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NSF 26-520: MPS Mathematical Sciences Research Programs (MPS MathSci)

Program Solicitation

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  • Posted: August 17, 2026

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Program Solicitation NSF 26-520

NSF Logo

U.S. National Science Foundation

Directorate for Mathematical and Physical Sciences

Full Proposal Deadline(s) (due by 5 p.m. submitting organization's local time):

     Proposals Accepted Anytime

Target submission dates vary by program; see relevant program webpages.

While proposals are accepted anytime, proposers are highly encouraged to submit by the target dates for the relevant program(s) to ensure consideration during the corresponding panel review cycle. Please check the program webpages for more information.

Important Information and Revision Notes

This solicitation consolidates most mathematical sciences funding opportunities within the NSF Directorate for Mathematical and Physical Sciences.

Proposals must be prepared in accordance with the NSF Proposal & Award Policies & Procedures Guide (PAPPG). Use the version of the guide that is in effect on the proposal's due date.

Summary of Program Requirements

General Information

Program Title:

MPS Mathematical Sciences Research Programs (MPS MathSci)

Synopsis of Program:

The U.S. National Science Foundation Directorate for Mathematical and Physical Sciences (NSF MPS) supports multiple research programs at the frontiers of discovery in theoretical and applied mathematical sciences.

Programs include:

NSF anticipates a portfolio of awards for these programs with a range of budgets, durations and scopes. Program budgets, number of awards, award sizes and durations are subject to the availability of funds.

NSF MPS is particularly interested in intellectually ambitious and potentially transformative foundational research. Proposals need not promise a near-term product, deployment, or commercial outcome, nor need they address later-stage development to be competitive.

NSF Priorities

The U.S. National Science Foundation (NSF) supports foundational research that leads to scientific breakthroughs and opens new frontiers of human knowledge. NSF investments in scientific discovery underpin technological innovation across industries, strengthening U.S. economic competitiveness, enhancing national security, and improving quality of life for all Americans.

NSF's priority under this funding opportunity is to advance foundational research, spanning both incremental advances that build systematically on prior scholarship and bold, high-risk inquiries capable of reshaping entire fields. NSF places particular emphasis on projects that challenge prevailing paradigms, ask important questions, develop new theories or methods, create research tools or datasets that enable further research, or open new lines of inquiry. Proposals need not promise a near-term product, deployment, or commercial outcome, nor must they address later-stage development in a named technology priority to be competitive. NSF further recognizes that the most consequential discoveries increasingly emerge at the boundary between disciplines, and it therefore strongly encourages proposals that forge novel connections across scientific domains.

Within this mandate, NSF is especially interested in intellectually ambitious and potentially transformative research; work that creates opportunities for exceptional early-career investigators; and proposals that leverage emerging technologies, including AI, advanced computation, and automation, to make new modes, methods, or scales of science possible. The use of these tools should be scientifically justified rather than incidental. Beyond accelerating existing workflows, such tools open fundamentally new scientific questions, reveal patterns invisible to prior methods, and enable experimental and analytical capabilities.

To support this vision, NSF seeks proposals spanning a wide range of funding levels and project durations. NSF is working to expand opportunities at both ends of this spectrum, including rapid grants that allow researchers to quickly test exploratory ideas and longer, larger awards that provide sustained support for ambitious, transformative research. For preliminary or time-sensitive work, NSF encourages investigators to use mechanisms such as Planning Proposal, RAPID, EAGER, and RAISE (see Chapter II.F of the PAPPG for more information). Where longer awards would benefit the pursuit of ambitious, transformative research and reduce administrative burden on investigators, NSF encourages proposals requesting up to five years of support. Investigators may consider the options above, and others, outside of the project sizes and durations specified in this funding opportunity.

NSF welcomes submissions from all researchers, particularly those earlier in their careers and those working in the foundational research areas highlighted in the Administration's FY28 Research and Development Budget Priorities Memorandum. NSF also expects the highest standards of scientific rigor, transparency, reproducibility, research integrity, and adherence to tenets of Gold Standard Science in proposals, as appropriate for the field of science and research modality.

Cognizant Program Officer(s):

Please note that the following information is current at the time of publishing. See program website for any updates to the points of contact.

Applicable Catalog of Federal Domestic Assistance (CFDA) Number(s):

  • 47.049 - Mathematical and Physical Sciences

Award Information

Anticipated Type of Award: Standard Grant or Continuing Grant

Estimated Number of Awards: 400 to 600

Anticipated Funding Amount: $200,000,000

Estimated program budget and number of awards are subject to the availability of funds.

Proposal Preparation and Submission Instructions

A. Proposal Preparation Instructions

  • Letters of Intent: Not required
  • Preliminary Proposal Submission: Not required

  • Full Proposals:

B. Budgetary Information

  • Cost Sharing Requirements:

    Inclusion of voluntary committed cost sharing is prohibited.

  • Indirect Cost (F&A) Limitations:

    Not Applicable

  • Other Budgetary Limitations:

    Not Applicable

C. Due Dates

  • Full Proposal Deadline(s) (due by 5 p.m. submitting organization's local time):

         Proposals Accepted Anytime

    Target submission dates vary by program; see relevant program webpages.

Proposal Review Information Criteria

Merit Review Criteria:

National Science Board approved criteria apply.

Award Administration Information

Award Conditions:

Standard NSF award conditions apply.

Reporting Requirements:

Standard NSF reporting requirements apply.

I. Introduction

The U.S. National Science Foundation Directorate for Mathematical and Physical Sciences (NSF MPS) supports research programs at the frontiers of discovery in theoretical and applied mathematical sciences. These programs advance foundational research and support the U.S. mathematical sciences workforce including students who will become the next generation of mathematical science professionals.

Foundational research in the mathematical sciences provides the fundamental language, concepts, and tools that enable advances across science, engineering, technology, and the economy. NSF support for foundational mathematical research has reliably produced transformative advances whose practical applications were not apparent at the time of discovery. NSF MPS supported research in the areas of algebra, number theory, and combinatorics, which underpins modern cryptography, cybersecurity, digital commerce, and national security. Similarly, NSF-supported research in probability theory, statistics, and computational methods has contributed to the mathematical foundations of data science, artificial intelligence (AI) and machine learning. Training today's large language models and other AI systems requires solving large-scale optimization problems enabled by these mathematical tools and techniques. Research in fields, such as algebra, geometry, differential equations, and topology substantially contributes to the study of condensed matter and quantum materials physics, including correlated, magnetic, and topological states; gravitational physics and geodesy; and the study of space and space-time.

In alignment with the Administration's Fiscal Year 2028 Research and Development Budget Priorities Memorandum, NSF MPS Mathematical Sciences programs support foundational research spanning pure and applied mathematics and statistics that remains the bedrock of American scientific and technological leadership. Key research areas include algebra, analysis, applied and computational mathematics; combinatorics, foundations, geometric analysis and topology; numerical analysis and uncertainty quantification; classical and quantum information theory and quantum computing; algorithms, computational complexity, cryptography, including post-quantum cryptography; statistics, probability, and the foundations of data science; and the mathematical foundations of high-performance and future computing. Cross-disciplinary research across these and other related areas generates new mathematical knowledge while enabling advances in other scientific and engineering disciplines. Together, these fields provide the mathematical foundations for advanced communication networks and secure information systems, quantum information science and future computing, and the modeling, simulation, and validation and verification capabilities that underpin critical technological innovation.

II. Program Description

This solicitation covers proposal submissions to the following NSF MPS programs. Research proposals that fit within a single program and interdisciplinary proposals that span multiple programs are both welcome. See the Proposal Preparation Instructions below for instructions to identify the relevant program.

See the individual program webpages for more information on the scope of each program. Target dates for proposal submissions are posted on each program's webpage.

Advances in formal mathematics, verification, and AI are creating new platforms for mathematical discovery. Proposers are encouraged, where appropriate, to take advantage of emerging tools that enable mathematical knowledge to be expressed in machine-readable form, facilitating its sharing, verification, and reuse. Proposals may integrate these platforms together with emerging AI capabilities to accelerate mathematical discovery. Proposals may also contribute foundational definitions, theorems, libraries, benchmarks, and other enabling tools to expand the range of mathematics these technologies may address when appropriate to exploring the mathematical frontier.

NSF MPS anticipates a portfolio of awards with a range of budgets and durations. Project budgets and durations must be commensurate with the scope of the proposed work. Estimated program budget, number of awards, and average award size/duration are subject to the availability of funds.

Proposals should advance one or more of the following measures of success:

  • Publications from research or other scholarly outputs
  • Improvements in student educational outcomes
  • Undergraduates, graduates or postdoctoral fellows supported
  • Undergraduate or graduate students trained in a specific critical area
  • Data sets established or expanded
  • New technologies or techniques established.

Core programs

  • Algebra and Number Theory: Supports research in algebra, algebraic and arithmetic geometry, number theory and representation theory.
  • Analysis: Supports research in analysis, including complex, harmonic, and real analysis, dynamical systems and ergodic theory, functional analysis, mathematical physics, operator theory and operator algebras, partial differential equations and calculus of variations.
  • Applied Mathematics: Supports mathematics research motivated by or affecting problems arising in science and engineering.
  • Combinatorics: Supports research on discrete structures. Focus areas include algebraic and geometric combinatorics, probabilistic and structural graph theory.
  • Computational Mathematics: Supports the development and analysis of innovative approaches to address the broad range of mathematical questions and challenges that arise from the implementation of numerical algorithms.
  • Foundations: Supports research in mathematical logic and foundations of mathematics, including set theory, model theory, computability theory and infinitary combinatorics, as well as applications to other areas such as artificial intelligence, formal verification, machine learning, quantum and more.
  • Geometric Analysis: Supports research in differential geometry, geometric group theory, geometric methods in modern mathematical physics, geometric partial differential equations and related geometric topics.
  • Mathematical Biology: Supports research in all areas of mathematical sciences relevant to the biological and life sciences.
  • Probability: Supports research on the theory and applications of probability including discrete probability, stochastic processes, limit theory, interacting particle systems, stochastic differential and partial differential equations and Markov processes.
  • Statistics: Supports research in statistical theory and methods, including research that leads to applications in any domain of science and engineering.
  • Topology: Supports research in algebraic topology, contact and symplectic structures, geometric topology, low dimensional topology and related topological topics.
  • Mathematical Sciences Research Infrastructure: Supports research infrastructure across the mathematical sciences community including training projects that complement existing opportunities.

Conferences and workshops

Proposals for conferences and workshops held in U.S.-based institutions may be submitted via the programs above. The topical area of the proposed conference or workshop must be within the scope of the program to which it is submitted.

Conference and workshop proposals that span multiple disciplinary programs, such as cross-cutting research activities, must be submitted to the Mathematical Sciences Research Infrastructure program.

For proposals seeking no more than $50,000, submit at least six months in advance of the conference or workshop date. For proposals seeking more than $50,000, submit at least nine months in advance of the conference or workshop date.

Mathematical Sciences Focused Research Groups

NSF MPS supports projects submitted by collaborative groups proposing to employ innovative methods to solve specific, major challenges in mathematics and statistics. Proposals should aim to solve outstanding problems of significant importance that require focused and synergistic group efforts. The solution of the proposed problems should have wide impacts in the mathematical and statistical sciences and potentially in other areas.

Mathematical Sciences Research Training Groups

NSF MPS supports efforts to strengthen the STEM workforce by improving graduate student research training and professional development. Submissions are invited in all areas of mathematical sciences and especially in the areas that align and integrate foundational research in mathematics and statistics with national priorities, such as the national missions called out in the Administration's FY 2028 Research and Development Budget Priorities Memorandum.

III. Award Information

Estimated program budget and number of awards are subject to the availability of funds.

IV. Eligibility Information

Who May Submit Proposals:

Proposals may only be submitted by the following:

  • Institutions of Higher Education (IHEs): Two- and four-year IHEs (including community colleges) accredited in, and having a campus located in the US, acting on behalf of their faculty members. Special Instructions for International Branch Campuses of US IHEs: If the proposal includes funding to be provided to an international branch campus of a US institution of higher education (including through use of sub-awards and consultant arrangements), the proposer must explain the benefit(s) to the project of performance at the international branch campus, and justify why the project activities cannot be performed at the US campus.
  • Non-profit, non-academic organizations: Independent museums, observatories, research laboratories, professional societies and similar organizations located in the U.S. that are directly associated with educational or research activities.
  • Tribal Nations: An American Indian or Alaska Native tribe, band, nation, pueblo, village, or community that the Secretary of the Interior acknowledges as a federally recognized tribe pursuant to the Federally Recognized Indian Tribe List Act of 1994, 25 U.S.C. §§ 5130-5131.

Who May Serve as PI:

There are no restrictions or limits.

Limit on Number of Proposals per Organization:

There are no restrictions or limits.

Limit on Number of Proposals Per PI or Co-PI:

There are no restrictions or limits.

V. Proposal Preparation and Submission Instructions

A. Proposal Preparation Instructions

Full Proposal Preparation Instructions: Proposers may opt to submit proposals in response to this Program Solicitation via Research.gov or Grants.gov.

You must prepare your proposal according to Chapter II.D.2 of the PAPPG, unless this solicitation specifies different instructions. Always use the version of the PAPPG in effect on your proposal's due date.

In determining which method to utilize in the electronic preparation and submission of the proposal, please note the following:

Collaborative Proposals. All collaborative proposals submitted as separate submissions from multiple organizations must be submitted via Research.gov. PAPPG Chapter II.E.3 provides additional information on collaborative proposals.

Follow all the Proposal Preparation instructions in the PAPPG, plus these additional instructions:

Proposals should be submitted to the appropriate mathematical sciences program(s) in research.gov. Titles should begin with an acronym selected from the following list. List the most relevant program acronym first. If more than one area is relevant, please see instructions below.

  • Algebra and Number Theory (ANT)
  • Analysis (Analysis)
  • Applied Mathematics (AM)
  • Combinatorics (Comb)
  • Computational Mathematics (CM)
  • Foundations (Fdns)
  • Geometric Analysis (GA)
  • Mathematical Biology (MB)
  • Probability (Prob)
  • Statistics (Stat)
  • Topology (Top)
  • Mathematical Sciences Focused Research Groups (FRG)
  • Mathematical Sciences Research Infrastructure (Inf)
  • Mathematical Sciences Research Training Groups (RTG)

The acronym should be followed by a colon, then the project's title. For example, title your proposal "ANT: Title" if you are submitting a proposal to the Algebra and Number Theory program.

If you submit a proposal as part of a set of collaborative proposals, the words "Collaborative Research" followed by a colon should appear at the beginning of the title, before the program acronym. For example, title your proposal "Collaborative Research: AM: Title" if you are submitting a collaborative proposal to the Applied Mathematics program. Please note that if submitting via Research.gov, the system will automatically insert the prepended title "Collaborative Research" when the collaborative set of proposals is created.

Proposals from predominantly undergraduate institutions (PUIs) should have a title that begins with the program acronym followed by a colon, then "RUI" followed by a colon, and then the title, for example, Stat: RUI: Title.

Proposals that extend beyond the scope of a single mathematical sciences program or area are welcome. In such cases, PIs should identify the acronym for the most relevant program or area, followed by any other relevant program acronym(s), separated by colons. For example, Top: CM: Title. In this example, the proposal would be submitted to the Topology program and would be considered by both the Computational Mathematics and Topology programs, with Topology as the primary program of interest.

Program officers will work collaboratively to ensure that these proposals are appropriately reviewed and considered for funding. NSF recommends submitting by the earliest target date listed on the relevant program pages.

Conference and travel proposals should identify the program(s) of interest in a similar manner. If submitting via Research.gov, the system will automatically insert the word "Conference" in the title when a conference proposal is created. For example, "Conference: Analysis: Title" for a conference proposal to the Analysis program.

B. Budgetary Information

Cost Sharing:

Inclusion of voluntary committed cost sharing is prohibited.

C. Research.gov/Grants.gov Requirements

You can submit proposals in response to this solicitation through Research.gov or Grants.gov, unless otherwise noted.

Information on how to prepare and submit proposals is available on the Submitting Your Proposal page on NSF.gov.

VI. NSF Proposal Processing and Review Procedures

Information on NSF's proposal processing and review procedures is available on the Overview of the NSF Proposal and Award Process page on NSF.gov.

A. Merit Review Principles and Criteria

All NSF proposals are evaluated through use of the two National Science Board-approved merit review criteria:

  • Intellectual Merit, which encompasses the potential to advance knowledge.
  • Broader Impacts, which encompass the potential to benefit society and contribute to the achievement of specific, desired societal outcomes.

Information on NSF's merit review principles and process can be found on the How We Make Funding Decisions page on NSF.gov.

B. Review and Selection Process

Proposals submitted in response to this program solicitation will be reviewed by

Ad hoc Review and/or Panel Review, or Internal NSF Review.

Proposals will be evaluated according to the standard NSF merit review criteria of intellectual merit and broader impacts. The review process will include ad hoc mail reviewers as needed in combination with review panels and internal NSF reviews. At least two primary reviewers will be assigned to each research proposal. Triage mechanism will be utilized as appropriate.

External review will not be required for conference, workshop, or symposium proposals up to $200,000.

After a proposal passes an initial compliance check, it will be reviewed by an NSF Program Officer. In most cases, three or more external experts will also review it (either as ad hoc reviewers, panelists or both).

Visit the Overview of the NSF Proposal and Award Process page for more information on the proposal review and selection process.

In alignment with Executive Order 14332 (Improving Oversight of Federal Grantmaking), all else being equal after merit review, NSF may give preference to institutions with lower indirect cost rates.

VII. Award Administration Information

A. Notification of the Award

Notification of an award is made to the submitting organization by an NSF Grants and Agreements Officer.

B. Award Conditions

Information on NSF award conditions can be found on the Award Terms and Conditions page on NSF.gov and Chapter VII of the PAPPG.

Administrative and National Policy Requirements:

Information on administrative and national policy requirements can be found on the National Policy Requirements for Recipients of NSF Awards page on NSF.gov.

Consistent with the requirements specified in 2 CFR § 200.332, recipients of NSF awards must adhere to the requirements for pass-through entities in establishing and managing subawards issued ensuring alignment with Administration and NSF policies and priorities.

In alignment with Executive Order 14332 (Improving Oversight of Federal Grantmaking), proposers should be aware that NSF awards offered under this funding opportunity may include termination for convenience provisions.

C. Reporting Requirements

Unless your award notice says otherwise, NSF requires the principal investigator of every grant to submit annual project reports and a project outcomes report for the general public. For complete reporting requirements, see Chapter VII of the PAPPG.

VIII. Agency Contacts

For questions related to the use of NSF systems contact:

  • Research.gov: NSF IT Service Desk at rgov@nsf.gov or 1-800-381-1532. The Service Desk is open from 7 a.m. to 9 p.m. Eastern time, Monday through Friday (except for federal holidays).

For questions relating to Grants.gov contact:

  • Grants.gov: The Grants.gov Contact Center at support@grants.gov or 1-800-518-4726. (Contact if the Authorized Organizational Representative (AOR) has not received a confirmation message from Grants.gov within 48 hours of submitting an application.)

Please note that the following information is current at the time of publishing. See the respective program webpage for any updates to the points of contact.

IX. Other Information

For information on NSF directorates, programs and funding opportunities, go to NSF.gov.

About the National Science Foundation

The U.S. National Science Foundation is an independent federal agency created by the "National Science Foundation Act of 1950." More information about NSF can be found on NSF.gov.

  • Location:

Randolph Building, 401 Dulany Street, Alexandria, VA 22314

  • General Information

(703) 292-5111

  • TDD (for the hearing-impaired):

(703) 292-5090

Privacy Act and Public Burden Statements

The information requested on proposal forms and project reports is solicited under the authority of the "National Science Foundation Act of 1950," as amended. More information can be found on the Privacy Act and Public Burden Statements page on NSF.gov.

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