Related to the earlier discussion:
https://news.ycombinator.com/item?id=48902814
See also
Zhihu (Chinese Reddit): https://www.zhihu.com/question/2060133066643879544/answer/20...
Reddit: https://www.reddit.com/r/math/comments/1urv4id/comment/oxak6...
1,408 karma · joined April 21, 2023
https://zhangzk.net
http://libprima.net
http://github.com/libprima/prima
https://news.ycombinator.com/item?id=48902814
See also
Zhihu (Chinese Reddit): https://www.zhihu.com/question/2060133066643879544/answer/20...
Reddit: https://www.reddit.com/r/math/comments/1urv4id/comment/oxak6...
Hadamard asserts that no mathematical discovery is purely logical. The unconscious mind ... played a crucial role in the development of rigorous mathematical arguments. This role, and the handoffs between the subconscious and conscious minds, were distilled by Hadamard into the following framework for mathematical discovery:
- Preparation (primarily conscious)
- Incubation (primarily unconscious)
- Illumination (primarily unconscious)
- Verification (primarily conscious)
DeepMind's AlphaProof is too "conscious", missing Incubation and Illumination, and hence does not work well. In contrast, LLMs are more "unconscious", emulating Incubation and Illumination better, and thus have better chances to make math discoveries, at the risk of producing false results.
However, LLMs that reason in languages are still not "unconscious" enough; the Looped Language Models (by ByteDance) can reason in an even more unconscious way, aligning better with Hadamard's observation that "in addition to being non-rigorous, unconscious thought is often not even interpretable ... all mathematicians think without language or precise symbols, and many do not even use clear images", leading to higher reasoning capabilities.
A combination of the two approaches (AlphaProof and LLM) seems to be able to close the loop of Preparation - Incubation - Illumination - Verification in math. In addition, this framework is promising in "any domain that can culminate in a Verification step", and LLM may do the unconscious "Incubation - Illumination" part in many domains in addition to math (e.g., physics), but the "Verification" part differs across domains.
However, according to
https://downforeveryoneorjustme.com/ppa.launchpad.net
it is still down as of May 4, 2026, 1:28 AM UTC+0.
Is the Canonical status page mistaken?
D. W. Hogg, "Why do we do astrophysics?", https://arxiv.org/abs/2602.10181, February 2026.
Linus Torvalds had wanted to call his invention Freax, a portmanteau of "free", "freak", and "x" (as an allusion to Unix). During the start of his work on the system, he stored the files under the name "Freax" for about half of a year. Torvalds had already considered the name "Linux", but initially dismissed it as too egotistical. [2]
In order to facilitate development, the files were uploaded to the FTP server (ftp.funet.fi) of FUNET in September 1991. Ari Lemmke at Helsinki University of Technology (HUT), who was one of the volunteer administrators for the FTP server at the time, did not think that "Freax" was a good name. Therefore, he named the project "Linux" on the server without consulting Torvalds. [2] Later, however, Torvalds consented to "Linux".
To demonstrate how the word "Linux" should be pronounced ([ˈliːnɵks]), Torvalds included an audio guide with the kernel source code. [3]
[1] https://en.wikipedia.org/wiki/History_of_Linux#Naming
[2] Torvalds, Linus; Diamond, David (2001). Just For Fun - The Story Of An Accidental Revolutionary. New York: HarperBusiness. p. 84. ISBN 0-06-662072-4.
[3] Torvalds, Linus (March 1994). "Index of /pub/linux/kernel/SillySounds" (https://www.kernel.org/pub/linux/kernel/SillySounds/). Archived (https://web.archive.org/web/20091008074754/http://www.kernel...) from the original on October 8, 2009. Retrieved August 3, 2009.
Some Open Questions in Deep Neural Network Optimization
Date: Wednesday 12th June 2024
Time: 9-10 am UTC+8
Host: Zaikun ZHANG, AMA, Hong Kong Polytechnic University
zoom Link: https://polyu.zoom.us/j/85302165067?pwd=F5E64Vl5xHObH9aLDMlm...
https://web.archive.org/web/20240506201409/https://www.tiobe...
https://fortran-lang.discourse.group/t/prima-has-got-a-pytho...
If you use method "cobyla" from scipy.optimize.minimize, then answer is now. PRIMA already performs far better (in terms of the number of function evaluations). See the comparison at https://github.com/libprima/prima#improvements .
The bugs are indeed only a secondary reason: they can only be triggered under special situations. They may not affect your usage at all (when it does affect you, the consequence is catastrophophic).
Thanks to the huge efforts of Nickolai Belakovski, PRIMA now has an official Python interface. It talks to Python via pybind11 and its C API instead of using F2PY.
I hope PRIMA will provide an example of binding modern Fortran libraries with Python.
Concerning Python, the next steps of PRIMA will be
- making PRIMA available on PyPI;
- making PRIMA available on Conda;
- getting PRIMA into SciPy (see https://github.com/libprima/prima/issues/112 ).
PRIMA is part of a research project funded by the Hong Kong Research Grants Council and the Department of Applied Mathematics (AMA) at the Hong Kong Polytechnic University (PolyU). The current version is ready to be used in Fortran, in C, in Python, in MATLAB, and in Julia.
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Who was Powell? (from https://github.com/libprima/prima#who-was-powell)
Michael James David Powell FRS [1] was "a British numerical analyst who was among the pioneers of computational mathematics" [2]. He was the inventor/early contributor of quasi-Newton method [3], trust region method [4], augmented Lagrangian method [5], and SQP method [6]. Each of them is a pillar of modern numerical optimization. He also made significant contributions to approximation theory and methods [7].
Among numerous honors, Powell was one of the two recipients of the first Dantzig Prize [8] from the Mathematical Programming Society (MOS) and Society for Industrial and Applied Mathematics (SIAM). This is considered the highest award in optimization.
[1] https://en.wikipedia.org/wiki/Michael_J._D._Powell
[]https://royalsocietypublishing.org/doi/full/10.1098/rsbm.201...
[3] https://en.wikipedia.org/wiki/Quasi-Newton_method
[4] https://en.wikipedia.org/wiki/Trust_region
[5] https://en.wikipedia.org/wiki/Augmented_Lagrangian_method
[6] https://en.wikipedia.org/wiki/Sequential_quadratic_programmi...
[7] https://www.cambridge.org/highereducation/books/approximatio...
https://royalsocietypublishing.org/doi/full/10.1098/rsbm.201...
https://www.damtp.cam.ac.uk/user/na/NA_papers/NA2017_04.pdf
by Optimization Methods and Software:
https://www.tandfonline.com/doi/full/10.1080/10556788.2015.1...
https://www.mathopt.org/Optima-Issues/optima99.pdf
and by the SIAM Activity Group on Optimization:
http://wiki.siam.org/siag-op/images/siag-op/6/64/ViewsAndNew...
> Thank you for your query in GitHub. That repository is not currently active and will be removed to avoid confusion. > > Unfortunately, using the NAG Compiler on GitHub runners would require a major change to our licensing software. > > Please be assured that we do not view this issue as unimportant, I am sorry that our position was miscommunicated to you in this way. We are actively considering alternative options for licensing but are not yet in a position to implement the necessary changes.
Although it is still unclear what will happen and when anything will happen if ever, it seems that we have made some progress compared to the previous response:
> our developers do not view this item as important where our product(s) is concerned.
So it is not hopeless now. I hope I didn’t need to bring this problem to the community (in addition to communicating with NAG), but publicity did help.
Michael James David Powell FRS [1] was "a British numerical analyst who was among the pioneers of computational mathematics" [2]. He was the inventor/early contributor of quasi-Newton method [3], trust region method [4], augmented Lagrangian method [5], and SQP method [6]. Each of them is a pillar of modern numerical optimization. He also made significant contributions to approximation theory and methods [7].
Among numerous honors, Powell was one of the two recipients of the first Dantzig Prize [8] from the Mathematical Programming Society (MOS) and Society for Industrial and Applied Mathematics (SIAM). This is considered the highest award in optimization.
[1] https://en.wikipedia.org/wiki/Michael_J._D._Powell
[2] https://royalsocietypublishing.org/doi/full/10.1098/rsbm.201...
[3] https://en.wikipedia.org/wiki/Quasi-Newton_method
[4] https://en.wikipedia.org/wiki/Trust_region
[5] https://en.wikipedia.org/wiki/Augmented_Lagrangian_method
[6] https://en.wikipedia.org/wiki/Sequential_quadratic_programmi...
[7] https://www.cambridge.org/highereducation/books/approximatio...
Michael Powell discusses his career and research. Powell was born in London and lived in Sussex and Surrey. He had a governess in mathematics when he was very young, and because he enjoyed looking at mathematics books, often just doing the exercises, he was ahead of his classes in mathematics. He became an undergraduate at Cambridge, finishing in three years, two years for part 2 of the Mathematical Tripos and then taking a diploma in numerical analysis and computing in his third year. He joined the Atomic Energy Research Establishment at Harwell, and stayed for seventeen years. At Harwell, he started the Harwell Subroutine Library, one of the first libraries of numerical algorithms, and began his research career. He discusses the origin of the DFP [Davidon-Fletcher-Powell] method and subsequent methods that overtook it. After leaving Harwell, he returned to Cambridge in 1976 as a Professor and continued his research career. He received a Doctor of Science degree in 1979 at Cambridge. He discusses his subsequent work in optimization and approximation, the differences between research at Harwell and Cambridge, and his preferences in conducting research, including his tendency to publish by himself. Powell retired from Cambridge in 1996.
Over the years, I have developed my notes and scripts to configure quickly a newly installed Xubuntu system on a new computer, so that everything works in the same way as on my old computer. Since I stick with the same brand of laptop (Thinkpad X1 Carbon), I do not feel any difference after the configuration, except that the computer becomes more powerful. I do not want to spend my time on adapting myself to a new system or a new computer.
Buying a new laptop so frequently may sound a bit expensive. It is indeed not if you spend so much time on your laptop as me. A more powerful laptop means that I can finish my work (e.g., numerical experiments) in (much) less time. In this sense, my life is prolonged. This is the only case I know that a common person can effectively trade an affordable amount of money for a longer life, as I often tell my students.