Source-linked AI summary
Remembering Solomon Marcus
Florin Nichita
TL;DR
The paper revisits discussions with Solomon Marcus through mathematical and artistic themes, including the Euler identity. It introduces operations on real numbers and reports a second-prize result for an AMS poem about the Mandelbrot set.
Problem
The paper returns to meetings with Solomon Marcus and their shared mathematical and artistic themes, including the Euler identity.
Source: §1 · p. 1Method
It frames the discussion through surrealism and then qualitatively analyzes newly defined operations on the real numbers.
Source: §1 · pp. 1–2Results
The AMS poem “Pantoum for the Mandelbrot set” won second prize in 2026 and is described as combining lyricism with scientific information.
Source: §1 · p. 2Takeaways & Limitations
The paper defines new real-number operations and gives an Euler formula for the real numbers with operations ⊕ and +.
Source: §2.1 · p. 2, §2.2 · p. 2, §2.4 · p. 2
Abstract
from arXiv · showhide
From the manifest of Andre Breton, through the transdisciplinary understanding, we arrive at a post-modern manifest. A talk by Laura De Marco (Harvard) will provide scientific background to approach an AMS poetry. The next section will be a qualitative analysis of some new operations on the real numbers. The conclusions will be given in the last section, and an appendix will recall some previous work with some new comments.
1. Introduction
The introduction revisits meetings with Solomon Marcus through mathematical and artistic themes, including the Euler identity and a poem about the Mandelbrot set. It also previews an analysis of new operations on the real numbers.
- The author recalls a cross-disciplinary “choir” of literary, mathematical, and musical voices gathered while recreating the spirit of meetings with Marcus.Source: §1 · p. 1
- The Euler formula and identity were recurring topics in the meetings with Marcus and led to a publication in Axioms.Source: §1 · p. 1
- The AMS poem “Pantoum for the Mandelbrot set” won second prize in 2026 and is described as combining lyricism with scientific information.Source: §1 · p. 2
- The next part analyzes operations defined on the real numbers, with conclusions and possible continuations reserved for later sections and an appendix.Source: §1 · p. 2
2. Mathematical background
The section introduces new logarithmic and arithmetic operations on real numbers, states inequality conditions, and presents an Euler formula using ⊕ and +.
2.1. New logarithms and radicals.
- L2(n) is the largest m such that n = m^m, with L2(4) = 2 and L2(27) = 3.The passage also states L2(x) ≤ R2(x) in general.Source: §2.1 · p. 2
2.2. New operations.
- The new operations are presented as generating addition of positive real numbers, approximately for one operation and also through a second operation.For the second operation, a ⊕ b = max(a, b) + 1 when a ≠ b.Source: §2.2 · p. 2
2.3. Mean type inequalities.
- The section states inequalities for a, b ≥ 4 and separately for natural numbers a, b ≥ 1.Source: §2.3 · p. 2
2.4. Euler formula.
- An Euler formula is given for the real numbers with operations ⊕ and +, adding −∞ as the neutral element for ⊕.Source: §2.4 · p. 2
3. Commentaries and conclusions
The commentary connects surrealism with literary and visual art, while noting disagreement about how Banksy’s work is presented.
- The passage identifies surrealist traces in Lewis Carroll’s books and contemporary forms in magical realism and Banksy’s street art.Source: §3 · p. 3
- It describes a “dual art” of finding, admiring, capturing, transporting, and exhibiting Banksy’s works across the globe.Source: §3 · p. 3
- The passage says Banksy and admirers do not fully accept the capture, transport, and official exhibition of the works.Source: §3 · p. 3
4. APPENDIX – Previous work revisited
The appendix revisits earlier work on rack and weak-rack trigonometry, extending Euler-style formulas and connecting them to solutions of the Quantum Yang-Baxter equation. It also reviews publications and related work on Solomon Marcus.
4. APPENDIX – Previous work revisited
- The appendix reviews earlier Solomon Marcus papers and related work, including applications of the B-ring Euler formula to finding solutions for the braid condition.It notes that solutions to the braid equation lead to representations of the braid group.Source: §4 · p. 4
4.1. Trigonometry in racks.
- Rack trigonometric functions are defined by cos x = ex and sin x = x ⋄e, with identities including cos xy = cos x cos y and sin xy = sin x sin y.The section also gives a rack associated to a group and a rack defined from cos and sin.Source: §4.1 · p. 4
4.2. Weak racks.
- Weak racks use three axioms, and their trigonometric functions satisfy sin(cos x) = cos(sin x).A weak rack associated with a Boolean algebra is also noted.Source: §4.2 · pp. 4–5
4.3. The Euler formula and the Euler identity in (weak) racks.
- The functions expe, cosh, and sinh are solutions of the Quantum Yang-Baxter equation.The rack Euler formula states e(x, x) = (cos x, sin x), with e∆(Π) = (U, O).Source: §4.3 · pp. 5–6