Provides linear algebra, optimization and numerical methods.
Pay82
Resists AI78
Barrier to entry88
A Applied mathematics background connects to 2 professions on this site, ranked by pay. Each card explains why the major still matters for that job.
Where it leads
Swaps some abstraction for differential equations, numerical methods and modeling; the natural base for applied research, industrial mathematics and the better-paid exits into engineering and finance.
Pay68
Resists AI70
Barrier to entry82
Where this major is taught
MIT
United StatesMajor quantum-information and engineering research programs.
University of Waterloo
CanadaHome to the Institute for Quantum Computing.
ETH Zurich
SwitzerlandStrong quantum-device and information research.
University of Oxford
United KingdomLeading trapped-ion and quantum-network research.
Delft University of Technology
NetherlandsKnown for quantum nanoscience and hardware.
University of Tokyo
JapanMajor quantum physics and technology research.
Seoul National University
South KoreaStrong physics and semiconductor research.
Technical University of Munich
GermanyConnects quantum research with German industry.
University of Göttingen
GermanyThe world's mathematical capital under Gauss, Riemann, Klein and Hilbert until the 1933 Nazi purges emptied it in a year; its seminar model shaped mathematics education everywhere.
École Normale Supérieure, Paris
FranceThe most concentrated producer of elite mathematicians anywhere: the large majority of France's Fields medalists — more per capita than any nation — passed through its rue d'Ulm campus.
University of Cambridge
United KingdomHome of Newton, Hardy, Littlewood and Ramanujan; its one-year Part III course has been a gateway into research mathematics since the era of the Mathematical Tripos.
Princeton University & the IAS
United StatesPrinceton's department plus the neighboring Institute for Advanced Study — refuge of Einstein, Gödel and von Neumann — form the densest cluster of research mathematics in the Americas; Wiles proved Fermat there.
Credentials on this path
PhD in quantum science or engineering
GlobalThe standard research credential for many hardware and architecture roles.
Cleanroom safety certification
GlobalRequired locally before working independently in microfabrication facilities.
Laser safety certification
GlobalRequired training for laboratories using hazardous optical systems.
IEEE quantum courses
GlobalProfessional education that supplements, rather than replaces, laboratory experience.
PhD in mathematics
WorldwideThe universal research credential: no laboratory license or state exam exists for mathematics, so the doctorate — an accepted original contribution — is the profession's one true gate, required for essentially every research and university post.
Habilitation / HDR
Germany, France & central EuropeA second, post-doctoral thesis traditionally required for full professorships in German-speaking countries (Habilitation) and for supervising doctorates in France (Habilitation à diriger des recherches) — a survival of the 19th-century German system that invented the research university.
Agrégation de mathématiques
FranceFrance's fiercely competitive national examination, held since the 18th century, which confers a lifetime civil-service teaching rank. Many French research mathematicians sit it as a rite of passage; its oral, performed at the blackboard before a jury, is legendary.
Chartered Mathematician (CMath)
United KingdomAwarded by the Institute of Mathematics and its Applications, the UK's professional designation for practicing mathematicians in industry and government — evidence of the field's applied wing formalizing itself the way engineering did.