Searching from Two Directions — From Mathematical Proofs to Science Funding

When two points are hard to connect, working from both ends can reveal a route that is hard to see from either end alone. The same idea applies to science funding. A grant program asks researchers to describe work they want to do. SciWard, an experimental funding platform, starts with a participant’s existing record and uses AI to find and assess documented research and open-source contributions. These two approaches can bring different work into view.

What a Roman tunnel teaches about searching from both ends

In the second century, Roman crews dug an aqueduct tunnel from opposite sides of a mountain near Saldae, in present-day Algeria. The two passages went off course and passed each other. The surveyor Nonius Datus returned to the site and directed the work that finally joined them. The crews could work from both sides at once, but they still needed a common line to meet. Read the inscription of Nonius Datus and its translation.

Two directions in mathematical discovery

Suppose you want to prove a difficult identity, P = Q. You can simplify or rewrite P along one chain, P = A = B = …, and independently rewrite Q along another, … = Y = Z = Q. If both chains reach the same expression, you can join them. Sometimes the helpful intermediate expression is easier to recognize when you have seen what each side can become.

The same idea works at a larger scale. In his essay The Two Cultures of Mathematics, Timothy Gowers distinguishes between problem-solving and theory-building. A problem-solver starts with a specific question and looks for the tools to answer it. A theory-builder starts with a structure, develops definitions and general results, and looks for the questions those results can answer. One theory can yield a family of theorems whose individual statements were hard to foresee. The two approaches meet when a concrete problem reveals what a theory should explain, or when a theory supplies the lemma a particular proof needs. Read Gowers’s essay.

How business and basic research meet

Businesses often start with a need and look for knowledge or technology that can meet it. Basic research often starts with a question about how the world works, before there is a clear commercial application. Both directions matter to the economy. In 1831, Michael Faraday discovered electromagnetic induction, a principle that became the basis of modern electric generators. A scientific result can give engineers and entrepreneurs options they could scarcely have specified in advance. See Faraday’s generator at the Royal Institution.

Years earlier, in an 1817 lecture on chlorine, Faraday quoted Benjamin Franklin’s reply to demands for immediate usefulness. “What is the use of an infant?” Faraday’s own answer was “Endeavour to make it useful.” The exchange captures how discovery and application can come from different people, at different times. Read John Tyndall’s account of Faraday’s lecture.

How SciWard searches for research from the other direction

Universities, journals, and grant agencies already do much of the work of finding and evaluating research. Proposal-based funding has a natural boundary, though. A panel convened to evaluate submitted proposals sees the work that applicants bring before it. A researcher may already have produced a useful proof, replication, or software tool without ever writing a proposal that brings the contribution to a funder’s attention. See how the U.S. National Science Foundation reviews proposals.

SciWard changes who takes the first step in finding the work. A participant connects a record such as ORCID or GitHub, and the system uses AI to look for and assess the contributions documented there. For example, an independent researcher could connect a GitHub account with an open-source tool that other scientists use. The evaluation can begin with the tool and its documentation, without requiring the researcher to write a grant proposal about it. The account helps locate the work. The work itself provides the evidence for evaluation. See how SciWard evaluates documented contributions.

This approach still depends on the records SciWard can access and the quality of its assessments. An incomplete record can hide a contribution, and an AI system can misjudge the significance of work it finds. SciWard is a beta, with independent validation pending. The question I want it to answer is whether a funding system that actively looks through existing work can surface valuable contributions that proposal-based review would otherwise miss. See SciWard’s testing plans and evidence.