I looked at Jiang's monograph for a little while last night. Here is what I could get from it (I am now quoting from memory, so my terminology and notation may not be exactly the same). If $F$ is a field (of "numbers"), then the field $\overline{F}$ of "isodual numbers" has the same underlying set and addtion operation, but multiplication is replaced by the operation $x \ \overline{\bullet}\ y := - (xy)$. The new multiplicative identity is $-1$.

This is mathematically valid, of course: i.e., $\overline{F}$ really is a field. Moreover it is isomorphic to $F$ via the map $x \mapsto -x$, although I couldn't find a clear statement of that. (But somewhat later on I saw references to the isotopy $F \rightarrow \overline{F}$.) Physically speaking, the isodual numbers are supposed to bear the same relation to the ordinary numbers as antimatter does to matter. (I don't know what that means, but I am not a physicist and so am not even going to worry about it.)

Jiang defines a new function $J_2(\omega)$, which is supposed to be some sort of repaired version of the Riemann zeta function. In one of his published works, he claims that the Riemann hypothesis is false -- in fact, he says, the zeta function has no zeros in the critical strip. [Logically speaking, wouldn't that make the Riemann Hypothesis true? Never mind.] From this definition, he immediately deduces proofs of Goldbach, twin primes, primes of the form $n^2+1$, and several other outstanding number theoretic conjectures -- literally immediately, in that I could find no argumentation for them. First these results are stated for "isonumbers" but later on they are stated for the usual integers.

That's about as far as I got. I also noticed, though, that many of the results described in this monograph were first published as papers by the journal Algebra, Groups and Geometries (founding editor: R.M. Santilli). These papers appear on MathSciNet but are not (going to be) reviewed.

I looked at Jiang's monograph for a little while last night. Here is what I could get from it (I am now quoting from memory, so my terminology and notation may not be exactly the same). If $F$ is a field (of "numbers"), then the field $\overline{F}$ of "isodual numbers" has the same underlying set and addition operation, but multiplication is replaced by the operation $x \ \overline{\bullet}\ y := - (xy)$. The new multiplicative identity is $-1$.

This is mathematically valid, of course: i.e., $\overline{F}$ really is a field. Moreover it is isomorphic to $F$ via the map $x \mapsto -x$, although I couldn't find a clear statement of that. (But somewhat later on I saw references to the isotopy $F \rightarrow \overline{F}$.) Physically speaking, the isodual numbers are supposed to bear the same relation to the ordinary numbers as antimatter does to matter. (I don't know what that means, but I am not a physicist and so am not even going to worry about it.)

Jiang defines a new function $J_2(\omega)$, which is supposed to be some sort of repaired version of the Riemann zeta function. In one of his published works, he claims that the Riemann hypothesis is false -- in fact, he says, the zeta function has no zeros in the critical strip. [Logically speaking, wouldn't that make the Riemann Hypothesis true? Never mind.] From this definition, he immediately deduces proofs of Goldbach, twin primes, primes of the form $n^2+1$, and several other outstanding number theoretic conjectures -- literally immediately, in that I could find no argumentation for them. First these results are stated for "isonumbers" but later on they are stated for the usual integers.

That's about as far as I got. I also noticed, though, that many of the results described in this monograph were first published as papers by the journal Algebra, Groups and Geometries (founding editor: R.M. Santilli). These papers appear on MathSciNet but are not (going to be) reviewed.

I looked at Jiang's monograph for a little while last night. Here is what I could get from it (I am now quoting from memory, so my terminology and notation may not be exactly the same). If $F$ is a field (of "numbers"), then the field $\overline{F}$ of "isodual numbers" has the same underlying set and addtion operation, but multiplication is replaced by the operation $x \ \overline{\bullet}\ y := - (xy)$. The new multiplicative identity is $-1$.

This is mathematically valid, of course: i.e., $\overline{F}$ really is a field. Moreover it is isomorphic to $F$ via the map $x \mapsto -x$, although I couldn't find a clear statement of that. (But somewhat later on I saw references to the isotopy $F \rightarrow \overline{F}$.) Physically speaking, the isodual numbers are supposed to bear the same relation to the ordinary numbers as antimatter does to matter. (I don't know what that means, but I am not a physicist and so am not even going to worry about it.)

Jiang defines a new function $J_2(\omega)$, which is supposed to be some sort of repaired version of the Riemann zeta function. In one of his published works, he claims that the Riemann hypothesis is false -- in fact, he says, the zeta function has no zeros in the critical strip. [Logically speaking, wouldn't that make the Riemann Hypothesis true? Never mind.] From this definition, he immediately deduces proofs of Goldbach, twin primes, primes of the form $n^2+1$, and several other outstanding number theoretic conjectures -- literally immediately, in that I could find no argumentation for them. First these results are stated for "isonumbers" but later on they are stated for the usual integers.

That's about as far as I got. I also noticed, though, that many of the results described in this monograph were first published as papers by the journal Algebra, groups and geometries. These papers appear on MathSciNet but are not (going to be) reviewed.

I looked at Jiang's monograph for a little while last night. Here is what I could get from it (I am now quoting from memory, so my terminology and notation may not be exactly the same). If $F$ is a field (of "numbers"), then the field $\overline{F}$ of "isodual numbers" has the same underlying set and addtion operation, but multiplication is replaced by the operation $x \ \overline{\bullet}\ y := - (xy)$. The new multiplicative identity is $-1$.

This is mathematically valid, of course: i.e., $\overline{F}$ really is a field. Moreover it is isomorphic to $F$ via the map $x \mapsto -x$, although I couldn't find a clear statement of that. (But somewhat later on I saw references to the isotopy $F \rightarrow \overline{F}$.) Physically speaking, the isodual numbers are supposed to bear the same relation to the ordinary numbers as antimatter does to matter. (I don't know what that means, but I am not a physicist and so am not even going to worry about it.)

Jiang defines a new function $J_2(\omega)$, which is supposed to be some sort of repaired version of the Riemann zeta function. In one of his published works, he claims that the Riemann hypothesis is false -- in fact, he says, the zeta function has no zeros in the critical strip. [Logically speaking, wouldn't that make the Riemann Hypothesis true? Never mind.] From this definition, he immediately deduces proofs of Goldbach, twin primes, primes of the form $n^2+1$, and several other outstanding number theoretic conjectures -- literally immediately, in that I could find no argumentation for them. First these results are stated for "isonumbers" but later on they are stated for the usual integers.

That's about as far as I got. I also noticed, though, that many of the results described in this monograph were first published as papers by the journal Algebra, Groups and Geometries (founding editor: R.M. Santilli). These papers appear on MathSciNet but are not (going to be) reviewed.