January 1, 2025

Rethinking passwords

The more frequent a behavior, the harder it is to be aware of its existence. Looking up, I count 260 unique passwords saved on my password manager. Many of these are insufficient by themselves and require a second method of authentication to validate my credentials. If passwords alone are not enough, why have them at all? If achieving sufficient security still demands a code from an app, an email, or a phone, why not rely solely on the strongest method?

Passwords are the vestigial tailbone—a remnant of simpler times when we only needed one six-character password for everything on the internet. That is no longer possible. To cope, we’ve added more characters, enforced special characters, and banned sequential patterns. Yet, the problem persists. Social logins were introduced as an alternative, but people are still sensible about sharing login information with the main login providers, the typical privacy issues bad guys.

My proposal is simple: get rid of passwords and authenticate via temporary codes, preferably email or authentication apps. Skip the password step - don’t have it, don’t ask it. Having a password doesn’t add any meaningful security to accounts and is a terrible user experience.

For 2025.

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June 16, 2024

Subjectivity in Mathematics

Objectivity lives in a sterile, formal, rule-based world. Subjectivity lives in the real world. Mathematical objectivity is meaningless; mathematical subjectivity is meaningful. Aristotle brought the first; the second’s are yet to be brought.

Mathematics, as it is practiced, is subjective and dependent on the shared intuition of the current community that composes the field. But to say it is subjective is not to say that it is arbitrary. Theorems and propositions still need to be fairly consistent. The moment we need to describe theorems in common language is the moment we lose symbolic and formal objectivity. There is always an interpretation narrow or literal enough that it turns out to be true and also a sufficiently wide interpretation such that it turns out to be false, or vice versa.

The proof of a theorem is the means to convince others to accept the theorem. Contrary to common belief, when doing mathematics, first you have the intuition of the solution, and only then are you able to prove it. Intuition precedes proof. The sequence of steps that compose a proof acts as a post-rationalisation that guides us in improving the soundness of our intuition.

The more certain and objective something is, the more meaningless it gets; meaning and objectivity usually go in opposite directions. That is perhaps why reading a book, contemplating a painting, or listening to a symphony, due to their inherent subjectivity, can be the most meaningful experiences we can have as humans.

Adapted from a longer format