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Pure Math Jobs in Ontario (NOW HIRING)

Principal RF Engineer You will own the mathematical and physical foundations of one of the few ... This is not a pure research position; the expectation is that you are building, testing, and ...

While we're focused on real‑world application rather than pure research, you'll be working with ... Bachelor's or Master's Degree in Computer Science, Mathematics, or a related field. * 2+ years of ...

... math and science olympiad winners to chess champions. We have a global mindset and big ambitions ... We're not looking for designers who've drifted toward pure strategy or metrics - this role demands ...

Pure Math information

What is a pure mathematician?

Pure mathematicians are professionals who study mathematics for its own sake, rather than for its direct application to practical problems. They focus on abstract concepts, theories, and structures such as number theory, algebra, geometry, and mathematical logic. Their work often involves proving new theorems, developing new mathematical frameworks, and advancing the overall understanding of mathematical principles, which can later have unexpected applications in science, technology, and engineering.

Does pure math pay well?

Pure math careers typically offer moderate to high salaries, especially for roles in academia, research, or data analysis that require advanced analytical and problem-solving skills. Salaries can vary based on experience, education level, and industry, with some positions in finance or technology offering higher compensation. Overall, pure math can be financially rewarding for those with specialized skills and advanced degrees.

What are the key skills and qualifications needed to thrive as a pure mathematician, and why are they important?

To thrive as a Pure Mathematician, you need advanced mathematical reasoning, abstract thinking, and a graduate degree (often a Ph.D.) in mathematics or a related field. Familiarity with mathematical software such as Mathematica, MATLAB, or LaTeX for documentation and research purposes is typically required. Strong analytical skills, perseverance, and effective written and verbal communication make someone stand out in this role. These skills are vital for developing new mathematical theories, publishing research, and collaborating with academic or industry peers.

What are some common challenges faced by professionals working in pure mathematics, and how can they be addressed?

Professionals in pure mathematics often encounter challenges such as working on abstract problems with solutions that may not have immediate practical applications. This can lead to periods of slow progress or difficulty in demonstrating the impact of their work. Collaboration with peers through seminars, conferences, and research groups is essential to gain new perspectives and overcome intellectual roadblocks. Additionally, regular communication within academic departments or research teams helps foster a supportive environment and facilitates the sharing of ideas, which can be crucial in advancing complex mathematical theories.

What is the difference between Pure Math vs Data Analyst?

AspectPure MathData Analyst
Required CredentialsMathematical degrees, often advancedBachelor's or master's in statistics, mathematics, or related fields
Work EnvironmentAcademic, research institutions, or theoretical settingsBusiness, finance, tech companies, often in office settings
Industry UsageResearch, academia, theoretical developmentData interpretation, reporting, decision-making support
Common Search/ComparisonPure Math vs Data Analyst

Pure Math focuses on theoretical and abstract mathematical concepts, often in academic or research environments. Data Analysts apply statistical and mathematical skills to interpret data and support business decisions. While both roles require strong math skills, Pure Math is more research-oriented, whereas Data Analysts are more application-focused in industry settings.

Where do pure mathematicians work?

Pure mathematicians typically work in academic institutions such as universities and research institutes, where they conduct theoretical research and teach. They may also find employment in government agencies, private research organizations, or industry roles that require advanced mathematical analysis and problem-solving skills.
What are popular job titles related to Pure Math jobs in Ontario? For Pure Math jobs in Ontario, the most frequently searched job titles are:
Infographic showing various Pure Math job openings in Ontario as of August 2026, with employment types broken down into 100% Full Time. Highlights an 100% In-person job distribution.

Principal RF Engineer

Spire

Cambridge, ON • On-site

Other

Re-posted 26 days ago


Job description

Principal RF Engineer

You will own the mathematical and physical foundations of one of the few operational commercial space-based RF geolocation systems in active customer use today. The core problem: estimating the position of RF emitters using time difference of arrival (TDOA), frequency difference of arrival (FDOA), and angle of arrival (AoA) measurements collected by a constellation of low Earth orbit (LEO) satellites. You will formulate estimation problems, develop and validate algorithms, characterize error sources, and drive performance improvements across all three measurement domains.

You will inherit a working production geolocation system. This is not a greenfield research project. The algorithms exist, they run, and they produce results for real customers. Your job is to understand the existing system deeply, identify where performance is limited, and systematically improve it. Over time you will also extend the system with new measurement types and capabilities as mission requirements evolve.

This is a hands-on, iterative role operating on real-world data with all its imperfections. Calibration is incomplete. Truth data is sparse. Operational constraints require pragmatic engineering tradeoffs. You will spend significant time examining real geolocation outputs, diagnosing performance issues, refining algorithms based on what the data shows, and shipping incremental improvements. The work cycle is not "design an algorithm and hand it off." It is: analyze outputs, identify the limiting error source, develop or refine an algorithmic solution, validate it against data, and repeat. You will work alongside software engineers who handle production implementation and infrastructure; your role is to ensure the algorithms are correct, well-understood, and continuously improving.

You will write code daily. Python is the primary tool for prototyping, simulation, data analysis, and algorithm validation. This is not a pure research position; the expectation is that you are building, testing, and iterating on working code, not producing papers.

Key Responsibilities

  • Own and continuously improve TDOA, FDOA, and AoA geolocation algorithms from mathematical first principles through to working prototype implementations.
  • Develop deep understanding of the existing production geolocation codebase. Identify design assumptions, performance bottlenecks, and areas where the underlying math can be strengthened.
  • Reason across the full sensing chain: from collection geometry and onboard constraints through estimation algorithms to operational product performance. Own the end-to-end understanding of how system-level decisions affect geolocation accuracy.
  • Develop and improve calibration approaches for timing, frequency, antenna, and geometry alignment across a multi-use distributed satellite constellation.
  • Analyze geolocation outputs against ground truth and known emitter positions to identify systematic errors, performance regressions, and improvement opportunities.
  • Model and characterize error sources: satellite ephemeris uncertainty, clock drift, ionospheric/tropospheric propagation effects, multipath, antenna calibration, and receiver noise.
  • Incorporate orbital mechanics into signal models, accounting for satellite motion, Doppler dynamics, and constellation geometry.
  • Conduct performance analysis: derive theoretical bounds, run Monte Carlo simulations, and validate against real satellite data.
  • Translate validated algorithm improvements into specifications that software engineers implement in production systems. Review those implementations for correctness.
  • Add new capabilities as mission requirements evolve: new measurement types, new constellation geometries, new operating conditions.
  • Investigate and resolve anomalies in geolocation outputs by tracing errors back through the signal processing and estimation chain.
  • Document algorithms, assumptions, and performance characteristics with sufficient rigor for defense customer technical review.

Required Qualifications

  • Advanced degree (MSc or PhD) in electrical engineering, physics, applied mathematics, aerospace engineering, or a closely related field, with thesis or research work in estimation theory, statistical signal processing, or a related discipline.
  • Strong mathematical foundation in estimation and detection theory, linear algebra, probability, and optimization.
  • Demonstrated ability to go from problem formulation to working code. Python proficiency required; you will prototype algorithms, run simulations, and analyze data in Python daily.
  • Comfort working with imperfect real-world datasets where calibration is incomplete, truth data is sparse, and operational constraints demand pragmatic tradeoffs.
  • Comfort with iterative, data-driven development: you examine outputs, form hypotheses about what is limiting performance, implement fixes, and measure the result.
  • Ability to read and understand an existing algorithmic codebase built by someone else, and to work within and improve that system rather than rewrite it.
  • Understanding of, or demonstrated ability to rapidly learn, RF propagation physics and the signal models underlying TDOA, FDOA, and AoA estimation.
  • Familiarity with orbital mechanics concepts sufficient to incorporate satellite position and velocity into geolocation models.
  • Ability to read, understand, and critically evaluate published research in signal processing and geolocation.

Additional Qualifications

  • Direct experience with TDOA, FDOA, AoA, or hybrid geolocation techniques.
  • Background in SIGINT, electronic warfare, passive radar, or GNSS signal processing.
  • Experience with SAR, InSAR, or other radar remote sensing (the estimation theory and signal processing fundamentals transfer directly).
  • Experience developing or improving calibration routines for distributed RF systems.
  • C++ reading proficiency sufficient to review and validate production implementations of your algorithms.
  • Prior work in a defense, intelligence, or aerospace context.
  • Experience with spaceborne RF systems, phased array antennas, or LEO satellite constellations.

About the Team

You will join a small, focused RF geolocation team that includes experienced software engineers handling full-stack and embedded implementation. Your role is the algorithmic and scientific core. You will work directly with the team lead who brings domain expertise in RF geolocation and defense customer requirements. The team operates remotely across multiple time zones.

Spire operates a hybrid work model, and this position will require you to work a minimum of three days per week in the office.

Access to US export-controlled software and/or technology may be required for this role. If needed, Spire will arrange the necessary licenses-this is not something candidates need to have before applying. #LI-DC1