Home / Federal careers / GS-1520
Mathematics
Performs professional mathematics work including mathematical research, analysis, and application of mathematical theories.
What GS-1520 pays
2025 base rates, before locality. Most federal employees add a locality adjustment on top.
| Grade | Step 1 | Step 2 | Step 3 | Step 4 | Step 5 | Step 6 | Step 7 | Step 8 | Step 9 | Step 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| GS-5 | $34,454 | $35,603 | $36,752 | $37,901 | $39,050 | $40,199 | $41,348 | $42,497 | $43,646 | $44,786 |
| GS-7 | $42,679 | $44,102 | $45,525 | $46,948 | $48,371 | $49,794 | $51,217 | $52,640 | $54,063 | $55,486 |
| GS-9 | $52,205 | $53,945 | $55,685 | $57,425 | $59,165 | $60,905 | $62,645 | $64,385 | $66,125 | $67,865 |
| GS-11 | $63,163 | $65,268 | $67,373 | $69,478 | $71,583 | $73,688 | $75,793 | $77,898 | $80,003 | $82,108 |
| GS-12 | $75,706 | $78,229 | $80,752 | $83,275 | $85,798 | $88,321 | $90,844 | $93,367 | $95,890 | $98,422 |
| GS-13 | $90,025 | $93,026 | $96,027 | $99,028 | $102,029 | $105,030 | $108,031 | $111,032 | $114,033 | $117,034 |
| GS-14 | $106,382 | $109,928 | $113,474 | $117,020 | $120,566 | $124,112 | $127,658 | $131,204 | $134,750 | $138,296 |
| GS-15 | $125,133 | $129,304 | $133,475 | $137,646 | $141,817 | $145,988 | $150,159 | $154,330 | $158,501 | $162,672 |
Base pay only. Locality pay adds 15 to 40 percent or more depending on where the job sits. Source: OPM 2025 General Schedule.
Qualification requirements
OPM's standard for GS-1520, as written.
Degree: mathematics; or the equivalent of a major that included at least 24 semester hours in mathematics.
or
Combination of education and experience -- courses equivalent to a major in mathematics (including at least 24 semester hours in mathematics), as shown in A above, plus appropriate experience or additional education.
The total course work in either A or B above must have included differential and integral calculus and, in addition, four advanced mathematics courses requiring calculus or equivalent mathematics courses as a prerequisite.
What this means if you served
- Write the duties, not the billet. OPM credits military experience on the work performed, and does not use rank or pay to judge specialized experience.
- Put the training and certifications you earned in service on the page. They count here.
- Claim your veterans preference on the application. It is not applied for you.
- This series carries a positive education requirement: a degree is required and experience cannot be substituted for it.
How to qualify for GS-1520
1Review Qualification Requirements
Read the OPM qualification standards above to understand the education and experience requirements for your target grade level.
2Find Your Grade Level
Grade follows the scope and complexity of the work you can document against the announcement, not the rank you held. OPM does not use military rank or pay when it evaluates specialized experience. Roughly: GS-5 entry, GS-7/9 junior, GS-11/12 journey, GS-13 and up senior.
3Gather Documentation
Collect your DD-214, SF-50 (if applicable), transcripts, certifications, and any training records that demonstrate your qualifications.
4Build Your Federal Resume
Two pages. USAJOBS has enforced that limit since 27 September 2025 and will not accept a longer resume from a Title 5 agency posting, so the space has to answer every qualification requirement. Include hours worked per week, supervisor contact details, and the accomplishments with numbers on them.
5Apply on USAJOBS
Search for open positions, carefully answer all assessment questions, and submit your application before the closing date.
Typical duties
- Conduct mathematical research
- Develop mathematical models
- Analyze mathematical problems
- Apply mathematical theories
- Prepare technical reports
- Collaborate with scientists and engineers
Key competencies
Mathematical Theory
Deep knowledge of mathematical principles and theorems.
Analysis
Strong skills in mathematical analysis and proof.
Applied Mathematics
Ability to apply math to practical problems.
Algorithm Development
Skill in developing mathematical algorithms.
Research
Ability to conduct original mathematical research.
Programming
Proficiency in mathematical computing software.
Technical Writing
Ability to prepare mathematical papers and reports.
Problem Solving
Skill in identifying mathematical approaches to problems.
Words the announcement will use
Use the ones your record actually supports. A rater is matching your experience against the specialized experience statement, and a keyword with nothing behind it does not survive that.
Questions about GS-1520
What is a federal Mathematician?
A GS-1520 Mathematician conducts mathematical research and applies mathematical theories to solve complex problems for the federal government. These professionals develop mathematical models, create algorithms, perform advanced analysis, and collaborate with scientists and engineers at agencies like NSA, DOD research facilities, NASA, NIST, and DOE national laboratories.
How much does a federal Mathematician make?
Federal Mathematicians earn between $34,454 (GS-5 Step 1) and $162,672 (GS-15 Step 10) on the 2025 GS scale. Most positions are at GS-11 through GS-14. A GS-13 Mathematician earns $90,025-$117,034. NSA (largest employer), DOD research facilities, and national laboratories offer positions. Senior research mathematicians can reach GS-15 or Senior Level (SL) positions.
What are the requirements for GS-1520 positions?
GS-1520 requires a degree in mathematics or equivalent with at least 24 semester hours in mathematics. Coursework must include differential and integral calculus plus four additional advanced math courses requiring calculus as prerequisite. Specialization in applied mathematics, statistics, or computational mathematics strengthens applications for most federal positions.
Can military experience substitute for education in GS-1520?
The required mathematics degree cannot be substituted with military experience alone. However, veterans with math degrees combined with military analytical experience are excellent candidates. Experience in cryptography, signals intelligence, weapons modeling, or technical intelligence provides relevant background. Many NSA mathematicians come from military intelligence backgrounds.
What is the career progression for Mathematician?
Mathematicians follow the GS-5/7/9/11/12 progression with journey level at GS-12 or GS-13. Senior mathematicians and research leads reach GS-14/15 or Senior Level positions. Career paths include specializing in cryptography (NSA), applied research (national labs), or theoretical mathematics. Some transition to research management or scientific leadership positions.
How do I apply for GS-1520 jobs on USAJOBS?
Search USAJOBS.gov for "Mathematician" or "Research Mathematician" under series 1520. NSA, DOD research facilities, NASA, NIST, and DOE labs are primary employers. Highlight your mathematical specialization, programming skills (Python, MATLAB, C++), and any publications. Many positions require security clearances—include clearance status in your resume. NSA hires heavily in this series.
Ready to apply for GS-1520?
A rater matches your record against the announcement's specialized experience statement, inside two pages. BMR writes that shape from your own experience: competency headers, real scope, hours per week, and the supervisor detail the rater checks.