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Your amateur research with the Wolfram Language?

I've heard the saying,

Better to remain silent and be thought a fool than to speak and to remove all doubt.

— ABRAHAM LINCOLN.

Although Lincoln is often praised for his eloquence, there were moments when his silence was, perhaps, detrimental. For instance, some people believed his initial reluctance to fully commit to the abolition of slavery was a form of silence that allowed the conflict to persist longer than necessary. However, his eventual strong stance and leadership during the Civil War ultimately led to the Emancipation Proclamation and the abolition of slavery.

It's a reminder that even the wisest among us can fail to fulfill their potential.

"Like as his presidential resolve helped heal a nation, amateur research has always been an essential part of humanity's development!"

Why Amateur Research Matters:

Rigorous math works within defined systems, like a map with boundaries. Gödel's theorems reveal that there will always be true statements outside those boundaries ("gaps"). These gaps could significantly impact our understanding, but rigorous math itself can't predict their effects.

Having spent years researching math with various Wolfram tools, discovering properties of the "MRB constant," and sharing them in the Wolfram Community, I have some advice for those who wish to pioneer new—or just "new to them"—mathematical ideas. I propose counseling by taking and answering questions from aspiring analysts.

My Journey

You will discover in the following examples that Mathematica has been my go-to tool for quantum leaps in discovery.

Your Journey

The Intersection of Critical Thinking and Mathematical Discovery Within You

Mark Twain’s apocryphal quote, “I’m in favor of progress; it’s change I don’t like,” encapsulates a profound human sentiment that echoes through the corridors of intellectual history. At its heart, this statement reflects the delicate balance between embracing new ideas and the inherent discomfort of moving beyond the familiar. (Educational humility is essential to mathematical maturity.) This tension is a driving force behind critical thinking, a process that has evolved and refined over centuries.

How about you? Do you have pointers for others or an interest in improving your research skills as an amateur? Since were here, how has the Wolfram community/site/products helped along the way? Pease let us know below.

Let's embark on this journey together and inspire more minds to discover the fascinating world of mathematics!
POSTED BY: Marvin Ray Burns
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A Penny for Their Thoughts?

I considered replying with the following two sentences but was lacking full awareness of where to go., Since I taught it my objectives, I asked Copilot to give some useful additions to it. While some of Copilot's pointers are redundant to what is already available within the Wolfram universe, even those could be worth taking a fresh look at.

Perhaps as we compile our successful amateur research methods, we can keep in mind the not yet ready for prime-time amateurs, i. e., pupils. Not to leave out the under-privileged ones.

1. Accessibility to Resources

Affordable Tools and Materials: Ensure that research tools and materials are affordable and accessible. Promoting open-source software and free online resources can help those with limited financial means.

Digital Divide: Address the digital divide by advocating for better internet access and providing offline resources for those with limited connectivity.

2. Mentorship and Support

Mentorship Programs: Establish mentorship programs where experienced researchers can guide and support beginners. This can help them navigate challenges and build confidence in their abilities.

Peer Support Groups: Create peer support groups where individuals can share their experiences, offer advice, and encourage each other. This fosters a sense of community and collaboration.

3. Educational Opportunities

Workshops and Webinars: Organize free or low-cost workshops and webinars to teach fundamental research skills and methodologies. These can be targeted at different skill levels to ensure inclusivity.

School Partnerships: Partner with schools, especially in underprivileged areas, to introduce students to research early on and provide them with the necessary tools and knowledge.

4. Encouraging Curiosity and Creativity

Safe Learning Environment: Create a safe and supportive environment where beginners feel comfortable asking questions and exploring new ideas without fear of judgment.

Celebrating Small Wins: Encourage and celebrate small achievements to build confidence and keep motivation high. Recognize the value of incremental progress in the research journey.

5. Promoting Diversity and Inclusion

Inclusive Research Practices: Promote diversity and inclusion in research by encouraging participation from individuals of all backgrounds. Highlight the importance of diverse perspectives in driving innovation.

Scholarships and Grants: Offer scholarships and grants specifically for underprivileged and underrepresented groups to support their research efforts and reduce financial barriers.

6. Providing Guidance and Resources

Clear Roadmaps: Develop clear and accessible roadmaps for beginners, outlining the steps and resources needed to start their research journey.

Resource Libraries: Create and maintain libraries of free educational resources, including articles, videos, and tutorials, to support self-directed learning.

7. Encouraging Collaboration

Research Collaboratives: Form research collaboratives where individuals can work together on projects, share knowledge, and learn from each other’s experiences.

Cross-Disciplinary Projects: Encourage cross-disciplinary projects that combine different fields of study, fostering innovation and broadening research perspectives.

Your thoughts, no matter how seemingly inconsequenciall, adds to our collective knowledge and propels us forward. Join me today—let's make groundbreaking discoveries and inspire future generations of researchers. Together, we can achieve extraordinary things!
POSTED BY: Marvin Ray Burns

[please read on]
POSTED BY: Marvin Ray Burns

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!

intro

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.

sum3

summary
POSTED BY: Marvin Ray Burns

enter image description here

Here is an example of what can be done using an AI assistant and Mathematica.

Written as n1/n, nth roots of natural numbers have always intrigued me. I first used the to describe the MRB constant in 1999.

I noticed, the researcher at Wolfram pointed out that my discovery was related to "Power Towers" as I read

MathWorld,

enter image description here
POSTED BY: Marvin Ray Burns

Pointer 10: Proceed with caution, but by all means proceed!

enter image description here enter image description here
POSTED BY: Marvin Ray Burns

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.
POSTED BY: Muhammad al-Hateel

Tip 9. Make Every Effort to Avoid the Dunning-Kruger Effect

        (Only be authoritative after you have read the authorities.)

enter image description here enter image description here
POSTED BY: Marvin Ray Burns

Pointer 8: Seek Help Wisely

If your discovery isn't earth-shaking or confidential, don't hesitate to ask for help! While this isn't legal advice, posting your idea online can serve as proof of your originality. However, if you want to keep it a secret, be strategic in whom you share it with. Always remember that understanding the help you receive will be much easier if you've already done your own research and studied related documentation.

Pointer 8a: Balance Humility and Confidence

No one likes to expose their ignorance or appear lazy. Conversely, if people think you're too smart and feel you’re wasting their time with questions, they might be less inclined to help. Striking a balance between humility and confidence is key.

Pointer 8b: Partner for Greater Reach

To share your discovery effectively, consider partnering with someone who has a broad audience or a well-visited platform. You might need to compromise on some aspects of your sharing plan to reach a larger audience. Sharing half of your discoveries with many people can be more impactful than sharing all of them with only a few, or just keeping them to yourself.

Pointer 8c: Timing and Legacy

Sometimes, your discovery might be ahead of its time. If you believe this is the case, consider yourself fortunate to leave a legacy that might be recognized and appreciated posthumously. History is full of such instances where pioneers were only recognized much later.
POSTED BY: Marvin Ray Burns

Dear Dr. Paul Shapshak,

Thank you for your kind words and interest in my work. Your acknowledgment means a lot, especially given the incredible journey I've undertaken in self-directed research over the last few decades.

Through trial and error, and a deep development of my intuition, I've unearthed secrets that have allowed me to contribute meaningfully to the field of mathematics and the Wolfram Community. Your response to my discussion on amateur research with Mathematica was the sole feedback, and while that fact initially left me disheartened, it did not deter me. I continued my explorations with renewed vigor, focusing on the MRB constant—my first and most significant original discovery. It is the branches that sprout from its definition and representations that continually inspire my mathematical pursuits.

I firmly believe that self-learning is the hallmark of our era. Platforms like YouTube, online classes, and the Wolfram Community epitomize this trend, enabling individuals to push the boundaries of their knowledge to ever more meaningful and rewarding limits. This approach to learning mirrors the journeys of historical giants like Newton and even Einstein, who were driven by the spirit of discovery.

I would be delighted to collaborate and discuss how we can further this shared passion for mathematical exploration.

Best wishes, Marvin
POSTED BY: Marvin Ray Burns

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.

enter image description here

This time the AI pulled off what it promised without error!
POSTED BY: Marvin Ray Burns

Pointer 7

Here is every step I take to make a discovery about the MRB constant (CMRB).
POSTED BY: Marvin Ray Burns

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

:

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.

enter image description here

enter image description here
POSTED BY: Marvin Ray Burns

Pointer 6a

Sometimes fewer than 16 digits will give you a more usable approximate closed form approximation than using all of the digits you have. Your digits could have an error.
POSTED BY: Marvin Ray Burns

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.
POSTED BY: Marvin Ray Burns

Pointer 4

Seek patterns, but never brag about them.
POSTED BY: Marvin Ray Burns

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.
POSTED BY: Marvin Ray Burns

Pointer 2

An idiot's well-done thought is sometimes better than a half-baked one from a genius.
POSTED BY: Marvin Ray Burns

Pointer 1

enter image description here
POSTED BY: Marvin Ray Burns

I will post some pointers that I have learned from experience. You can still add anything you think might be beneficial.
POSTED BY: Marvin Ray Burns

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
POSTED BY: Paul Shapshak, PhD
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