac{k(k+1)}{2}\right)^2\right)\tag{4}$$ $$2^kCos^k(A)Cos(k+m)A = \sum_{r=0}^{k} \binom{k}{r}Cos(m+2r)A \tag{5}$$ $$2^kCos^k(A)Sin(k+m)A = \sum_{r=0}^{k} \binom{k}{r}Sin(m+2r)A \tag{6}$$ $$a⁴-b⁴=(a²+b²)²-(b(a+b))²-(b(a-b))² \tag{7}$$ To mention a few of them. I have realized that (2) is called Candido's identity while other results are trivial and not worth publishing. I have also realised that the cause of all these trivial results is as a result of the fact that I hate reading undergraduate maths textbooks which I cannot probably attribute to being my fault because I have not studied maths as a course, which means that understanding undergraduate maths textbooks in the least will be difficult. Instead, I prefer to surf the internet and look for some formulas or identities, understand them and see if there is a way I can develop and bring something new out of them. I loved reading secondary school textbooks at the start but I stopped doing that when I realized they didn't help me that much. So, I prefer to do with the little knowledge I have acquired so far but that is not helping as well since I will always end up discovering not so novel results.

Now, my ultimate dream is to publish at least one mathematical result but I can't seem to stop discovering trivial results. What advice do you have for me?

J. W. Tanner
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Shuaib Lateef
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    Candidly, my advice is to examine your motivations: Why do you want to publish at least one mathematical result? (Insatiable mathematical drive? Satisfaction of accomplishment? Esteem of peers? Immortality...?) <> Pursuing recreational mathematics, where open questions tend to lie "closer to the surface", may be advisable as well. <> In any event, best wishes with your future mathematical endeavors! – Andrew D. Hwang Jun 28 '21 at 13:54
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    It is not realistic to be lazy in reading mathematical books (or internet articles) and then expect to find a result really worth to be published. Math is, as anything else, hard work , if one actually wants to make progress. – Peter Jun 28 '21 at 15:11
  • @AndrewD.Hwang, thanks so much for this advice. – Shuaib Lateef Jun 28 '21 at 17:09
  • @Peter, I understand your point. Thanks so much – Shuaib Lateef Jun 28 '21 at 17:11

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"Swallow the bitter pill", I mean read the textbooks. But first get advice on which ones are well-written. If that experience kills your passion, it will be sad, but the compensation will be that you have avoided following a path that you don't really enjoy.

Simon
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