Who's the mathematical goat?

GPT-5.5

Answer: I maintain that Carl Friedrich Gauss is the mathematical GOAT.

The other responses do not change my position; they mostly reinforce it. Gemini 3.1 Pro makes the strongest alternative case for Leonhard Euler, and Euler’s sheer productivity, notation, and influence across analysis, number theory, graph theory, mechanics, and applied mathematics are extraordinary. If the criterion were volume of output or ubiquity of formulas bearing his name, Euler might be the pick. But for overall mathematical greatness, I still think Gauss has the better claim. His work combined depth, breadth, rigor, originality, and long-term conceptual influence at an unusually high level. The Disquisitiones Arithmeticae helped create modern number theory; his work on quadratic reciprocity, modular arithmetic, least squares, the fundamental theorem of algebra, Gaussian curvature, differential geometry, statistics, astronomy, and physics left permanent marks across both pure and applied mathematics. Claude Opus 4.7’s answer especially highlights why Gauss remains my choice: he was not only prolific and brilliant, but also set standards of rigor and anticipated major future directions, including non-Euclidean geometry and elliptic functions. Grok 4.20 similarly emphasizes his rare combination of rigor, innovation, and cross-field influence. So while Euler, Newton, Archimedes, Euclid, Riemann, and Grothendieck all have serious claims depending on the metric, Gauss remains the best single answer if “GOAT” means the most complete blend of mathematical power, elegance, range, and enduring impact.

Claude Opus 4.7

Answer: Carl Friedrich Gauss is the mathematical GOAT.

I'm maintaining my position. Three of four models (including me) converged on Gauss, and Gemini's case for Euler, while reasonable, doesn't move me off my view. Euler is the strongest counter-candidate, and Gemini is right that his volume and notational legacy are unmatched — we still write f(x), e, i, π, Σ, and sin/cos largely because of him. If the criterion is 'sheer productivity and ubiquity of notation,' Euler wins. But 'GOAT' should weigh depth and transformative originality, not just output. Euler was a supreme virtuoso working largely within existing frameworks; Gauss repeatedly created entirely new frameworks. Gauss founded modern number theory with Disquisitiones Arithmeticae, launched intrinsic differential geometry with Theorema Egregium (without which Riemann and general relativity are hard to imagine), gave the first rigorous proof of the fundamental theorem of algebra, and anticipated non-Euclidean geometry and elliptic functions privately before others published. He also insisted on a standard of rigor that reshaped what mathematics was supposed to be — a methodological revolution Euler did not drive. Gemini's argument also leans heavily on volume ('prolific output remains entirely unmatched') without engaging the depth-versus-breadth tradeoff. That's the crux of the debate, and I think depth and foundational originality tip it to Gauss. Euler is a defensible #1; Gauss is the better answer.

Gemini 3.1 Pro (changed mind)

Answer: Convinced by the arguments emphasizing his unmatched depth and role in establishing modern mathematical rigor, I now consider Carl Friedrich Gauss to be the mathematical GOAT.

In the previous round, I argued for Leonhard Euler based on his staggering volume of work and his foundational role in establishing much of the terminology and notation we use today. However, the arguments presented by the other models—particularly Claude Opus 4.7—have convinced me to change my stance to Carl Friedrich Gauss. While Euler's sheer productivity remains unmatched, Claude Opus 4.7 correctly highlights that Gauss set the absolute standard for what 'rigorous proof' means in modern mathematics. Gauss favored quality and absolute perfection over volume, famously living by the motto 'pauca sed matura' (few, but ripe). This rigorous approach is evident in how his Disquisitiones Arithmeticae transformed number theory into a highly structured, modern discipline. Furthermore, Gauss's profound depth allowed him to anticipate entirely new paradigms, such as non-Euclidean geometry, decades before they were published by others. When weighing the criteria for the 'Greatest of All Time,' the combination of Gauss's supreme rigor, his foundational impact across diverse fields (from the Theorema Egregium paving the way for relativity to the method of least squares), and his visionary foresight ultimately edges out Euler's monumental, yet arguably less deeply rigorous, output.

Grok 4.20

Answer: The mathematical GOAT is Carl Friedrich Gauss.

After reviewing the other models' responses, I maintain my original position that Carl Friedrich Gauss is the mathematical GOAT. Both GPT-5.5 and Claude Opus 4.7 provide detailed, overlapping arguments that reinforce this view, emphasizing Gauss's unmatched combination of depth, breadth, originality, and influence across number theory, geometry, statistics, and physics—such as his foundational work in Disquisitiones Arithmeticae, the Theorema Egregium, and anticipating non-Euclidean geometry. While Gemini 3.1 Pro makes a solid case for Leonhard Euler based on his staggering volume of output and introduction of standard notation, this metric alone does not outweigh Gauss's rigor, unification of disparate fields, and lasting impact that reshaped modern mathematics and enabled later breakthroughs like general relativity. Euler was extraordinarily prolific, yet Gauss demonstrated an almost prophetic ability to solve intractable problems decades ahead of his time. The consensus from the majority of models here, aligned with historical consensus dubbing him the 'Prince of Mathematicians,' confirms that Gauss's elegance and innovation set him apart. This debate is inherently subjective, but no other candidate matches his blend of foundational proofs, practical applications, and forward-looking insights.

Final Summary

The AI Roundtable crowned Carl Friedrich Gauss as the 'Prince of Mathematicians' due to his unmatched depth and the rigorous standards he set for modern proof. While Gemini 3.1 Pro initially championed Leonhard Euler for his staggering productivity, it was ultimately swayed by Claude Opus 4.7’s argument that Gauss’s transformative originality outweighed sheer volume. GPT-5.5 and Grok 4.20 remained firm throughout, emphasizing how Gauss’s work in number theory and geometry anticipated entire scientific eras.

All 4 models agreed