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   Terence Tao (tao@mathstodon.xyz)'s status on Sunday, 25-May-2025 23:55:26 JST Terence Tao

   The NSF has reduced spending on the basic sciences by 50% or more in 2025, with similar cuts proposed for next year as well. For instance, through to May 21 of this year, the funding awarded to the mathematical sciences is currently $32 million, compared to the 10-year average of $113 million. (These are of course large numbers for an individual person, but with the US population of 340 million, this amounts to spending less than 22 cents per American per year on basic mathematical research, compared to the 10-year average of 80 cents per American per year.) https://www.nytimes.com/interactive/2025/05/22/upshot/nsf-grants-trump-cuts.html

   I myself have been fortunate to be supported by a small fraction of this 80 cents for almost the entirety of my professional career, allowing me to conduct research in the summer, invite speakers to my department, and to support graduate students. For now, I can continue these activities at a minimal level using by existing (and relatively modest) NSF grant https://www.nsf.gov/awardsearch/showAward?AWD_ID=2347850 , but already I do not have the resources to put into any future long-term projects. For instance, my experiments with using new technologies for mathematical workflows is being conducted purely by myself and contributions from unpaid online volunteers; I am applying for funding from several sources for these projects, but I am expecting the process to be extremely competitive. (1/3)

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     Terence Tao (tao@mathstodon.xyz)'s status on Sunday, 25-May-2025 23:55:24 JST Terence Tao

     in reply to

     But when cellphone adoption became widespread, it became necessary to figure out how to efficiently encode the signals of multiple cellular devices in the wireless spectrum in such a way that they do not interfere with each other. As it turns out, many of the mathematical techniques and insights generated by exploring these discrete and high-dimensional versions of the sphere packing problem have been of immense value for this problem - not just in the "positive" sense of designing efficient signal encoding methods, but also in the "negative" sense of also giving theoretical upper bounds on such efficiency, thus setting the right benchmarks to evaluate progress, and to avoid wasting resources on attempting encodings that are mathematically impossible.

     Such contributions to tangible technological advances are subtle and indirect; but without such basic research, many such advances would have taken far longer to be developed, and some may not have been pursued at all. The cuts to funding for such reseearch - which will particularly impact the next generation of researchers - may save a few cents a year in the short term, but greatly reduce the capacity to solve many challenging technological problems of significant real-world impact in the future. (3/3)

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     Terence Tao (tao@mathstodon.xyz)'s status on Sunday, 25-May-2025 23:55:25 JST Terence Tao

     in reply to

     Basic mathematical research pursues questions that are often quite far from actual practical application; but they contribute, in a largely invisible way, to the broader research ecosystem that eventually does generate such application. For instance, consider the problem of packing spheres into space as efficiently as possible - a question first proposed by Kepler in 1611. At a practical level, the solution to this problem has been "known" to greengrocers for centuries - one should stack the spheres in a hexagonal close packing. But mathematicians spent decades to work out how to establish the optimality of this packing, culminating in a formally verified proof in 2012.

     Mathematicians also explored variants of this sphere packing problem in other geometries than three-dimensional Euclidean space: for instance in higher dimensions, with the famous recent breakthroughs of Viazovska in 8 and 24 dimensions, or in more discrete geometries over finite fields. Such curiosity-driven questions appear to lack immediate application - nobody had a need to pack eight-dimensional oranges together, for instance. (2/3)

     Paul Cantrell repeated this.