Mathematics Research Specialist (Algebraic… at Crossing… · Remote

Role & Responsibilities

• Investigate challenging problems in Algebraic Geometry and related areas of pure mathematics.
• Develop, review, and refine advanced mathematical proofs, conjectures, and theoretical frameworks.
• Identify mathematical patterns, structures, assumptions, and gaps and formalize them into reusable specifications.
• Apply rigorous multi-step mathematical reasoning, including proof construction, counterexamples, and verification.
• Translate abstract mathematical concepts into structured frameworks for computational or AI-based reasoning systems.
• Evaluate mathematical arguments for correctness, rigor, completeness, and logical consistency.
• Communicate complex mathematical concepts clearly to research and technical teams.
• Document research findings, methodologies, and mathematical frameworks with clarity and precision.

Qualifications Required

• Ph.D. in Mathematics or a closely related field.
• Strong expertise in Algebraic Geometry.
• Strong experience in advanced mathematical proof development and theoretical analysis.
• At least 2 years of relevant research experience.
• Strong record of peer-reviewed publications in recognized mathematical journals.
• Excellent mathematical reasoning, problem-solving, and analytical skills.
• Ability to work on ambiguous, exploratory, and open-ended mathematical problems.
• Strong written and verbal communication skills.

Preferred Candidate Profile

• Research experience in areas such as schemes, varieties, morphisms, sheaves, divisors, curves, or cohomology.
• Knowledge of related fields such as commutative algebra, category theory, number theory, topology, or representation theory.
• Experience with mathematical or theorem-proving tools such as SageMath, Mathematica, Lean, Coq, or Isabelle.
• Experience translating mathematical reasoning into formal or computational frameworks.
• Experience evaluating mathematical reasoning, theorem-proving systems, or AI/LLM systems.
• Ability to communicate advanced mathematical concepts to both technical and non-technical audiences.