## 2.51 Mathematics

Category: Logic and Mathematics

Keywords: mathematics, arithmetic, numbers, mathematical, proofs, infinity, axioms, counting, infinitely, theorems, proved, prime, proof, hilbert, numerical

Number of Articles: 420
Percentage of Total: 1.3%
Rank: 23rd

Weighted Number of Articles: 333.3
Percentage of Total: 1%
Rank: 40th

Mean Publication Year: 1978.7
Weighted Mean Publication Year: 1974.9
Median Publication Year: 1982
Modal Publication Year: 1993

Topic with Most Overlap: Sets and Grue (0.0422)
Topic this Overlaps Most With: Sets and Grue (0.0335)
Topic with Least Overlap: Emotions (0.00019)
Topic this Overlaps Least With: Duties (0.00025)

Table 2.121: Characteristic articles of the mathematics topic.
Table 2.122: Highly cited articles in the mathematics topic.

When I did a new model run, one of the first things I checked was whether the model had found the philosophy of mathematics topic. And the quickest way to check for that was whether it had clearly put the two big Benacerraf papers in the same topic. Most models passed this test, but some of them did so less clearly than others. This model run just passes the test. Here are the probability distributions over the ninety topics for the two articles.12

Table 2.123: Paul Benacerraf, “What Numbers Could Not Be.”
Subject Probability
Mathematics 0.3073
Ordinary language 0.2166
Sets and grue 0.1680
Meaning and use 0.0633
Denoting 0.0370
Personal identity 0.0226
Universals and particulars 0.0220
Verification 0.0208
Norms 0.0202

That makes sense—it is a philosophy of mathematics article, but it is largely about sets, and it can’t escape the fact that it’s written during the era of ordinary language philosophy. But the second table is a closer run thing.

Table 2.124: Paul Benacerraf, “Mathematical Truth.”
Subject Probability
Mathematics 0.2001
Truth 0.1713
Ordinary language 0.1198
Norms 0.0744
Knowledge 0.0637
Concepts 0.0539
Definitions 0.0465
Theories and realism 0.0347
Analytic/synthetic 0.0246
Verification 0.0245
Justification 0.0216
Propositions and implications 0.0207

Again, this sort of makes sense—the article is about truth. But the model is much less sure how to classify this article, as evidenced by the number of topics that get a probability between 4.6 percent and 7.4 percent.

What the model is working with is a conception of philosophy of mathematics that is centered around two debates. One is the nature of infinity, the other is the nature of proof. That’s not a terrible take on twentieth-century philosophy of mathematics, but it does mean that papers like “Mathematical Truth” get treated as less than fully paradigmatic.

I mostly look at how big a topic is by eyeballing the twelve journal graph. But in this case that would be highly misleading. Because this topic is spread across many journals, and many years, those twelve lines look like they barely have a pulse. But the tables show that, depending on size is measured, this is the twenty-third or fourtieth biggest topic. So many other topics are concentrated in a small number of journals or times, and they make a bigger visual impact than topics like this that keep chugging along.

1. Remember that these tables are cropped at 2%; the model assigns probabilities to all 90 topics but I’m not showing them all here.↩︎