I’ve planned 300 hours for the details of Wiles’ Proof of Fermat’s Last Theorem.

I bought another one for backup.

fig.3. the antecedent →Taniyama-Shimura conjecture. （fig.3: 有限の中の無限 by 西来路文郎清水健一)

fig.4.0. Conversion between e^iθ and l^p onto 0 for consideration of unsolved α, and l^p on Fourier transform.

note:
(1)~(11) for a time machine,

three of the requirements:
(1) { , , } as the coordinates ← generation energy.
(2) {0, 1} ← any prime number.
(3) the 0s of imaginary time changes the locations at the observation and the practice, because the real numbers are given to the imaginary time fields.

the conditions:
(4) the generation energy exists in the objective side, i.e. we don’t need send any energy to restore.
(5) there are the different phases of time, of + and - direction, already.
(6) as how a structure is, (4) and (5) can be applied the existence including the thinking of in quantum reaction exists in the quantum leaps.
(7) (6)’s yet unknown structure can be figured out in the inner/outer reflexives of the first scheme method, of the perfect language, especially when these structures are in our galaxy scale or beyond.

the links:
(8) Tachyon, an imaginary number field as super light speed.
https://kyonissho.com/kyos-blog/blog/2023/03/22/tachyon-an-imaginary-number-field-as-super-light-speed/
(9) Studying Quantum Biology
https://kyonissho.com/kyos-blog/blog/2022/01/05/studying-quantum-biology-4/
(10) The zero of life/existence dimension of any reason concept
https://kyonissho.com/kyos-blog/blog/2021/07/15/the-zero-of-life-existence-dimension-of-any-reason-concept/

(11) a way of thinking of a time machine;
e.g. when a generation energy is applied (fig.5.0.3a and fig.5.0.3b) to where a causality (e.g. thinking ability) arises (fig.5.0.1) as the suitable reproduction (fig.5.0.2b when the generation energy (green lines) was selected; fig.5.0.2a) via imaginary time in + or - direction, the sent causality will be restored there in existence.

And (12), great progress, news:

Article:
Time Is on My Sides: Researchers Show Double-Slit Experiment Also Applies to Time

Quotation:
”The results seem to have mind-blowing practical implications, too — especially appreciate how the scientists drape “time reversal” in the middle of the list below. …”

URL:
https://thequantuminsider.com/2023/04/04/time-is-on-my-sides-researchers-show-double-slit-experiment-also-applies-to-time/

fig.5.0.1. fig.16.3 of Studying Quantum Biology.

fig.5.0.2a. fig.3.1. the generation energy path → life; against entropy, of Tachyon, an imaginary number field as super light speed.

fig.5.0.2b. when the generation energy distribution ((b) of green generation energy’s lines reaching the object’s blue axes) was selected.

fig.5.0.3a. fig.15.1 of Studying Quantum Biology.

fig.5.0.3b. fig.15.2 of Studying Quantum Biology.

Link:
Studying Quantum Biology
Studying Quantum Biology – Kyo’s Blog (kyonissho.com)

Now I truly believe that God as all flooding energy exists in the entire universe, neither only on Earth, nor only in the Solar System, nor only in our Galaxy.

I’ll study next with Halmos in fig.5.1 not for Wiles’ this great book but for my approach.

When (x^d + y^d ≠ z^d)’s d → ∞, it means ∞ + ∞ ≠ ∞, I’ll study this with below book, mathematics of infinity.

I didn’t read this book itself, but I learned Cantor’s approach handles infinity (∞) as א (aleph), and realizes mathematics of infinities.

One of the three major books of Minkowski.

I received this book today. I think the mathematics of imaginary time, that Minkowski had realized, is described in this book.

Minkowski was Einstein’s teacher.

When (C → H) → 0, then imaginary number → ∞, the addition theorem unavailable there, and this is the half thing, while 0s of the imaginary time makes at least, two isometric spaces be one, Borrel conversion inflates from there, generation energy arises beyond time *a.
An imaginary number field is required to observe there.

*a:
+ and - of all amount are equal, based on projection to 0 is ubiquitous.
If you think projection to n, to think projection to imaginary 0 is better.

fig.8.1. ; generation energy (Genesis energy).

There are many cases of fig.8.1, e.g. fig.8.2.

fig.8.2. an instance as F7 and F5 of Galois field.

Fp ∋ n, T, ∵ Galois field.
n → ¬p, n → Galois’ imaginary number, T, ∵ any prime number → 0 in the ring.

Below, when α ⊂ Galois’ imaginary number, e.g. (3) means the distance (0 + 0 = 0) with (p - 1 + 1 = p = 0) is in distance 0, then Galois’s imaginary number = null.

In 0 time length by light speed,
(1) d ≧ 3: x^d + y^d = z^d + α
(2) d = 0: x^0 + y^0 = z^0 + α, ∵ 1 + 1 = 1 + α, α = 1
(3) d =2: x^2 + y^2 = z^2, d = 1: x^1 + y^1 = z^1
In dimension 0, 1 of step to n in Galois field is suitable (2)‘s α = 1 | α is extra-dimension.
Isometric phenomenon in the 0 without α of extra-dimension is possible only in (3), and we almost analyze phenomena with the inverse square law, 1/(f^2) | f is function.

And above, Galois field is suitable to spin.

fig.8.5. Fp | p ∋ n, n = {0, 1, 2, … , p-1}

When (Galois’s imaginary number α) ⊃ (all n\0), F3 = F5 = F7 in fig.8.5.

fig.8.6. compare {x2, x1}f^l_set with {1, 2, 3, 4, 5, 6}F7_set, {1}Fp_set, {0}Fp_set.

fig.8.7. abc conjecture and F2. complement arising; past or/and future spins (or/and in plural).

I’ve shown interval -> m with a geometric spin figure, the expression becomes simple, especially F2 is very special and important to discover.
Although, if you need an algebraic expression, it is …
when c is a combined number, Fc has a Galois’ imaginary number. If p - 1 = a and p - 1 + 1 = b, and a and b are evaluated as same rank, although (p - 1)’s next is p. But p - 1 + 1 isn’t c, c is a combined number. If a is calculated as p - 1, then b can’t decide number, but b’s next is 0. Or if b is calculated as p - 1, a can’t decide number, but a is regarded as having a same complement of {0, 10, 100, … , ∞} with b.

fig.8.8b. cf. F4 and F2, here (β : β) = (1 : 1). ref. 有限の中の無限西来路文郎清水健一

Or e.g. 655373 and 655379 are prime numbers, if F655378 of combined number is considered, [0, 0]interval is [655378 - 655373] = 5, 5 is a prime number, and m is -5. See fig.8.9.

fig.8.9a. generated by 素数チェッカ (Prime Number Checker) for iPhone.

E.g. 71290143685248119147 is a prime number. A big number but 0 in Fp, in [0, 10, 100, … , ∞]complement. If the spin has a combined number, there is another 0 in the same spin, some αx and βy are not fixed (* here, x and y are subscripts), but exist in m of [0, 0]interval in the spin. 71290143685248119147170 is the next prime number, but [0, 0]interval → m, and only F2 is an even prime number including Galois’ imaginary number, spinning.

fig.8.9b. generated by 素数チェッカ (Prime Number Checker) for iPhone.

And reading the Wiles’ proof different, below as α = Galois’ imaginary number, as imaginary number field is materializing spar-time’s objects.

Here, 0 by imaginary time → α, and {(E ⊥ δp) → function} in fig.9 is a case of 0 cone to reproduce reality, because there is energy.

Very beautiful space-time is observed, the generation energy is seemingly making all creation appears as we are imagining of the world now, and we will travel toward more unknown.

The quantum mechanics is mainly described with Hilbert space. Only any short range quantum field can be described with Hilbert space, we need to describe any large scale quantum field. I’m trying it with the generation energy (Genesis energy).

fig.10.0. over ((quadrangular number) → (+α = ¬0)).

fig.10.0:
Fermat’s conjecture, and Pythagorean theory\{¬0; figurate number}set.

fig.10.1. for ellipse, triangle, f(x/(l^2)) in galaxy/universe. ref. ellipse, Wikipedia.

fig.10.1:
(1) Johannes Kepler (1571~1630) discovered the orbits in our solar system are elliptic curve.
(2) Pierre de Fermat (1601~1665).
(3) f(x/(l^2))\{¬0; figurate number}set.

fig.10.2’s α is from n^d’s inner product.

If (a^d + b^d)^(1/d) = (z^d)^(1/d) is a norm to a side of projection to the isometric space.
The cases are (the right side : the left side), to consider
(1) rational number : rational number
(2) irrational number : rational number
(3) rational number : irrational number
(4) irrational number : irrational number
E.g. x = y = 2,
if (x^d + y^d)^(1/d) = (2x^d)^(1/d) = (z^d)^(1/d), (x^(d+1))^(1/d) = (z^d)^(1/d),
x^((d+1)/d) ≠ z^1, d=1 → x^2 is in the inverse square space, but (2) or (4) of F.
E.g. x = y ≠ 2,
if (x^d + y^d)^(1/d) = (2x^d)^(1/d) = (z^d)^(1/d),
2^(1/d) × x^1 = 2^(1/d) × y^1 ≠ z^1 in an isometric space, {2^(1/d) → β | β ∈ α}, (2) or (4) of F.

fig.10.3. (a^d + b^d + β)^(1/d) → norm, of fig.10.2. ref. Norm of Wikipedia.

fig.10.3’s β is from all area α.

fig.10.4. figurate number, of fig.10.0. ref. Figurate number of Wikipedia.

fig.10.5. e.g., of fig.10.4, the orange is P3(n): y(y+1)(y+2)/6=mod(x,3), the purple is P4(n): y(y+1)(y+2)(y+3)/24=mod(x,4). this graph has been generated by Quick Graph+.

fig.10.6. in order to observe the projection, P4(n) has been put on y-axis. e.g. the light-green is x=3 and y=3, lighter-green is x=4.

fig.10.7. fig.10.6 has been converted only of Galois field. see fig.10.2 again.

The world is not just as we see with our eyes.

By the way,

Hitler used Enigma to generate the cypher for the blitz’s tactics. Enigma’s base was Galois field.
USA realized ENIAC, UK realized Turing machine, in order to break Enigma. And Enigma’s code generating was broken with the speed.
ENIAC and Turing machine were the first computers, but destroyed after the WWII. I think if ENIAC or Turing machine were used to generate cyphers, nobody broke it then.

I could read some little stories of ENIAC. It might make a matrix with F2 and F5 of Galois field, 2 × 5 = 10 of the Enigma’s decimal. And if a present expression is used, it was a dual core processing.

“The Imitation Game” is a movie of Turing, Turing machine, and the team.