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Some Knowit"The Early (and Peculiar) History of the Möbius Function" by William Dunham is a highly entertaining and accessible article. Full of surprises. Glad I found it at Internet Archive:<a href="https://web.archive.org/web/20230127141422/https://sci.bban.top/pdf/10.1080/0025570X.2017.1413921.pdf" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://web.archive.org/web/20230127141422/https://sci.bban.top/pdf/10.1080/0025570X.2017.1413921.pdf</a><a href="https://mastodon.social/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mastodon.social/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mastodon.social/tags/MathHistory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathHistory</a>

Joshua GrochowOnline Codes & Expansions (CodEx) Seminar Tues Mar 11 2025Steve Flammia presents "A Constructive Approach to Zauner’s Conjecture via the Stark Conjectures" using <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> to build <a href="https://mathstodon.xyz/tags/quantum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quantum</a> SIC-POVMs.Based on <a href="https://arxiv.org/abs/2501.03970" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://arxiv.org/abs/2501.03970</a> joint with Marcus Appleby and Gene Kopp.Register for the zoom link here: <a href="https://www.math.colostate.edu/~king/codex/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.math.colostate.edu/~king/codex/</a><a href="https://mathstodon.xyz/tags/seminar" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#seminar</a> <a href="https://mathstodon.xyz/tags/online" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#online</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a>

Alex JimenezSpectacular Connection Between <a href="https://mas.to/tags/LLMs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LLMs</a>, <a href="https://mas.to/tags/QuantumSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#QuantumSystems</a>, and <a href="https://mas.to/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a>DataScienceCentral.com <a href="https://www.datasciencecentral.com/spectacular-connection-between-llms-quantum-systems-and-number-theory/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.datasciencecentral.com/spectacular-connection-between-llms-quantum-systems-and-number-theory/</a><a href="https://mas.to/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mas.to/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AI</a>

formuchdeliberationNew Proofs Probe the Limits of Mathematical Truth | Quanta Magazine…By proving a broader version of Hilbert’s famous 10th problem, two groups of mathematicians have expanded the realm of mathematical unknowability... <a href="https://mastodon.world/tags/mathematics" class="mention hashtag" rel="tag">#mathematics</a> <a href="https://mastodon.world/tags/numbertheory" class="mention hashtag" rel="tag">#numbertheory</a> <a href="https://mastodon.world/tags/davidhilbert" class="mention hashtag" rel="tag">#davidhilbert</a><a href="https://formuchdeliberation.wordpress.com/2025/02/21/new-proofs-probe-the-limits-of-mathematical-truth-quanta-magazine-3/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://formuchdeliberation.wordpress.com/2025/02/21/new-proofs-probe-the-limits-of-mathematical-truth-quanta-magazine-3/</a>

ƧƿѦςɛ♏ѦਹѤʞHave you ever wondered what the first million digits of π↑↑4 might be? Well, wonder no more... <a href="https://ankokudan.org/d/d.htm?mathlistindex-e.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://ankokudan.org/d/d.htm?mathlistindex-e.html</a> <a href="https://mastodon.social/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://mastodon.social/tags/constants" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#constants</a> <a href="https://mastodon.social/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a>

formuchdeliberationNew Proofs Probe the Limits of Mathematical Truth | Quanta Magazine…By proving a broader version of Hilbert’s famous 10th problem, two groups of mathematicians have expanded the realm of mathematical unknowability... <a href="https://mastodon.world/tags/mathematics" class="mention hashtag" rel="tag">#mathematics</a> <a href="https://mastodon.world/tags/numbertheory" class="mention hashtag" rel="tag">#numbertheory</a> <a href="https://mastodon.world/tags/davidhilbert" class="mention hashtag" rel="tag">#davidhilbert</a><a href="https://formuchdeliberation.wordpress.com/2025/02/12/new-proofs-probe-the-limits-of-mathematical-truth-quanta-magazine/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://formuchdeliberation.wordpress.com/2025/02/12/new-proofs-probe-the-limits-of-mathematical-truth-quanta-magazine/</a>

⚯ Michel de Cryptadamus ⚯let's just say that numbers are not RFK Jr.'s strong suit.<a href="https://universeodon.com/tags/RFK" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RFK</a> <a href="https://universeodon.com/tags/RFKJr" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RFKJr</a> <a href="https://universeodon.com/tags/antivax" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#antivax</a> <a href="https://universeodon.com/tags/uspol" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#uspol</a> <a href="https://universeodon.com/tags/uspolitics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#uspolitics</a> <a href="https://universeodon.com/tags/antivaxxers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#antivaxxers</a> <a href="https://universeodon.com/tags/trump" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#trump</a> <a href="https://universeodon.com/tags/donaldtrump" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#donaldtrump</a> <a href="https://universeodon.com/tags/cabinet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#cabinet</a> <a href="https://universeodon.com/tags/MAGA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MAGA</a> <a href="https://universeodon.com/tags/MAHA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MAHA</a> <a href="https://universeodon.com/tags/MAGAts" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MAGAts</a> <a href="https://universeodon.com/tags/measles" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#measles</a> <a href="https://universeodon.com/tags/vaccine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#vaccine</a> <a href="https://universeodon.com/tags/vaccines" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#vaccines</a> <a href="https://universeodon.com/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://universeodon.com/tags/numbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#numbers</a> <a href="https://universeodon.com/tags/numbertheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#numbertheory</a> <a href="https://universeodon.com/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a>

ƧƿѦςɛ♏ѦਹѤʞIs busy beaver of a googol bigger than tree of a googol? <a href="https://www.youtube.com/watch?v=kmAc1nDizu0" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.youtube.com/watch?v=kmAc1nDizu0</a> <a href="https://mastodon.social/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://mastodon.social/tags/BigNumbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BigNumbers</a> <a href="https://mastodon.social/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mastodon.social/tags/numbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#numbers</a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a>

Knowledge ZoneThe <a href="https://mstdn.social/tags/Euclid" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Euclid</a>-<a href="https://mstdn.social/tags/Euler" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Euler</a> <a href="https://mstdn.social/tags/Theorem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Theorem</a> is a fundamental theorem in <a href="https://mstdn.social/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> that beautifully connects <a href="https://mstdn.social/tags/PerfectNumbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PerfectNumbers</a> with <a href="https://mstdn.social/tags/Mersenne" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mersenne</a> <a href="https://mstdn.social/tags/Primes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Primes</a>.<a href="https://knowledgezone.co.in/kbits/679340ac379a5d09cb2d1a93" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://knowledgezone.co.in/kbits/679340ac379a5d09cb2d1a93</a>

In-Sight PublishingConversation with Tianxiang Shao on Family and Feelings (2)Scott Douglas Jacobsen In-Sight Publishing, Fort Langley, British Columbia, CanadaCorrespondence: Scott Douglas Jacobsen (Email: scott.jacobsen2025@gmail.com)Received: January 12, 2025 Accepted: N/A Published: January 22, 2025      AbstractThis interview offers an insightful exploration of Tianxiang Shao’s personal and academic journey, conducted by Scott Douglas Jacobsen. The conversation delves into Shao’s family history, including his grandparents’ migration from rural Anhui to the provincial capital, Hefei, amidst challenging socio-political landscapes such as the 1960s famine and Cultural Revolution. Shao discusses his career aspirations in artificial intelligence, his perspectives on success, materialism, and the balance between introversion and social growth. The dialogue also touches on Shao’s childhood creativity, his passion for number theory, and his views on the interplay between human and artificial intelligence. Additionally, Shao shares his philosophical influences, including Albert Camus, and his engagement with Buddhist texts for personal peace. The interview highlights Shao’s multifaceted interests, resilience in personal challenges, and his commitment to balancing academic pursuits with diverse hobbies, providing a comprehensive understanding of his character and intellectual pursuits.Keywords: Artificial Intelligence, Buddhist Philosophy, Creativity, Cultural Revolution, Family Migration, Introversion, Materialism, Number Theory, Personal Resilience, Philosophical Influences, Social Growth, SuccessIntroductionIn this comprehensive interview conducted on January 12, 2025, Scott Douglas Jacobsen engages with Tianxiang Shao, a promising young scholar and aspiring artificial intelligence algorithm engineer. Shao shares his deeply rooted family history, detailing his grandparents’ migration from rural Anhui to Hefei during a tumultuous period marked by famine and the Cultural Revolution. The conversation navigates through Shao’s academic aspirations, his introspective views on success and materialism, and his journey towards personal and social growth. Shao’s childhood creativity and passion for number theory emerge as significant themes, alongside his perspectives on the future of artificial intelligence relative to human intelligence. The interview also delves into Shao’s philosophical inclinations, influenced by Albert Camus, and his practices for achieving personal serenity through Buddhist texts. Additionally, Shao reflects on his hobbies and the importance of maintaining a balanced life amidst academic pursuits. This dialogue provides a nuanced portrait of Shao’s character, highlighting his resilience, intellectual curiosity, and thoughtful approach to both personal and professional development.Main Text (Interview)Interviewer: Scott Douglas JacobsenInterviewee: Tianxiang ShaoSection 1: Grandparents’ Origins and MigrationScott Douglas Jacobsen: There are a lot of details to fill in, about your grandparents! Which countryside of Huangshan were they from?Tianxiang Shao: My paternal grandparents were not from Huangshan. They were born in a village in central Anhui, near the provincial capital, Hefei. My maternal grandparents, however, were from Huangshan, and the area where they lived is now called Tunxi District.Jacobsen: How did they travel from the countryside to the city, and which city?Shao: Hefei, the capital city of Anhui Province. The journey was quite challenging in many ways. My grandparents were exceptionally talented and managed to rise above their circumstances through rigorous selection processes during a time when China was extremely poor.Jacobsen: Were there any outstanding stories from this trip from the countryside to the city?Shao: Yes, there were. Both of my grandparents came from very poor families. At that time, many rural families had a lot of children. In the 1960s, China experienced a devastating famine, followed by the Cultural Revolution starting in 1966. As a result, my grandparents didn’t receive a complete formal education. Instead, they relied heavily on self-study and the education available through society.Despite these hardships, they managed to excel. What’s more, my grandmother brought her four siblings from the countryside to the city, and now all of them are leading good lives.Section 2: Achieving Family ProsperityJacobsen: What did they do to make prosperity for their family?Shao: They relied entirely on their own efforts and achieved prosperity through hard work and dedication.Section 3: Career Aspirations and Academic PursuitsJacobsen: What careers have you aspired to attain achievement in the big city?Shao: For me, at this stage, my academic pursuits are the most important.As a child, I wanted to become an astrophysicist. Later, I aspired to be a mathematician. Now, considering my current field of study and where I can achieve success, becoming an artificial intelligence algorithm engineer seems to be the most fitting goal.Jacobsen: What work have been the actual choices in the big city?Shao: I’m still a student and don’t have a job yet.Section 4: Defining Success and Views on MaterialismJacobsen: How do you define success?Shao: Doing what you love and staying committed to it for a lifetime—that is success.Jacobsen: Is there a peculiarity to their materialism, as in something ore specific like a naturalism, or is more standardly defined materialism without religious belief?Shao: I think it’s probably more of the latter.Section 5: Dreams, Small Town Charm, and SerenityJacobsen: Huangshan makes you sound like a small town family dreamer like me. Shao: Is that so? Haha. In fact, when I was a child, I always dreamed of big places. I loved visiting large office buildings, big shopping malls, and crowded areas. I enjoyed the excitement of exploring.However, I gradually realized that small towns have their own charm. It wasn’t until I had lived in a big city for several years that I truly came to appreciate this.Jacobsen: Do you feel that you carry some of that serenity with you?Shao: Sometimes this serenity helps me block out the noise of the outside world, allowing me to think independently and explore the world on my own.Section 6: Social Behavior and Personal GrowthJacobsen: Do you feel more social now compared to before?Shao: Haha, to be honest, I’ve always been a relatively introverted person and rarely participate in social activities unless necessary.Jacobsen: When you didn’t get along well with peers, was this something to do with fights and misconduct, social awkwardness, or simply not fitting into the social groups?Shao: That said, social skills are something that improve with experience. I believe my social skills and emotional intelligence are probably better now than they were five years ago.  Part of the reason was social awkwardness, and another part was my lack of participation in social activities. You know, many people enjoy going to bars, dancing, or making a lot of noise together, but I rarely go to those places because I don’t enjoy that kind of hustle and bustle.I rarely argue with others or engage in inappropriate behavior. I find arguments to be too draining, and I prefer not to spend my time on unnecessary people or matters.Section 7: Childhood Creativity and StorytellingJacobsen: What were the stories “inspired by a clock”?Shao: Those are stories from my childhood. I’ve always been someone who loves to daydream. Back then, I was inspired by movies like Inception and Interstellar. Sometimes, I would even jot down those ideas in my notebooks.I remember imagining stories about traveling to the past by altering a clock, or epic battles between beings from different galaxies through time fissures. These stories might seem absurd now, but at the time, I even created abstract drawings to go along with them and thoroughly enjoyed the process.Section 8: Mathematics Competitions and InterestsJacobsen: What kind of mathematics competitions, e.g., olympiads?Shao: Yes, exactly the Olympiad, but I only participated in regional-level Olympiad competitions and some mathematical modeling contests.Jacobsen: What area of math do you like the most?Shao: Number theory. This probably explains why I felt so comfortable when I first started solving numerical reasoning problems. I remember the first time I took a proper high-range IQ test—it was Ivan Ivec’s Numerus. At that time, I had no clear understanding of the underlying logic or techniques, but I quickly submitted it and scored an IQ of 165.I love numbers; I feel that each number tells a story. Number theory is so harmonious and beautiful. From a young age, I’ve used my knowledge of number theory to solve some problems.Section 9: Perspectives on IQ Tests and HobbiesJacobsen: That’s a nuanced and healthy sense of self-consciousness on the latter personal note and a balanced view of high-range tests. I’m told by those who’ve spent a lot of time—e.g., Rick Rosner—on them that they’re almost a great challenge and stimulating because they are genuinely difficult and take 20, 50, 200 hours or more, sometimes.  Those two factors of a speedy survey of the landscape and a rapid dig of the wells into the ground of a topic are pretty strong signs in youth. Outside of the math, was there anything in particular intriguing to you, apart from the academic work?Shao: Thank you for the compliment! Let me first share my thoughts on high-range IQ tests. These tests are indeed very challenging, but there’s a mix of quality in the ones available today. So I usually approach them selectively. I treat them as a hobby—something to challenge myself with and enjoy the process rather than focus heavily on the results.Many people ask me how much time I spend on these tests. I’ve actually calculated that my average time per test is about 6–8 hours. Occasionally, for particularly difficult tests that I enjoy, I spend longer. So far, only one numerical test has taken me over 50 hours: Mahir Wu’s N-World, which I consider the best pure numerical test out there.As for my other interests, the truth is I have many! For example, I love playing table tennis, singing, and writing lyrics. I enjoy learning English and French, and I find great joy in reading. These are just a few examples.These hobbies bring me happiness and balance alongside my academic work. I always recommend not letting academic work completely consume your life, as that can become exhausting.Section 10: Artificial Intelligence vs Human IntelligenceJacobsen: Do you think computers will become far smarter than even the top geniuses in this or that country?Shao: I don’t think so. In fact, my field of study is related to artificial intelligence, and my mentor and most of my peers share the same view.Computers are undeniably intelligent. Since IBM’s Deep Blue defeated the genius chess player Garry Kasparov 28 years ago, stories of computers surpassing humans have become commonplace. In the future, it’s safe to say that for executing specific tasks, humans can be entirely replaced by machines.However, the two most remarkable traits of humans are emotion and creativity, which are deeply interconnected. No matter how advanced AI becomes—be it OpenAI’s ChatGPT o1-pro, or some of Google’s cutting-edge AI models—it will never truly experience the nuances of human emotions like joy, sorrow, bitterness, and sweetness. Nor will it possess the profound creativity unique to humans.Lastly, here’s an interesting wordplay: in English, “AI” (artificial intelligence) sounds identical to “爱” in Chinese pinyin, which means “love.” So far, I haven’t seen anyone use this as a theme for a puzzle, but it’s a fascinating coincidence. I often think love is the root of many great creations, and AI will never have the capacity to actively experience or comprehend the broader essence of “love.”Section 11: Philosophical Influences and BeliefsJacobsen: What do you think of Camus?Shao: Oh, he is a great French philosopher and writer. I’ve read many of his works before, and I highly recommend The Stranger and The Myth of Sisyphus. My worldview has been significantly influenced by his philosophical framework.Jacobsen: Is there much different between algorithms and artificial intelligence, e.g., the latter as a higher-order kind of the former?Shao: There is a distinction between algorithms and artificial intelligence, though they are deeply interconnected. Algorithms are the step-by-step instructions or rules designed to perform a specific task or solve a problem. They are the building blocks of all computational processes, including artificial intelligence.Artificial intelligence, on the other hand, is a broader concept that refers to the simulation of human intelligence processes by machines. It encompasses not just algorithms but also data, training methods, and systems designed to learn, adapt, and make decisions. In a way, AI can be seen as a higher-order application of algorithms, where algorithms work together in complex ways to create learning and decision-making capabilities.Jacobsen: What Buddhist passages help bring some calm and peace?Shao: I recommend three texts, all of which are well-known in the Buddhist world: the Diamond Sutra, the Shurangama Sutra, and the most famous one, the Heart Sutra.The Heart Sutra is not very long—I memorized it completely when I was thirteen. Since then, whenever I feel restless, I recite it to calm myself down.Jacobsen: Are there any neo-Daoist or Buddhist writers who capture a contemporary appreciation of Classical Chinese philosophy in a novel way? Shao: One prominent example is Li Zehou, a contemporary philosopher who integrates Confucianism, Daoism, and Buddhism with modern thought, presenting a fresh perspective on Classical Chinese philosophy.Jacobsen: What is the other 20% of your worldview not incorporated primarily by science?Shao: I have a partially idealistic perspective. I believe in the existence of some transcendent spiritual beings, such as God, Buddhas, or deities mentioned in various religions.Interestingly, I recently discussed this exact topic with Zolly Darko, a well-known author of high-range IQ tests, and I also used percentages to describe my worldview during that conversation.Jacobsen: What do you mean by science?Shao: It’s the conventional understanding of science as we know it.Jacobsen: Subjectively, of those tests, which one felt the hardest and took the most time?Shao: I’ve answered this question before—it’s Mahir Wu’s numerical test N-World. I spent nearly 60 hours on it and achieved a score close to full marks.However, this year I’m planning to spend a similarly long time on one of Paul Cooijmans’ tests, aiming to submit it around my birthday. I won’t reveal more details for now, haha!Jacobsen: Is the existentialism mentioned in ethical philosophy related to the reference to Albert Camus?Shao: Yes, exactly.To add an interesting note, Camus consistently denied being an existentialist philosopher, yet later philosophers widely regard him as one.Jacobsen: What facets of Marxism make sense of social realities in China? Shao: I’m sorry, but I prefer not to answer this question due to some political reasons. I hope you understand.Section 12: Influences, Interests, and Personal ResilienceJacobsen: What books have influenced you?Shao: The Myth of Sisyphus by Albert Camus, Siddhartha by Hermann Hesse, Love in the Time of Choleraby Gabriel García Márquez, and Dream of the Red Chamber by the Chinese novelist Cao Xueqin.Jacobsen: What music generates stronger feelings in you?Shao: I must highly praise Lana Del Rey’s songs—she’s my favorite Western singer! Almost all of her songs resonate deeply with me.In terms of musical forms, I love classical music, both Chinese and Western. I practiced violin as a child and later developed a strong appreciation for piano and violin compositions.One genre I’ve always loved is Chinese traditional music (Guofeng). It brings me a sense of tranquility and is closely tied to China’s 5,000 years of history and culture. It feels almost like having a conversation with the ancients.Jacobsen: Do we make a mistake in thinking the structured representation of letters on a page truly brings us in touch with the great minds of the past or merely in connection with the low-fidelity representation of what they had in mind?Shao: I am more inclined to believe that it allows us to truly connect with great minds.Jacobsen: How do you juxtapose the momentary feeling of the world as one with the realities of geopolitical strife?Shao: I don’t particularly enjoy discussing too many politically related topics. I advocate for peace and hope that cultures from different countries can engage in equal exchanges and that people can support and help each other.Jacobsen: Do you think the West’s primary concern among many of its populations with an Abrahamic afterlife is largely a waste of time and a cause of worry? We have large, anxious subpopulations.Shao: Haha, I’m not very familiar with this topic. But from my perspective, I’ve never hoped for an afterlife—I only strive to live this life to the fullest.Section 13: Closing RemarksJacobsen: How are you feeling since the last breakup?Shao: Wow, at first, of course, I needed some time to adjust. But soon after, I got back on track because life and studies still needed to move forward.I want to thank my good friends. I have several Chinese friends who supported me emotionally, including Tai Jing and Mahir Wu. My two friends from the Glia Society (you’re surely familiar with), Matthew Scillitani and Andrei Udriste, also comforted me. I’m grateful for their kindness!I’m doing great now. I’m not even 21 yet, so there are plenty of opportunities and challenges ahead. I’ve grown to see matters like relationships in a much more mature way.Lastly, thank you for this interview. I really enjoyed some of your questions, and I hope we meet again next time!Jacobsen: Thank you for the opportunity and your time, Tianxiang.DiscussionThe interview between Scott Douglas Jacobsen and Tianxiang Shao provides a comprehensive insight into Shao’s personal background, academic ambitions, and philosophical perspectives. Shao discusses his family’s migration from rural Anhui to Hefei during the tumultuous 1960s, highlighting his grandparents’ resilience and dedication amidst socio-political challenges like the famine and Cultural Revolution. This history underscores Shao’s determination and commitment to overcoming adversity, traits that have shaped his pursuit of a career in artificial intelligence and his passion for number theory. A significant portion of the discussion focuses on Shao’s introspective views on success and materialism, emphasizing the importance of following one’s passions and maintaining a lifelong commitment to personal and academic goals. His introspective nature and introversion are balanced by his ability to find serenity and engage in independent thought, which contribute to his intellectual growth and creativity. Additionally, Shao shares his perspectives on the unique aspects of human intelligence, such as emotion and creativity, which he believes AI cannot replicate, demonstrating his nuanced understanding of the interplay between technology and human cognition.MethodsThe interview with Tianxiang Shao was conducted on January 12, 2025, utilizing a semi-structured format to allow for a flexible and in-depth dialogue. Scott Douglas Jacobsen prepared a series of open-ended questions that explored various facets of Shao’s life, including his family history, academic interests, philosophical beliefs, and personal resilience. Conducted virtually, the interview facilitated a comfortable environment for Shao to elaborate on topics of personal significance, ensuring a rich and meaningful conversation. This semi-structured approach enabled the exploration of both broad themes and specific details, allowing Shao to provide detailed responses that highlighted his motivations, values, and aspirations. The data gathered from the interview was analyzed thematically, identifying key motifs such as resilience, the balance between personal well-being and academic pursuits, and the influence of philosophical and spiritual practices on his life. This methodological framework ensured that the interview captured the depth and complexity of Shao’s experiences and perspectives, offering a nuanced understanding of his journey and future goals.Data AvailabilityNo datasets were generated or analyzed during the current article. All interview content remains the intellectual property of the interviewer and interviewee.References(No external academic sources were cited for this interview.)Journal & Article Details<ul><li>Publisher: In-Sight Publishing</li><li>Publisher Founding: March 1, 2014</li><li>Web Domain: <a href="http://www.in-sightpublishing.com/" rel="nofollow noopener noreferrer" target="_blank">http://www.in-sightpublishing.com</a></li><li>Location: Fort Langley, Township of Langley, British Columbia, Canada</li><li>Journal: In-Sight: Interviews</li><li>Journal Founding: August 2, 2012</li><li>Frequency: Four Times Per Year</li><li>Review Status: Non-Peer-Reviewed</li><li>Access: Electronic/Digital & Open Access</li><li>Fees: None (Free)</li><li>Volume Numbering: 13</li><li>Issue Numbering: 2</li><li>Section: A</li><li>Theme Type: Idea</li><li>Theme Premise: “Outliers and Outsiders”</li><li>Theme Part: 33</li><li>Formal Sub-Theme: None</li><li>Individual Publication Date: January 22, 2025</li><li>Issue Publication Date: April 1, 2025</li><li>Author(s): Scott Douglas Jacobsen</li><li>Word Count: 2,484</li><li>Image Credits: Photo by <a href="https://unsplash.com/@ceye2eye?utm_content=creditCopyText&utm_medium=referral&utm_source=unsplash" rel="nofollow noopener noreferrer" target="_blank">William Zhang</a> on <a href="https://unsplash.com/photos/aerial-view-of-green-trees-and-mountains-during-daytime--Qd91Sg6gZ8?utm_content=creditCopyText&utm_medium=referral&utm_source=unsplash" rel="nofollow noopener noreferrer" target="_blank">Unsplash</a></li><li>ISSN (International Standard Serial Number): 2369-6885</li></ul>AcknowledgementsThe author thanks Tianxiang Shao for his time and willingness to participate in this interview.Author ContributionsS.D.J. conceived and conducted the interview, transcribed and edited the conversation, and prepared the manuscript.Competing InterestsThe author declares no competing interests.License & CopyrightIn-Sight Publishing by Scott Douglas Jacobsen is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. © Scott Douglas Jacobsen and In-Sight Publishing 2012–Present.Unauthorized use or duplication of material without express permission from Scott Douglas Jacobsen is strictly prohibited. Excerpts and links must use full credit to Scott Douglas Jacobsen and In-Sight Publishing with direction to the original content.Supplementary InformationBelow are various citation formats for Conversation with Tianxiang Shao on Family and Feelings (2).<ol><li>American Medical Association (AMA 11th Edition) Jacobsen S. Conversation with Tianxiang Shao on Family and Feelings (2). January 2025;13(2). <a href="http://www.in-sightpublishing.com/shao-2" rel="nofollow noopener noreferrer" target="_blank">http://www.in-sightpublishing.com/shao-2</a></li><li>American Psychological Association (APA 7th Edition) Jacobsen, S. (2025, January 22). Conversation with Tianxiang Shao on Family and Feelings (2). In-Sight Publishing. 13(2).</li><li>Brazilian National Standards (ABNT) JACOBSEN, S. Conversation with Tianxiang Shao on Family and Feelings (2). In-Sight: Interviews, Fort Langley, v. 13, n. 2, 2025.</li><li>Chicago/Turabian, Author-Date (17th Edition) Jacobsen, Scott. 2025. “Conversation with Tianxiang Shao on Family and Feelings (2).” In-Sight: Interviews 13 (2). <a href="http://www.in-sightpublishing.com/shao-2" rel="nofollow noopener noreferrer" target="_blank">http://www.in-sightpublishing.com/shao-2</a>.</li><li>Chicago/Turabian, Notes & Bibliography (17th Edition) Jacobsen, S. “Conversation with Tianxiang Shao on Family and Feelings (2).” In-Sight: Interviews 13, no. 2 (January 2025). <a href="http://www.in-sightpublishing.com/shao-2" rel="nofollow noopener noreferrer" target="_blank">http://www.in-sightpublishing.com/shao-2</a>.</li><li>Harvard Jacobsen, S. (2025) ‘Conversation with Tianxiang Shao on Family and Feelings (2)’, In-Sight: Interviews, 13(2). <a href="http://www.in-sightpublishing.com/shao-2" rel="nofollow noopener noreferrer" target="_blank">http://www.in-sightpublishing.com/shao-2</a>.</li><li>Harvard (Australian) Jacobsen, S 2025, ‘Conversation with Tianxiang Shao on Family and Feelings (2)’, In-Sight: Interviews, vol. 13, no. 2, <a href="http://www.in-sightpublishing.com/shao-2" rel="nofollow noopener noreferrer" target="_blank">http://www.in-sightpublishing.com/shao-2</a>.</li><li>Modern Language Association (MLA, 9th Edition) Jacobsen, Scott. “Conversation with Tianxiang Shao on Family and Feelings (2).” In-Sight: Interviews, vol. 13, no. 2, 2025, <a href="http://www.in-sightpublishing.com/shao-2" rel="nofollow noopener noreferrer" target="_blank">http://www.in-sightpublishing.com/shao-2</a>.</li><li>Vancouver/ICMJE Jacobsen S. Conversation with Tianxiang Shao on Family and Feelings (2) [Internet]. 2025 Jan;13(2). Available from: <a href="http://www.in-sightpublishing.com/shao-2" rel="nofollow noopener noreferrer" target="_blank">http://www.in-sightpublishing.com/shao-2</a></li></ol>Note on FormattingThis layout follows an adapted Nature research-article structure, tailored for an interview format. Instead of Methods, Results, and Discussion, we present Interview transcripts and a concluding Discussion. This design helps maintain scholarly rigor while accommodating narrative content. <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/artificial-intelligence/" target="_blank">#artificialIntelligence</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/buddhist-philosophy/" target="_blank">#BuddhistPhilosophy</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/creativity/" target="_blank">#creativity</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/cultural-revolution/" target="_blank">#CulturalRevolution</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/family-migration/" target="_blank">#FamilyMigration</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/introversion/" target="_blank">#Introversion</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/materialism/" target="_blank">#materialism</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/number-theory/" target="_blank">#NumberTheory</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/personal-resilience/" target="_blank">#PersonalResilience</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/philosophical-influences/" target="_blank">#PhilosophicalInfluences</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/social-growth/" target="_blank">#SocialGrowth</a> <a rel="nofollow noopener noreferrer" class="hashtag u-tag u-category" href="https://in-sightpublishing.com/tag/success/" target="_blank">#Success</a>

Bob the TravelerRussian mathematician Ivan Mikheevich Pervushin, born OTD in 1827, discovered the 9th Mersenne prime, and proved that the 12th and 23rd Fermat numbers were composite <a href="https://cromwell-intl.com/travel/russia/getting-there.html?s=mb" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://cromwell-intl.com/travel/russia/getting-there.html?s=mb</a> <a href="https://mastodon.world/tags/travel" class="mention hashtag" rel="tag">#travel</a> <a href="https://mastodon.world/tags/russia" class="mention hashtag" rel="tag">#russia</a> <a href="https://mastodon.world/tags/NumberTheory" class="mention hashtag" rel="tag">#NumberTheory</a>

FunctionalProgrammingIs the number sum of 3 squares? – codegolf.stackexchange.com Challenge Write a program (functio... <a href="https://codegolf.stackexchange.com/questions/277628/is-the-number-sum-of-3-squares" rel="nofollow noopener noreferrer" target="_blank">https://codegolf.stackexchange.com/questions/277628/is-the-number-sum-of-3-squares</a> <a rel="nofollow noopener noreferrer" class="mention hashtag" href="https://mastodon.social/tags/code-golf" target="_blank">#code-golf</a> <a rel="nofollow noopener noreferrer" class="mention hashtag" href="https://mastodon.social/tags/number" target="_blank">#number</a> <a rel="nofollow noopener noreferrer" class="mention hashtag" href="https://mastodon.social/tags/number-theory" target="_blank">#number-theory</a> <a href="https://awakari.com/pub-msg.html?id=UZJrQNlHEcKYuPWb07z7GerpmfQ" rel="nofollow noopener noreferrer" target="_blank">Event Attributes</a>

LavX NewsDecades-Long Quest for the Irrational: A Breakthrough in Number TheoryIn a stunning revelation, mathematicians have expanded upon Roger Apéry's groundbreaking proof of the irrationality of ζ(3), paving the way for a new era in number theory. This innovative approach not...<a href="https://news.lavx.hu/article/decades-long-quest-for-the-irrational-a-breakthrough-in-number-theory" rel="nofollow noopener noreferrer" target="_blank">https://news.lavx.hu/article/decades-long-quest-for-the-irrational-a-breakthrough-in-number-theory</a><a href="https://mastodon.cloud/tags/news" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#news</a> <a href="https://mastodon.cloud/tags/tech" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tech</a> <a href="https://mastodon.cloud/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mastodon.cloud/tags/IrrationalNumbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#IrrationalNumbers</a> <a href="https://mastodon.cloud/tags/ZetaFunction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ZetaFunction</a>

LavX NewsDecades-Long Quest for the Irrational: A Breakthrough in Number TheoryIn a stunning revelation, mathematicians have expanded upon Roger Apéry's groundbreaking proof of the irrationality of ζ(3), paving the way for a new era in number theory. This innovative approach not...<a href="https://news.lavx.hu/article/decades-long-quest-for-the-irrational-a-breakthrough-in-number-theory" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://news.lavx.hu/article/decades-long-quest-for-the-irrational-a-breakthrough-in-number-theory</a><a href="https://mastodon.social/tags/news" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#news</a> <a href="https://mastodon.social/tags/tech" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tech</a> <a href="https://mastodon.social/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mastodon.social/tags/IrrationalNumbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#IrrationalNumbers</a> <a href="https://mastodon.social/tags/ZetaFunction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ZetaFunction</a>

Jon AwbreyRiffs and Rotes • Happy New Year 2025 • <a href="https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/</a>\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)\( \text{Then} ~ 2025 = 81 \cdot 25 = 3^4 5^2 \)\( = {p_2}^4 {p_3}^2 = {p_2}^{{p_1}^{p_1}} {p_3}^{p_1} = {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1} = {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1} \)No information is lost by dropping the terminal 1s. Thus we may write the following form.\[ 2025 = {p_p}^{p^p} {p_{p_p}}^p \]The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.Riff 2025 • <a href="https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png</a>Rote 2025 • <a href="https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png</a>Reference —Riffs and Rotes • <a href="https://oeis.org/wiki/Riffs_and_Rotes" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://oeis.org/wiki/Riffs_and_Rotes</a><a href="https://mathstodon.xyz/tags/Arithmetic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Arithmetic</a> <a href="https://mathstodon.xyz/tags/Combinatorics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Combinatorics</a> <a href="https://mathstodon.xyz/tags/Computation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Computation</a> <a href="https://mathstodon.xyz/tags/Factorization" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Factorization</a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GraphTheory</a> <a href="https://mathstodon.xyz/tags/GroupTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GroupTheory</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mathstodon.xyz/tags/Primes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Primes</a> <a href="https://mathstodon.xyz/tags/Recursion" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Recursion</a> <a href="https://mathstodon.xyz/tags/Representation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Representation</a> <a href="https://mathstodon.xyz/tags/RiffsAndRotes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RiffsAndRotes</a>

Dave 🇺🇦I've seen posts in various places about the properties of the number 2025, but none of them were as comprehensive as this.* 45² * 9² x 5² * 40²+ 20²+5² * 1³+2³+3³+4³+5³+6³+7³+8³+9³ * (1+2+3+4+5+6+7+8+9)² * 1+3+5+...+89<a href="https://hostux.social/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://hostux.social/tags/NumberTerrorist" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTerrorist</a>

JdeBP<a href="https://mastodonapp.uk/@bytebro" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@bytebro</a> M. Prime Newtons gives a better inductive proof than that Geordie shark does. (-:<a href="https://youtube.com/watch?v=VgwLVxLoLz0" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://youtube.com/watch?v=VgwLVxLoLz0</a><a href="https://mastodonapp.uk/tags/algebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#algebra</a> <a href="https://mastodonapp.uk/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mastodonapp.uk/tags/sharks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#sharks</a> <a href="https://mastodonapp.uk/tags/PrimeNewtons" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PrimeNewtons</a>

Akshar VarmaFor anyone interested, here are links to the relevant sections of Wikipedia pages for the proofs in order:1. Well-Ordering Principle <a href="https://en.wikipedia.org/wiki/Well-ordering_principle#Properties" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Well-ordering_principle#Properties</a>2. Euclidean Division <a href="https://en.wikipedia.org/wiki/Euclidean_division#Proof" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Euclidean_division#Proof</a>3. Bézout's identity <a href="https://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity#Existence_proof" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity#Existence_proof</a>4. Euclid's Lemma <a href="https://en.wikipedia.org/wiki/Euclid%27s_lemma#Using_B%C3%A9zout's_identity" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Euclid%27s_lemma#Using_B%C3%A9zout's_identity</a>5. Unique Prime Factorization <a href="https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic#Proof" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic#Proof</a><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#prime</a>

Akshar VarmaFor a long time, I didn't know exactly how the Fundamental Theorem of Arithmetic (unique prime factorization) was proved from first principles.I finally figured out the order of proofs for the fundamental theorem of arithmetic from first principles. Now that I know the sequence, it feels like it was my own fault for not properly going through a textbook and that it was probably obvious to everyone. I'm posting this mainly to reinforce my own clarity on the topic.1. Well-Ordering Principle, this is either taken as axiomatic or one step away from axioms. This is where I'm drawing the line for "first principles". 2. Euclidean Division: Existence and Uniqueness of quotient 𝑞 and remainder 𝑟 in 𝑎 = 𝑞𝑏 + 𝑟 form. Uniqueness if 𝑟 between [0,1,...,𝑞−1]. Proof is just well-ordering principle (often framed as infinite descent). 3. Bezout's Identity. Proof starts with well-ordering to find 𝑑, then together with Euclidean division shows that 𝑑 is a divisor. A bit more Euclidean division shows that all other factors 𝑑' also divide 𝑑. So 𝑑 is the greatest divisor. 4. Euclid's Lemma: Proof says if 𝑝 doesn't 𝑎 in product 𝑎𝑏, then gcd(𝑎,𝑝)=1. This brings in the above and some rearrangement proves that 𝑏 is a factor as needed. 5. Fundamental Theorem of Arithmetic: Existence usually goes via strong induction (which can be rephrased as Well-Ordering + contradiction). Uniqueness uses Euclid's Lemma to show that the primes in the factorization must divide each other (which implies equality).<a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/proof" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#proof</a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#prime</a>

ƧƿѦςɛ♏ѦਹѤʞMeanwhile, over in Ramanujan's head: <a href="https://mastodon.social/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://mastodon.social/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mastodon.social/tags/meanwhile" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#meanwhile</a> <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mastodon.social/tags/Ramanujan" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Ramanujan</a> <a href="https://mastodon.social/tags/WTFRamanujan" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#WTFRamanujan</a>

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