[please read on]

Follow-up to the Dec 10 Example

Remember, this is more than my Eurica Moment. Its purpose to show you how you might make even better descries than these!

Another Follow-up to the Dec 10 Example

The following notebook of exploring conditions and results of the convergence of the sequence of partial integrations could serve as an example of how one might navigate an un or undercharged course.

Yet Another Follow-up to the Dec 10 Example

Embarking on the journey of amateur math research can be both thrilling and challenging. Throughout my exploration, I've focused on finding innovative methods to push the boundaries of our mathematical understanding. My particular area of fascination has been the MRB constant, a constant named after my initials, which has driven much of my recent work.

In my latest research, I've been tackling the challenge of computing many digits of the MRB constant using only basic mathematical operations such as addition, subtraction, multiplication, division, and loops. This endeavor is remarkable, given that brute-forcing such calculations would require an unmanageable number of expansions. Through persistence and creative problem-solving, I have successfully computed over 800 digits of the MRB constant.

Here is the notebook with raw results.

Click here so I don't clutter up the reply.

Here is a condensed version.

Sir, this was a most beautiful post. I'd like to thank you for sharing this with us, especially your past negative experiences. This sincerity about one's negative experiences helps others, like me, get over their own ones and be reassured about them. Knowing that your journey culminated in real-world achievements such as the MRB Constant is even more inspiring. I wish you an even longer trail of achievements, and this one would be only a beginning.

I think my approach to Wolfram Language is generally akin to yours, fueled by utter unhindered curiosity. I view it as, above all, a unifying framework. One that can bridge much (all?) scientific knowledge into one whole by lowering the costs to access different scientific disciplines. With the costs of entry minimized or removed, only curiosity becomes our limit. Now we can toy around with scientific concepts as we please, shuffle them, reorganize them, transpose them across different disciplines, or simply: innovate. And as a genuinely curious one myself, I can't think of any better endeavor to embark on for a lifetime.

Although I'm not that mathematically savvy, despite holding immense love for it, I'd be honored if I could help in any way or generally just stay in contact. I think it's an important form of wealth to be around truly curious minds.

You can use Bing AI and Google CPT to make Mathematica code. They will give you a good start, but occasionally you must make a few corrections.

This time the AI pulled off what it promised without error!

Pointer 6b: The Importance of Accurate Initial Digits and Avoiding Extraneous Ones in Wolfram Alpha

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When using tools like Wolfram Alpha to explore mathematical constants, the accuracy of initial digits is crucial. For example, entering the correct initial digits of π (pi) will yield the constant itself, whereas including additional incorrect digits will not. There are other closed-form approximations that offer better matches, highlighting the need for precision in mathematical explorations.

Ensuring accurate inputs allows for more reliable and meaningful results, making your research and discoveries more robust.

Pointer 5

Diffrences[of a table] and Ratios[of the table], sometimes followed by "=="s of some of their results always are a great start at analyzing it.

Pointer 5a

When passing a decimal value into a "==", only include the digits; never leave the precision stuff (`...). That way Wolfram Alpha will tell you the accuracy of the possible closed form by giving the correct digits in bold print.

Pointer 3

Utilize the power of Wolfram Alpha (W|A) by using the double equal sign (==) for lookups and the F1 key to access Mathematica documentation. These tools can greatly enhance your efficiency and understanding.

Pointer 3 a

Which is more remarkable, the monkey typing Shakespeare or the real McCoy? (Although very slow, luck can do more than talent, just use technology and AI to speed it up!) There exists something like guided luck. Think of it as when you see a card face down and you remember that you got chocolate on all the aces. If the card has chocolate on it, you might not know which suit it is, but you know its rank is ace. For guessing what it is, you've dramatically reduced the odds of being wrong. Paying attention to patterns and recognizing expansions and other representations of numbers, will give you intuition on what luck may bring.

Pointer 3.5

Make generous use of Wolfram Alpha (the double ==) and let the documentation make you a coding expert. And use AI to write code snippets that confuse you. AI might not get it exactly correct, but with the documentation (through f1 on the confusing command) fixing it is usually a lot easier.

Pointer 3.5 a

Clever trial and error, combined with even a small but growing knowledge base and the speed of modern technology, is sometimes faster than genius-level knowledge from decades ago at human speed. Embrace this method to rapidly enhance your problem-solving abilities and make significant progress in your research.

By leveraging modern tools and resources, you can achieve remarkable results through persistent experimentation and learning.

Pointer 1

8-28-22 Hi Marvin, First, many thanks for your service. Next, congratulations on your discoveries and work. Yes, I’m interested to join your team and hope to participate. Please let me know. Best wishes, Paul Shapshak, PhD Pshapshak@gmail.com