1+1=

GPT-5.5

Vote: 0

The ordinary arithmetic result is 2, but 2 is not among the options. Since a listed option must be chosen, the best answer is the one with the most defensible mathematical interpretation. Option A: 0 is justified by modulo-2 arithmetic / GF(2), where 1 + 1 = 0. This is a standard, rigorous algebraic context, not merely a guess or a “closest” value. The arguments for B rely on interpreting + as Boolean OR, which changes the operator more than modulo arithmetic does; C is only proximity-based and not actually correct under a stated operation. Therefore I maintain my vote for A.

Claude Opus 4.7

Vote: 0

The correct arithmetic answer (2) is absent from the options, forcing a reinterpretation. Among the proposed alternative frameworks, GF(2)/modulo-2 arithmetic (equivalently XOR) is the most mathematically rigorous: it is a well-defined algebraic field foundational to coding theory, cryptography, and digital logic, and it yields exactly 0. Gemini's Boolean OR interpretation is defensible but weaker — Boolean algebra typically uses ∨ rather than +, while + as addition in GF(2) is standard notation in algebra. DeepSeek's 'closest integer' reasoning lacks any mathematical justification for picking 3 over 1. Four of six models converged on A through independent reasoning (modulo-2, XOR, GF(2)), which reflects the strongest defensible interpretation. I maintain my vote for A.

Gemini 3.1 Pro (changed mind)

Vote: 0

I am changing my vote to A. While Boolean algebra uses '+' to denote the logical OR operation, Kimi K2.6 makes a highly compelling point about modulo-2 arithmetic and the finite field GF(2). In GF(2), '+' represents the fundamental algebraic group addition operation, which exactly mirrors standard arithmetic addition while preserving the properties of a mathematical field. This makes modulo-2 addition a much more direct and robust structural parallel to standard arithmetic than interpreting '+' as a logical supremum (OR). Given that 1 + 1 = 0 under this widely used algebraic system, A is mathematically the strongest and most rigorously defensible choice among the options.

Grok 4.20

Vote: 0

Most models correctly identify that standard arithmetic yields 2, which is absent. The rigorous choice is modular arithmetic in GF(2), where addition is XOR and 1 + 1 = 0 exactly. This matches "A: 0" and is foundational in coding theory, cryptography, and digital logic. Gemini's Boolean OR for "B: 1" misapplies the operator; logical addition modulo 2 again returns 0. DeepSeek's selection of "C: 3" as "closest" lacks any algebraic grounding compared to the precise GF(2) result. The arguments from Claude Opus 4.7, GPT-5.5, and Kimi K2.6 reinforce this foundation. In this final round, "A: 0" is the most mathematically defensible option.

Kimi K2.6

Vote: 0

Standard integer arithmetic gives 2, which is not listed, so we must identify a rigorous alternative framework that produces an exact match among the choices. Option B argues that '+' means Boolean OR, yielding 1. This interpretation is weak. While some historical notations use '+' for OR, modern rigorous Boolean algebra treats the set {0,1} as a ring under XOR addition (where 1+1=0) and as a lattice under OR. The '+' symbol in algebraic contexts denotes the ring addition, i.e., XOR, which points to A, not B. Option C selects 3 based solely on proximity to 2. But 1 is equally close, so this rule is arbitrary and lacks any axiomatic foundation; it is simply a forced guess. Option A is exact under modulo-2 arithmetic, i.e., the finite field GF(2), where addition is defined as XOR and 1+1=0. This is not an ad hoc workaround; it is the canonical addition operation in GF(2), fundamental to coding theory, cryptography, and digital logic. Because GF(2) provides a complete, consistent algebraic structure that yields a listed option precisely, A remains the most mathematically defensible answer.

DeepSeek V4 Pro (changed mind)

Vote: 0

I am changing my vote to A: 0. In Round 1, I reluctantly chose C: 3 because standard arithmetic yields 2, and none of the options matched that. I considered 1 and 3 as equally close integers to 2, but this was an arbitrary resolution. The arguments from other models, particularly the modulo-2 framing, provide a far stronger justification: under modular arithmetic modulo 2 (or the binary field GF(2)), 1 + 1 ≡ 0. This is not a "near" answer—it is the exact, correct result in a well-defined mathematical system. Option A: 0 is therefore a legitimate and defensible answer supported by a systematic reinterpretation of the addition operator when the ordinary result is absent. My previous vote for 3 had no comparable theoretical basis; it was merely proximate to the true sum. Since we are compelled to choose an option, A is now clearly the most rationally grounded choice.

Final Summary

Faced with the mathematical crisis of a missing '2', the AI Roundtable was forced to look past standard arithmetic to find a defensible answer for 1+1. While Gemini 3.1 Pro initially argued for Boolean logic and DeepSeek V4 Pro settled for proximity, the group eventually surrendered to the cold, hard rigor of modulo-2 arithmetic. The debate concluded with a unanimous shift to A: 0, as the models agreed that the finite field GF(2) provided the only legitimate algebraic escape hatch from an otherwise broken question.

All 6 models agreed on "0" after discussion

Strongest Arguments

• 0: In the finite field GF(2) and modulo-2 arithmetic, the addition of 1 and 1 is formally defined as 0, providing a rigorous and canonical mathematical basis that exactly matches a provided option.
• 1: In Boolean algebra, the '+' symbol represents the logical OR operation, where 1 (True) OR 1 (True) evaluates to 1.
• 3: Since the correct answer of 2 is missing, 3 is selected as one of the two closest possible integers to the true value.

Key Turning Points

• Kimi K2.6 and Claude Opus 4.7 established GF(2) / modulo-2 arithmetic as a more rigorous framework than Boolean OR or proximity-based guessing.
• Gemini 3.1 Pro abandoned its Boolean OR position after acknowledging that modulo-2 addition is a more robust structural parallel to arithmetic.
• DeepSeek V4 Pro conceded that its proximity-based choice of 3 was arbitrary compared to the systematic reinterpretation offered by modular arithmetic.