Community chat: https://t.me/hamster_kombat_chat_2
Twitter: x.com/hamster_kombat
YouTube: https://www.youtube.com/@HamsterKombat_Official
Bot: https://t.me/hamster_kombat_bot
Game: https://t.me/hamster_kombat_bot/
Last updated 2 months, 2 weeks ago
Your easy, fun crypto trading app for buying and trading any crypto on the market
Last updated 2 months, 1 week ago
Turn your endless taps into a financial tool.
Join @tapswap_bot
Collaboration - @taping_Guru
Last updated 2 weeks, 5 days ago
This paper from Weil, presented at the 1979's Conference of the International Congress of Mathematics, is one of the finest papers to read on the importance of having a thorough understanding of history of mathematics. It is terrible that most of those who have been doing mathematics in recent times, have not been exposed to the history, nor do they learn the importance of it. As Weil quotes Leibniz in the paper:
Its use is not just that History my give everyone his due and that others may look forward to similar praise, but also that the art of discovery be promoted and its method known through illustrious examples.
This is crucial for a working mathematician in any field, and all of the prominent mathematicians, including Weil and the Bourbakis, had a good understanding of the history. I specifically blame the curriculum in K-12 and undergraduate courses, that either do not have an emphasis on history nor present the methods through an historical pedagogy. I believe one would only be limited to knowing a concept through the merely reduced caricatures of others in standard reference textbooks, until one dares open the original texts. And indeed, one should do this all the way back to the Greeks, from Archimedes through Euler, Gauss, Galois and the 20th century mathematicians
Not only does one appreciate mathematics better with a historical outlook, one appreciates the connections and dialogues of mathematics with other foundational fields such as logic, philosophy and physics. And as is apparent to anyone who has picked a math book from the 1800s and 2020s, the latter ones have no emphasis on these dialogues. It shows mathematics as some isolated study focused on these obscure objects, but if you had a background in Philosophy of Math, you could ask and read about the answers on why these objects are understood in a certain way, why do we understand the principle of induction in this particular manner? Similarly, the delightful intersections between physics and mathematics obviously are the richest.
I argue that without a historical outlook, one remains limited to doing meaningful contemporary research in any area of mathematics. As the number theorist and historian of mathematics Harold Edwards says in his paper *Read the Masters!:
Mathematics, like philosophy, is virtually inseparable from its history.*
André Weil, History of Mathematics: Why and How (1978)
I'd just like to interject for a moment. What you’re referring to as AI, is in fact, Generative AI, or as I’ve recently taken to calling it, Gen/AI. AI is not a wasteful grift unto itself, but rather another particular subfield of a larger field of AI, made useful by the low-cost motion detection, OCR utilities and other vital technologies used everywhere for a long time. Many people use many AI systems every day, without realizing it. Through a peculiar turn of events, the version of AI which is widely used today is often called “AI”, and many curious individuals are not aware that it is basically only the Gen/AI system which is a highly marketed grift. There really is a Gen/AI, and these marketing victims and grifters people are using it, but it is just a part of the much broader field of AI. Gen/AI is the one people take issue with: the subset of AI wasting tons of money, energy and other vital resources for little to no real-world benefit. Gen/AI is an essential part of the field of AI, but the most useless one; it can only cast shadow on the many AI systems we use every day that are energy-efficient solutions for real-world problems. Gen/AI is regularly criticised under the name of just "AI", but all the so-called "AI" systems are really just Gen/AI systems.
True love of God is amor Dei intellectualis: it includes knowledge as a necessary element and a necessary condition. No one can love what he has not, in some sense, known. Love by itself, without any admixture of knowledge, would be an impossibility. Whatever is loved is, by that very act, considered good; it is conceived of sub ratione boni. This knowledge of the good must spur on and give wings to the will, even though the What, i.e., the simple essence of the good in itself, remains inaccessible to knowledge. Here too, then, knowing and not knowing coincide. The principle of docta ignorantia as 'knowing ignorance' re-affirms itself once again.
Ernst Cassirer on the theology of Nicholas Cusanus, in The Individual and Cosmos in Renaissance Philosophy (1963)
Burckhardt called Pico’s oration one of the most noble bequests of the culture of the Renaissance. And indeed, it summarizes with grand simplicity and in pregnant form the whole intent of the Renaissance and its entire concept of knowledge. In this oration, we can clearly see the polarity upon which is based the moral and intellectual tension so characteristic of the Renaissance.
What is required of man’s will and knowledge is that they be completely turned towards the world and yet completely distinguish themselves from it. Will and knowledge may, or rather, must devote themselves to every part of the universe; for only by going through the entire universe can man traverse the circle of his own possibilities. But this complete openness towards the world must never signify a dissolution in it, a mystical-pantheistic losing of oneself. For the human will possesses itself only inasmuch as it is conscious that no single goal will fulfil it; and human knowledge possesses itself only inasmuch as it knows that no single object of knowledge can suffice for it. Thus, this turning towards the whole of the cosmos always implies the ability not to be bound to any one part.
Ernst Cassirer on Pico della Mirandola's Oratio de hominis dignitate (Oration on the Dignity of Man) [1486]
"Instead of asking "what is philosophy?", one should perhaps ask what kind of contents, i.e., what kind of mental activities, spiritual dimensions, methods, attitudes, practices, or even behavioral and ritual patterns may be subscribed under the name of "philosophy" when understood in the ancient sense of the way leading to wisdom... the main task of this philosophy remains essentially the same: to change perverted human nature, to transform it, eventually leading it to happiness and to a restored divine identity. This task is in fact directly inherited from the ancient "philosophies," that is, from the mysteries of death, transformation, and spiritual rebirth, and the related cosmogonical theories, systems of archetypal symbolism, and ritualized exercises of the "normative divine life."
~ Algis Uzdavinys, Philosophy as a Rite of Rebirth: From Ancient Egypt to Neoplatonism, 2008
Community chat: https://t.me/hamster_kombat_chat_2
Twitter: x.com/hamster_kombat
YouTube: https://www.youtube.com/@HamsterKombat_Official
Bot: https://t.me/hamster_kombat_bot
Game: https://t.me/hamster_kombat_bot/
Last updated 2 months, 2 weeks ago
Your easy, fun crypto trading app for buying and trading any crypto on the market
Last updated 2 months, 1 week ago
Turn your endless taps into a financial tool.
Join @tapswap_bot
Collaboration - @taping_Guru
Last updated 2 weeks, 5 days ago