Intuitive Finding of Theory｜Salvaging the Reasoning of a Theory
A New Theory Within Myself
Those who propose new theories first seek the initial inspiration within themselves. Rather than relying on logic or language, they quantumly perceive today’s events as reactions (feedback) to the action of describing a subjective theme. Based on this intuitive, non-verbal perception, they search for theorems and theories, later translating their discoveries into human-interpretable language. Therefore, one sets forth assertions, describes a subject, and records these statements—much like dowsing. Subsequently, reality shifts and provides feedback either on the same or following day. Through repeated cycles of this process, the theorem becomes refined and polished.
Utilizing unseen forces
In other words, they continually refine their formulas through unseen forces. This approach—prioritizing action over theory, dynamics over causality, and adjusting theoretical descriptions through real-time daily feedback—occurs almost like automatic writing. Consequently, they often experience frustration when forgetting the reasoning behind the formulas they’ve created, sometimes as early as the very next day. Salvaging the original reasoning behind a groundbreaking equation is challenging.
Intuitive finding of theory
Historically, theoretical physicists and mathematicians have frequently described discovering theories or equations through intuitive actions or internal sensations, followed by the difficult process of translating these feelings into language or logic.
Salvaging the reasoning of a theory
The reasoning behind a theory often disappears easily. Retrieving the forgotten logic behind a theory is difficult. Many have expressed distress that once their intuitive insights and sensations are converted into words, the original intuition or reasoning behind their equations fades or becomes inaccessible. Salvaging the reasoning of a theory is a subset of discovering the theory itself.
There are documented accounts, anecdotes, letters, and memoirs from historical figures or their contemporaries describing their struggles with intuitive insights and the difficulty of translating those insights into formal mathematical or physical terms, as well as the challenge of recovering forgotten proofs of theories.
1. Carl Friedrich Gauss (1777–1855)
Gauss notoriously withheld detailed proofs, claiming clarity in the moment but failing to write them down. Gauss himself admitted this struggle explicitly in a letter:
- Letter to Janos Bolyai (1799–1860), regarding hyperbolic geometry, in which Gauss claimed he had discovered similar results but didn’t publish because the task of writing proofs clearly was burdensome.
- Gauss famously noted in private correspondence: “I have had my results for a long time, but I still struggle to find the best way to present the proofs clearly.”
Reference: Gauss’s correspondence published in Gauss Werke.
2. Michael Faraday (1791–1867)
Faraday repeatedly expressed frustration in translating intuitive ideas into mathematical language, as recorded in his correspondence and lab notebooks. He wrote explicitly about needing mathematical assistance:
- In letters exchanged with William Thomson (Lord Kelvin) and James Clerk Maxwell, Faraday openly acknowledged his difficulty: “I cannot sufficiently express these ideas mathematically.”
- Faraday notably remarked: “I perceive them clearly, but cannot give them mathematical form.”
Reference: Faraday’s letters and notebooks (published in Experimental Researches in Electricity and Faraday’s Diary).
3. Henri Poincaré (1854–1912)
Poincaré famously documented his intuitive struggles explicitly in his influential essay on mathematical creativity:
- In his essay “Mathematical Creation” from Science et Méthode (Science and Method, 1908), he clearly described the phenomenon of intuitive flashes and the difficulty retaining them: “Often, when I awake in the morning, the solution to a mathematical difficulty appears clearly to me…but the difficulty is holding it long enough to transcribe it.”
- He further elaborated: “Once I have written it down, the whole path disappears; the steps become invisible.”
Reference: Henri Poincaré, Science et Méthode, Chapter “Mathematical Creation,” 1908.
4. Albert Einstein (1879–1955)
Einstein described repeatedly his struggle to translate intuition into mathematics explicitly in letters, notes, and conversations, particularly during his development of General Relativity.
- In correspondence with mathematician Marcel Grossmann, Einstein explicitly admitted frustration: “Grossmann, you must help me or else I’ll go crazy! My intuition about the principles is clear, but I cannot turn it into mathematics clearly enough.”
- Einstein also famously reflected in personal writings: “The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought.”
Reference: Letters between Einstein and Marcel Grossmann, published in Einstein’s Collected Papers, Volumes 4 and 5.
5. Srinivasa Ramanujan (1887–1920)
Ramanujan’s notebooks themselves are concrete written evidence. He typically wrote down results without proofs. In letters to G.H. Hardy, he explicitly acknowledged intuitive leaps without formal proofs:
- Ramanujan famously wrote to Hardy: “An equation for me has no meaning unless it expresses a thought of God.”
- Hardy explicitly described Ramanujan’s method: “Ramanujan’s ideas came as intuitive leaps, and the difficulties lay in reconstructing the path after he had written the equation.”
Reference: Ramanujan’s Notebooks, Hardy’s memoir “Ramanujan,” and letters published in “Ramanujan: Letters and Commentary” by Bruce C. Berndt and Robert A. Rankin.
6. Paul Dirac (1902–1984)
Dirac clearly and explicitly wrote about intuition and mathematical expression. He famously spoke about his intuitive struggle in interviews and essays:
- In his essay, “The Evolution of the Physicist’s Picture of Nature,” Dirac explicitly stated: “I found that I could follow a mathematical path clearly, but once the insight was gone, I would have trouble retracing it.”
- He further acknowledged publicly in interviews (recorded by historians of physics): “The difficulty is that the original intuitive picture fades so quickly once it’s been formalized mathematically.”
Reference: Dirac’s writings, essays collected in Directions in Physics, and interviews recorded in Abraham Pais’s biography of Dirac, as well as other historical works by Graham Farmelo.
Summary:
These are explicit, verifiable historical references where these great minds openly described their struggle to salvage intuitive clarity and translate it clearly into formal mathematical language, often forgetting even shortly after making their discoveries.