The Future of Mathematics: 1965 to 2065. Prepared for MAA Centenary Volume, 2015
Bibliographic record
Abstract
Abstract. William Gibson, the science fiction writer, who coined the term cyberspace well before he purchased his first personal computer has commented that the future is already here but that it is very poorly distributed. Mindful of the dangers of futurology, I shall look forward and back fifty years while where possible eschewing the unknowable. 1 The bigger picture It’s generally the way with progress that it looks much greater than it really is. Wittgenstein, 1889-1951, “whereof one cannot speak, thereof one must be silent”) (Ludwig The world will change. It will probably change for the better. It won’t seem better to me.... There was no respect for youth when I was young, and now that I am old, there is no respect for age. I missed it coming and going. (J. B. Priestley, 1894-1984) I was asked to take on a daunting and futile task—that of talking about the future of our discipline. I negotiated myself back to the current title. At least that way, I can be demonstrably wrong about past events even as I fail miserably when looking at the future. Or I could take the coward’s way out as Ken Davidson and I did when we agreed to write Mathematics in Canada. The Future of Mathematics in Canada 50 years later. [10]. We fairly accurately reprised the present (1995) and then made milquetoast predictions about the very proximate future. These were so conservative that I shuddered when I reread the article—just fifteen years later—in preparation for my current remit. ‘Futurology ’ is the domain of fools and flim-flam artists. It can be very profitable. I prefer science fiction like Daniel H. Wilson Robocalypse (2001) to fiction masquerading as science—my view of Ray Kurzweil’s The Singularity is Near (2005). The further out one looks the less one can say, and the loonier the results are likely to be in retrospect. An astonishing example is a recent attempt by
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.007 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.156 | 0.072 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".